1 Study Background

This study aimed to identify the factor structure of the Defense Style Questionnaire (DSQ). Specifically, it compared three previously hypothesized factor structures: a one-factor solution (Trijsburg et al., 2000), a three-factor solution (Andrews et al., 1993), and a four-factor solution (Ruuttu et al., 2006).

2 Preparations

2.1 Loading packages

2.2 Specifying Factor Models

# Specify CFA models
model_1f <- '
  Factor1 =~ dsq_sublimation + dsq_humor + dsq_anticipation + dsq_suppression
    + dsq_pseudo_altruism + dsq_idealization + dsq_reaction_formation + dsq_undoing
    + dsq_rationalization + dsq_projection + dsq_passive_aggression + dsq_acting_out
    + dsq_isolation + dsq_autistic_fantasy + dsq_denial + dsq_displacement
    + dsq_dissociation + dsq_splitting + dsq_devaluation + dsq_somatization
'
model_3f <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_rationalization + dsq_isolation + dsq_dissociation + dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
'
model_4f <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_isolation + dsq_dissociation + dsq_devaluation + dsq_splitting + dsq_denial
'

2.2.1 Specifying Factor Models for Knekt Study (no Rationalization)

model_1f_norat <- '
  Factor1 =~ dsq_sublimation + dsq_humor + dsq_anticipation + dsq_suppression
    + dsq_pseudo_altruism + dsq_idealization + dsq_reaction_formation + dsq_undoing
    + dsq_projection + dsq_passive_aggression + dsq_acting_out
    + dsq_isolation + dsq_autistic_fantasy + dsq_denial + dsq_displacement
    + dsq_dissociation + dsq_splitting + dsq_devaluation + dsq_somatization
'
model_3f_norat <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_isolation + dsq_dissociation + dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
'
model_4f_norat <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature         =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression
                     + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_isolation + dsq_dissociation + dsq_devaluation + dsq_splitting + dsq_denial
'

2.3 Reading-in and Cleaning Data

# Set working directory and load data
#setwd("//cnas-wrkgrp.ru.nl/wrkgrp/FSW-BSI-EPT-PhD_Fritz_Wienicke/CFA Defense Mechanisms")
#setwd("C:/Users/fritz/OneDrive/Desktop/Defense mechanisms/Datasets")
DSQ_Data <- read.spss("Database_combined_v1.sav", to.data.frame = TRUE, use.value.labels = FALSE)

# Define DSQ item names
dsq_vars <- c(
  "dsq_sublimation","dsq_humor","dsq_anticipation","dsq_suppression",
  "dsq_pseudo_altruism","dsq_idealization","dsq_reaction_formation","dsq_undoing",
  "dsq_rationalization","dsq_projection","dsq_passive_aggression","dsq_acting_out",
  "dsq_isolation","dsq_autistic_fantasy","dsq_denial","dsq_displacement",
  "dsq_dissociation","dsq_splitting","dsq_devaluation","dsq_somatization"
)

# Flag and drop cases with ALL DSQ items missing
rows_all_missing <- apply(DSQ_Data[ , dsq_vars], 1, function(x) all(is.na(x)))
DSQ_Data$all_dsq_missing <- rows_all_missing
DSQ_Data <- DSQ_Data[!DSQ_Data$all_dsq_missing, ]
DSQ_Data$all_dsq_missing <- NULL

# Convert key variables to factors with labels
DSQ_Data$StudyID <- factor(DSQ_Data$StudyID,
                           levels = c(1,3,4),
                           labels = c("Dekker_2008/Van_2009","Dos_Santos_2020","Knekt_2004"))
DSQ_Data$PatientID <- as.factor(DSQ_Data$PatientID)
DSQ_Data$gender <- factor(DSQ_Data$gender, levels = c(1,2), labels = c("male","female"))
DSQ_Data$marital_status <- factor(DSQ_Data$marital_status,
                                  levels=c(1,2,3),labels=c("single","cohabiting or married","Separated, divorced or widowed"))
DSQ_Data$employment_status <- factor(DSQ_Data$employment_status,
                                     levels=c(1,2,3),labels=c("Working","Studying","Not working or studying"))
DSQ_Data$education_level <- factor(DSQ_Data$education_level,
                                   levels=c(1,2,3,4),labels=c("Basic education","Secondary education",
                                                              "Vocational education","Tertiary education"))
DSQ_Data$diagnosis <- factor(DSQ_Data$diagnosis,
                             levels=c(1,3),
                             labels=c("DSM-IV, mood disorder only","DSM-IV, comorbid mood and anxiety disorder"))

# Define subsets
dekker_df <- subset(DSQ_Data, StudyID == "Dekker_2008/Van_2009")
ds_df     <- subset(DSQ_Data, StudyID == "Dos_Santos_2020")
kn_df     <- subset(DSQ_Data, StudyID == "Knekt_2004")
DSQ_Data_mg <- filter(DSQ_Data, StudyID != "Knekt_2004")

3 Multigroup CFA

3.1 One Factor Solution

# Fit models
fit1_comb  <- cfa(model_1f, data = DSQ_Data_mg, group = "StudyID", estimator = "mlr", missing = "fiml")

# Inspect 1-factor
summary(fit1_comb,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 176 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       120
## 
##   Number of observations per group:                   
##     Dekker_2008/Van_2009                           151
##     Dos_Santos_2020                                210
##   Number of missing patterns per group:               
##     Dekker_2008/Van_2009                            18
##     Dos_Santos_2020                                  3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               935.276     899.576
##   Degrees of freedom                               340         340
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.040
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     Dekker_2008/Van_2009                       423.312     423.312
##     Dos_Santos_2020                            476.264     476.264
## 
## Model Test Baseline Model:
## 
##   Test statistic                              1390.926    1256.752
##   Degrees of freedom                               380         380
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.107
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.411       0.362
##   Tucker-Lewis Index (TLI)                       0.342       0.287
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.417
##   Robust Tucker-Lewis Index (TLI)                            0.349
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -18767.143  -18767.143
##   Scaling correction factor                                  1.147
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -18299.505  -18299.505
##   Scaling correction factor                                  1.068
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               37774.287   37774.287
##   Bayesian (BIC)                             38240.952   38240.952
##   Sample-size adjusted Bayesian (SABIC)      37860.249   37860.249
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.098       0.095
##   90 Percent confidence interval - lower         0.091       0.088
##   90 Percent confidence interval - upper         0.106       0.103
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    1.000       1.000
##                                                                   
##   Robust RMSEA                                               0.099
##   90 Percent confidence interval - lower                     0.091
##   90 Percent confidence interval - upper                     0.108
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.117       0.117
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [Dekker_2008/Van_2009]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Factor1 =~                                                            
##     dsq_sublimatin    1.000                               0.536    0.145
##     dsq_humor        -0.236    1.605   -0.147    0.883   -0.126   -0.030
##     dsq_anticipatn    0.583    0.615    0.948    0.343    0.312    0.102
##     dsq_suppressin    2.253    1.846    1.221    0.222    1.208    0.311
##     dsq_psed_ltrsm    0.734    0.563    1.304    0.192    0.394    0.130
##     dsq_idealizatn    2.333    2.323    1.004    0.315    1.251    0.327
##     dsq_rctn_frmtn    1.256    1.323    0.949    0.342    0.674    0.179
##     dsq_undoing       2.539    2.859    0.888    0.375    1.362    0.343
##     dsq_rationlztn    0.677    0.611    1.110    0.267    0.363    0.122
##     dsq_projection    3.272    4.148    0.789    0.430    1.755    0.464
##     dsq_pssv_ggrss    3.311    3.543    0.934    0.350    1.776    0.555
##     dsq_acting_out    3.287    3.533    0.930    0.352    1.763    0.418
##     dsq_isolation     2.873    3.308    0.869    0.385    1.541    0.339
##     dsq_tstc_fntsy    3.052    3.718    0.821    0.412    1.637    0.383
##     dsq_denial        2.270    2.702    0.840    0.401    1.218    0.371
##     dsq_displacmnt    2.115    2.578    0.820    0.412    1.134    0.277
##     dsq_dissociatn    2.822    3.518    0.802    0.422    1.513    0.410
##     dsq_splitting     4.228    4.706    0.898    0.369    2.268    0.596
##     dsq_devaluatin    3.935    4.606    0.854    0.393    2.111    0.663
##     dsq_somatizatn    2.309    2.595    0.890    0.374    1.238    0.350
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin   10.016    0.308   32.524    0.000   10.016    2.709
##    .dsq_humor         9.300    0.347   26.830    0.000    9.300    2.214
##    .dsq_anticipatn   10.130    0.253   39.961    0.000   10.130    3.322
##    .dsq_suppressin    8.575    0.321   26.749    0.000    8.575    2.206
##    .dsq_psed_ltrsm   12.707    0.254   50.061    0.000   12.707    4.187
##    .dsq_idealizatn    7.962    0.314   25.368    0.000    7.962    2.080
##    .dsq_rctn_frmtn    9.898    0.310   31.967    0.000    9.898    2.629
##    .dsq_undoing      11.142    0.333   33.503    0.000   11.142    2.806
##    .dsq_rationlztn    8.830    0.245   36.025    0.000    8.830    2.971
##    .dsq_projection    9.348    0.312   29.926    0.000    9.348    2.469
##    .dsq_pssv_ggrss    7.757    0.269   28.885    0.000    7.757    2.426
##    .dsq_acting_out    9.440    0.348   27.125    0.000    9.440    2.238
##    .dsq_isolation     8.587    0.378   22.738    0.000    8.587    1.887
##    .dsq_tstc_fntsy    9.194    0.352   26.093    0.000    9.194    2.153
##    .dsq_denial        6.883    0.269   25.568    0.000    6.883    2.100
##    .dsq_displacmnt    8.150    0.342   23.844    0.000    8.150    1.992
##    .dsq_dissociatn    9.579    0.304   31.540    0.000    9.579    2.596
##    .dsq_splitting     9.718    0.311   31.275    0.000    9.718    2.552
##    .dsq_devaluatin    9.754    0.262   37.273    0.000    9.754    3.064
##    .dsq_somatizatn   11.442    0.289   39.623    0.000   11.442    3.236
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin   13.382    1.464    9.138    0.000   13.382    0.979
##    .dsq_humor        17.622    1.497   11.768    0.000   17.622    0.999
##    .dsq_anticipatn    9.201    1.006    9.144    0.000    9.201    0.989
##    .dsq_suppressin   13.646    1.794    7.607    0.000   13.646    0.903
##    .dsq_psed_ltrsm    9.057    1.162    7.795    0.000    9.057    0.983
##    .dsq_idealizatn   13.083    1.611    8.119    0.000   13.083    0.893
##    .dsq_rctn_frmtn   13.725    1.531    8.964    0.000   13.725    0.968
##    .dsq_undoing      13.917    1.396    9.970    0.000   13.917    0.882
##    .dsq_rationlztn    8.701    0.939    9.267    0.000    8.701    0.985
##    .dsq_projection   11.253    1.445    7.787    0.000   11.253    0.785
##    .dsq_pssv_ggrss    7.072    0.947    7.466    0.000    7.072    0.692
##    .dsq_acting_out   14.678    1.801    8.148    0.000   14.678    0.825
##    .dsq_isolation    18.341    1.798   10.199    0.000   18.341    0.885
##    .dsq_tstc_fntsy   15.559    1.854    8.394    0.000   15.559    0.853
##    .dsq_denial        9.265    0.987    9.391    0.000    9.265    0.862
##    .dsq_displacmnt   15.453    1.670    9.255    0.000   15.453    0.923
##    .dsq_dissociatn   11.325    1.583    7.153    0.000   11.325    0.832
##    .dsq_splitting     9.358    1.671    5.601    0.000    9.358    0.645
##    .dsq_devaluatin    5.682    0.945    6.014    0.000    5.682    0.561
##    .dsq_somatizatn   10.965    1.087   10.084    0.000   10.965    0.877
##     Factor1           0.288    0.634    0.454    0.650    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_sublimatin    0.021
##     dsq_humor         0.001
##     dsq_anticipatn    0.011
##     dsq_suppressin    0.097
##     dsq_psed_ltrsm    0.017
##     dsq_idealizatn    0.107
##     dsq_rctn_frmtn    0.032
##     dsq_undoing       0.118
##     dsq_rationlztn    0.015
##     dsq_projection    0.215
##     dsq_pssv_ggrss    0.308
##     dsq_acting_out    0.175
##     dsq_isolation     0.115
##     dsq_tstc_fntsy    0.147
##     dsq_denial        0.138
##     dsq_displacmnt    0.077
##     dsq_dissociatn    0.168
##     dsq_splitting     0.355
##     dsq_devaluatin    0.439
##     dsq_somatizatn    0.123
## 
## 
## Group 2 [Dos_Santos_2020]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Factor1 =~                                                            
##     dsq_sublimatin    1.000                               1.627    0.409
##     dsq_humor         1.409    0.658    2.141    0.032    2.293    0.510
##     dsq_anticipatn    1.259    0.319    3.942    0.000    2.049    0.482
##     dsq_suppressin    1.108    0.368    3.014    0.003    1.803    0.445
##     dsq_psed_ltrsm    0.430    0.219    1.963    0.050    0.700    0.188
##     dsq_idealizatn    1.058    0.334    3.163    0.002    1.721    0.424
##     dsq_rctn_frmtn    1.019    0.457    2.227    0.026    1.657    0.412
##     dsq_undoing       0.698    0.392    1.781    0.075    1.136    0.278
##     dsq_rationlztn    1.675    0.725    2.311    0.021    2.726    0.667
##     dsq_projection   -0.127    0.890   -0.143    0.886   -0.207   -0.052
##     dsq_pssv_ggrss   -0.064    0.796   -0.081    0.935   -0.105   -0.027
##     dsq_acting_out    0.048    0.842    0.057    0.954    0.078    0.016
##     dsq_isolation     0.083    0.705    0.118    0.906    0.135    0.028
##     dsq_tstc_fntsy    0.136    1.065    0.128    0.898    0.221    0.042
##     dsq_denial        0.666    0.347    1.923    0.055    1.084    0.323
##     dsq_displacmnt   -0.110    0.551   -0.200    0.841   -0.180   -0.044
##     dsq_dissociatn    1.018    0.274    3.718    0.000    1.657    0.530
##     dsq_splitting     0.335    0.540    0.621    0.535    0.545    0.133
##     dsq_devaluatin    0.142    0.529    0.268    0.789    0.231    0.071
##     dsq_somatizatn   -0.451    0.712   -0.634    0.526   -0.735   -0.154
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin    9.796    0.283   34.584    0.000    9.796    2.462
##    .dsq_humor         8.238    0.319   25.833    0.000    8.238    1.830
##    .dsq_anticipatn   11.805    0.304   38.891    0.000   11.805    2.777
##    .dsq_suppressin    6.755    0.289   23.402    0.000    6.755    1.667
##    .dsq_psed_ltrsm   11.027    0.264   41.736    0.000   11.027    2.967
##    .dsq_idealizatn    8.089    0.289   28.012    0.000    8.089    1.993
##    .dsq_rctn_frmtn    8.948    0.286   31.249    0.000    8.948    2.223
##    .dsq_undoing       9.445    0.291   32.462    0.000    9.445    2.309
##    .dsq_rationlztn    8.428    0.290   29.028    0.000    8.428    2.064
##    .dsq_projection    8.142    0.283   28.732    0.000    8.142    2.037
##    .dsq_pssv_ggrss    8.743    0.277   31.579    0.000    8.743    2.245
##    .dsq_acting_out   10.707    0.348   30.788    0.000   10.707    2.189
##    .dsq_isolation     9.833    0.348   28.215    0.000    9.833    2.004
##    .dsq_tstc_fntsy   10.292    0.377   27.295    0.000   10.292    1.940
##    .dsq_denial        5.379    0.239   22.479    0.000    5.379    1.602
##    .dsq_displacmnt   10.026    0.291   34.492    0.000   10.026    2.447
##    .dsq_dissociatn    5.251    0.223   23.515    0.000    5.251    1.679
##    .dsq_splitting     9.998    0.292   34.183    0.000    9.998    2.431
##    .dsq_devaluatin    7.171    0.230   31.166    0.000    7.171    2.214
##    .dsq_somatizatn   11.506    0.389   29.568    0.000   11.506    2.412
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin   13.188    1.647    8.007    0.000   13.188    0.833
##    .dsq_humor        14.998    2.721    5.513    0.000   14.998    0.740
##    .dsq_anticipatn   13.875    1.674    8.290    0.000   13.875    0.768
##    .dsq_suppressin   13.175    1.906    6.913    0.000   13.175    0.802
##    .dsq_psed_ltrsm   13.327    1.320   10.097    0.000   13.327    0.965
##    .dsq_idealizatn   13.509    2.406    5.615    0.000   13.509    0.820
##    .dsq_rctn_frmtn   13.459    1.796    7.493    0.000   13.459    0.830
##    .dsq_undoing      15.443    2.260    6.834    0.000   15.443    0.923
##    .dsq_rationlztn    9.254    3.360    2.754    0.006    9.254    0.555
##    .dsq_projection   15.937    1.390   11.466    0.000   15.937    0.997
##    .dsq_pssv_ggrss   15.160    1.440   10.531    0.000   15.160    0.999
##    .dsq_acting_out   23.918    1.747   13.695    0.000   23.918    1.000
##    .dsq_isolation    24.050    1.813   13.262    0.000   24.050    0.999
##    .dsq_tstc_fntsy   28.087    2.043   13.751    0.000   28.087    0.998
##    .dsq_denial       10.102    1.422    7.102    0.000   10.102    0.896
##    .dsq_displacmnt   16.750    1.485   11.281    0.000   16.750    0.998
##    .dsq_dissociatn    7.031    1.131    6.214    0.000    7.031    0.719
##    .dsq_splitting    16.622    1.819    9.140    0.000   16.622    0.982
##    .dsq_devaluatin   10.432    1.083    9.637    0.000   10.432    0.995
##    .dsq_somatizatn   22.225    2.313    9.610    0.000   22.225    0.976
##     Factor1           2.648    1.383    1.915    0.055    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_sublimatin    0.167
##     dsq_humor         0.260
##     dsq_anticipatn    0.232
##     dsq_suppressin    0.198
##     dsq_psed_ltrsm    0.035
##     dsq_idealizatn    0.180
##     dsq_rctn_frmtn    0.170
##     dsq_undoing       0.077
##     dsq_rationlztn    0.445
##     dsq_projection    0.003
##     dsq_pssv_ggrss    0.001
##     dsq_acting_out    0.000
##     dsq_isolation     0.001
##     dsq_tstc_fntsy    0.002
##     dsq_denial        0.104
##     dsq_displacmnt    0.002
##     dsq_dissociatn    0.281
##     dsq_splitting     0.018
##     dsq_devaluatin    0.005
##     dsq_somatizatn    0.024

3.2 Three Factor Solution

fit3_comb  <- cfa(model_3f, data = DSQ_Data_mg, group = "StudyID", estimator = "mlr", missing = "fiml")
# Inspect 3-factor
summary(fit3_comb,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 452 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       126
## 
##   Number of observations per group:                   
##     Dekker_2008/Van_2009                           151
##     Dos_Santos_2020                                210
##   Number of missing patterns per group:               
##     Dekker_2008/Van_2009                            18
##     Dos_Santos_2020                                  3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               724.231     675.132
##   Degrees of freedom                               334         334
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.073
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     Dekker_2008/Van_2009                       325.959     325.959
##     Dos_Santos_2020                            349.173     349.173
## 
## Model Test Baseline Model:
## 
##   Test statistic                              1390.926    1256.752
##   Degrees of freedom                               380         380
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.107
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.614       0.611
##   Tucker-Lewis Index (TLI)                       0.561       0.557
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.629
##   Robust Tucker-Lewis Index (TLI)                            0.578
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -18661.621  -18661.621
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -18299.505  -18299.505
##   Scaling correction factor                                  1.068
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               37575.241   37575.241
##   Bayesian (BIC)                             38065.240   38065.240
##   Sample-size adjusted Bayesian (SABIC)      37665.501   37665.501
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.080       0.075
##   90 Percent confidence interval - lower         0.072       0.067
##   90 Percent confidence interval - upper         0.088       0.083
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.545       0.162
##                                                                   
##   Robust RMSEA                                               0.080
##   90 Percent confidence interval - lower                     0.071
##   90 Percent confidence interval - upper                     0.089
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.501
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.101       0.101
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [Dekker_2008/Van_2009]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               2.754    0.654
##     dsq_suppressin    0.566    0.223    2.543    0.011    1.559    0.401
##     dsq_sublimatin    0.771    0.256    3.013    0.003    2.124    0.574
##     dsq_anticipatn    0.703    0.162    4.334    0.000    1.936    0.634
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.359    0.360
##     dsq_idealizatn    1.202    1.403    0.857    0.392    1.633    0.426
##     dsq_psed_ltrsm    1.218    0.488    2.496    0.013    1.655    0.546
##     dsq_undoing       1.128    0.413    2.734    0.006    1.533    0.385
##   Immature =~                                                           
##     dsq_rationlztn    1.000                               0.201    0.068
##     dsq_isolation     7.621   13.033    0.585    0.559    1.532    0.337
##     dsq_dissociatn    7.967   14.397    0.553    0.580    1.602    0.434
##     dsq_devaluatin   10.897   19.246    0.566    0.571    2.191    0.688
##     dsq_splitting    10.947   18.910    0.579    0.563    2.201    0.578
##     dsq_denial        6.006   10.181    0.590    0.555    1.207    0.368
##     dsq_tstc_fntsy    8.495   15.376    0.552    0.581    1.708    0.400
##     dsq_displacmnt    5.614    9.941    0.565    0.572    1.129    0.276
##     dsq_pssv_ggrss    8.683   14.601    0.595    0.552    1.746    0.545
##     dsq_somatizatn    5.966   10.879    0.548    0.583    1.199    0.339
##     dsq_acting_out    8.505   14.522    0.586    0.558    1.710    0.406
##     dsq_projection    9.677   17.666    0.548    0.584    1.945    0.514
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.475    0.976    2.536    0.011    0.662    0.662
##     Immature          0.002    0.094    0.024    0.981    0.004    0.004
##   Neurotic ~~                                                           
##     Immature          0.106    0.189    0.563    0.574    0.390    0.390
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.295    0.347   26.805    0.000    9.295    2.208
##    .dsq_suppressin    8.557    0.321   26.693    0.000    8.557    2.200
##    .dsq_sublimatin   10.019    0.307   32.634    0.000   10.019    2.706
##    .dsq_anticipatn   10.120    0.253   40.019    0.000   10.120    3.313
##    .dsq_rctn_frmtn    9.887    0.311   31.838    0.000    9.887    2.623
##    .dsq_idealizatn    7.962    0.314   25.351    0.000    7.962    2.080
##    .dsq_psed_ltrsm   12.698    0.254   49.971    0.000   12.698    4.192
##    .dsq_undoing      11.136    0.334   33.377    0.000   11.136    2.800
##    .dsq_rationlztn    8.829    0.245   36.041    0.000    8.829    2.970
##    .dsq_isolation     8.588    0.378   22.737    0.000    8.588    1.886
##    .dsq_dissociatn    9.583    0.303   31.594    0.000    9.583    2.599
##    .dsq_devaluatin    9.763    0.262   37.279    0.000    9.763    3.064
##    .dsq_splitting     9.718    0.311   31.278    0.000    9.718    2.552
##    .dsq_denial        6.886    0.269   25.555    0.000    6.886    2.100
##    .dsq_tstc_fntsy    9.190    0.352   26.081    0.000    9.190    2.153
##    .dsq_displacmnt    8.152    0.342   23.834    0.000    8.152    1.992
##    .dsq_pssv_ggrss    7.752    0.269   28.835    0.000    7.752    2.421
##    .dsq_somatizatn   11.442    0.289   39.627    0.000   11.442    3.236
##    .dsq_acting_out    9.439    0.348   27.149    0.000    9.439    2.239
##    .dsq_projection    9.350    0.312   29.933    0.000    9.350    2.469
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.138    2.431    4.170    0.000   10.138    0.572
##    .dsq_suppressin   12.690    1.866    6.801    0.000   12.690    0.839
##    .dsq_sublimatin    9.193    1.722    5.338    0.000    9.193    0.671
##    .dsq_anticipatn    5.582    1.092    5.113    0.000    5.582    0.598
##    .dsq_rctn_frmtn   12.361    2.543    4.862    0.000   12.361    0.870
##    .dsq_idealizatn   11.991    3.017    3.974    0.000   11.991    0.818
##    .dsq_psed_ltrsm    6.434    2.501    2.572    0.010    6.434    0.701
##    .dsq_undoing      13.467    2.589    5.202    0.000   13.467    0.851
##    .dsq_rationlztn    8.794    0.920    9.560    0.000    8.794    0.995
##    .dsq_isolation    18.380    1.852    9.923    0.000   18.380    0.887
##    .dsq_dissociatn   11.035    1.522    7.248    0.000   11.035    0.811
##    .dsq_devaluatin    5.354    0.819    6.535    0.000    5.354    0.527
##    .dsq_splitting     9.656    1.677    5.757    0.000    9.656    0.666
##    .dsq_denial        9.292    1.029    9.033    0.000    9.292    0.864
##    .dsq_tstc_fntsy   15.311    1.775    8.624    0.000   15.311    0.840
##    .dsq_displacmnt   15.477    1.685    9.186    0.000   15.477    0.924
##    .dsq_pssv_ggrss    7.205    0.973    7.402    0.000    7.205    0.703
##    .dsq_somatizatn   11.060    1.075   10.292    0.000   11.060    0.885
##    .dsq_acting_out   14.844    1.778    8.351    0.000   14.844    0.835
##    .dsq_projection   10.552    1.281    8.240    0.000   10.552    0.736
##     Mature            7.585    2.659    2.853    0.004    1.000    1.000
##     Neurotic          1.846    2.345    0.787    0.431    1.000    1.000
##     Immature          0.040    0.140    0.288    0.773    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.428
##     dsq_suppressin    0.161
##     dsq_sublimatin    0.329
##     dsq_anticipatn    0.402
##     dsq_rctn_frmtn    0.130
##     dsq_idealizatn    0.182
##     dsq_psed_ltrsm    0.299
##     dsq_undoing       0.149
##     dsq_rationlztn    0.005
##     dsq_isolation     0.113
##     dsq_dissociatn    0.189
##     dsq_devaluatin    0.473
##     dsq_splitting     0.334
##     dsq_denial        0.136
##     dsq_tstc_fntsy    0.160
##     dsq_displacmnt    0.076
##     dsq_pssv_ggrss    0.297
##     dsq_somatizatn    0.115
##     dsq_acting_out    0.165
##     dsq_projection    0.264
## 
## 
## Group 2 [Dos_Santos_2020]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               2.003    0.445
##     dsq_suppressin    0.912    0.256    3.559    0.000    1.826    0.451
##     dsq_sublimatin    0.711    0.282    2.522    0.012    1.424    0.358
##     dsq_anticipatn    1.169    0.313    3.736    0.000    2.343    0.551
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.492    0.371
##     dsq_idealizatn    1.286    0.460    2.795    0.005    1.918    0.473
##     dsq_psed_ltrsm    0.543    0.278    1.954    0.051    0.810    0.218
##     dsq_undoing       1.115    0.602    1.851    0.064    1.663    0.407
##   Immature =~                                                           
##     dsq_rationlztn    1.000                               0.483    0.118
##     dsq_isolation    -3.516    3.717   -0.946    0.344   -1.697   -0.346
##     dsq_dissociatn   -0.414    1.026   -0.403    0.687   -0.200   -0.064
##     dsq_devaluatin   -3.159    3.357   -0.941    0.347   -1.525   -0.471
##     dsq_splitting    -2.905    3.303   -0.879    0.379   -1.402   -0.341
##     dsq_denial       -1.658    2.104   -0.788    0.431   -0.800   -0.238
##     dsq_tstc_fntsy   -7.032    7.298   -0.964    0.335   -3.394   -0.640
##     dsq_displacmnt   -3.222    3.240   -0.995    0.320   -1.555   -0.380
##     dsq_pssv_ggrss   -5.151    5.233   -0.984    0.325   -2.486   -0.638
##     dsq_somatizatn   -3.368    3.384   -0.995    0.320   -1.626   -0.341
##     dsq_acting_out   -5.166    5.472   -0.944    0.345   -2.493   -0.510
##     dsq_projection   -5.162    5.225   -0.988    0.323   -2.491   -0.623
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.841    1.258    2.258    0.024    0.950    0.950
##     Immature          0.009    0.167    0.054    0.957    0.009    0.009
##   Neurotic ~~                                                           
##     Immature         -0.194    0.150   -1.299    0.194   -0.270   -0.270
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.247    0.319   25.813    0.000    8.247    1.832
##    .dsq_suppressin    6.762    0.288   23.479    0.000    6.762    1.669
##    .dsq_sublimatin    9.803    0.283   34.666    0.000    9.803    2.463
##    .dsq_anticipatn   11.813    0.302   39.081    0.000   11.813    2.779
##    .dsq_rctn_frmtn    8.958    0.286   31.312    0.000    8.958    2.225
##    .dsq_idealizatn    8.101    0.288   28.128    0.000    8.101    1.996
##    .dsq_psed_ltrsm   11.032    0.264   41.790    0.000   11.032    2.968
##    .dsq_undoing       9.453    0.290   32.580    0.000    9.453    2.311
##    .dsq_rationlztn    8.435    0.289   29.152    0.000    8.435    2.065
##    .dsq_isolation     9.848    0.349   28.228    0.000    9.848    2.007
##    .dsq_dissociatn    5.259    0.222   23.650    0.000    5.259    1.682
##    .dsq_devaluatin    7.185    0.230   31.224    0.000    7.185    2.219
##    .dsq_splitting    10.012    0.292   34.286    0.000   10.012    2.434
##    .dsq_denial        5.391    0.239   22.516    0.000    5.391    1.605
##    .dsq_tstc_fntsy   10.323    0.376   27.429    0.000   10.323    1.946
##    .dsq_displacmnt   10.039    0.291   34.539    0.000   10.039    2.450
##    .dsq_pssv_ggrss    8.764    0.277   31.694    0.000    8.764    2.249
##    .dsq_somatizatn   11.555    0.387   29.840    0.000   11.555    2.423
##    .dsq_acting_out   10.729    0.348   30.873    0.000   10.729    2.193
##    .dsq_projection    8.163    0.283   28.859    0.000    8.163    2.042
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        16.243    1.886    8.613    0.000   16.243    0.802
##    .dsq_suppressin   13.088    2.015    6.494    0.000   13.088    0.797
##    .dsq_sublimatin   13.807    1.628    8.484    0.000   13.807    0.872
##    .dsq_anticipatn   12.584    1.779    7.073    0.000   12.584    0.696
##    .dsq_rctn_frmtn   13.979    2.052    6.813    0.000   13.979    0.863
##    .dsq_idealizatn   12.791    1.754    7.294    0.000   12.791    0.777
##    .dsq_psed_ltrsm   13.161    1.355    9.716    0.000   13.161    0.953
##    .dsq_undoing      13.966    1.832    7.623    0.000   13.966    0.835
##    .dsq_rationlztn   16.448    1.470   11.192    0.000   16.448    0.986
##    .dsq_isolation    21.193    1.878   11.284    0.000   21.193    0.880
##    .dsq_dissociatn    9.737    0.941   10.347    0.000    9.737    0.996
##    .dsq_devaluatin    8.165    0.893    9.143    0.000    8.165    0.778
##    .dsq_splitting    14.957    1.620    9.235    0.000   14.957    0.884
##    .dsq_denial       10.638    0.971   10.955    0.000   10.638    0.943
##    .dsq_tstc_fntsy   16.636    2.314    7.188    0.000   16.636    0.591
##    .dsq_displacmnt   14.367    1.355   10.604    0.000   14.367    0.856
##    .dsq_pssv_ggrss    9.000    1.362    6.605    0.000    9.000    0.593
##    .dsq_somatizatn   20.110    2.234    9.002    0.000   20.110    0.884
##    .dsq_acting_out   17.718    1.826    9.706    0.000   17.718    0.740
##    .dsq_projection    9.783    1.345    7.274    0.000    9.783    0.612
##     Mature            4.014    1.805    2.223    0.026    1.000    1.000
##     Neurotic          2.226    1.761    1.264    0.206    1.000    1.000
##     Immature          0.233    0.481    0.484    0.628    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.198
##     dsq_suppressin    0.203
##     dsq_sublimatin    0.128
##     dsq_anticipatn    0.304
##     dsq_rctn_frmtn    0.137
##     dsq_idealizatn    0.223
##     dsq_psed_ltrsm    0.047
##     dsq_undoing       0.165
##     dsq_rationlztn    0.014
##     dsq_isolation     0.120
##     dsq_dissociatn    0.004
##     dsq_devaluatin    0.222
##     dsq_splitting     0.116
##     dsq_denial        0.057
##     dsq_tstc_fntsy    0.409
##     dsq_displacmnt    0.144
##     dsq_pssv_ggrss    0.407
##     dsq_somatizatn    0.116
##     dsq_acting_out    0.260
##     dsq_projection    0.388

3.3 Four Factor Solution

fit4_comb  <- cfa(model_4f, data = DSQ_Data_mg, group = "StudyID", estimator = "mlr", missing = "fiml")
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite in group 1; use lavInspect(fit, "cov.lv") to 
##    investigate.
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite in group 2; use lavInspect(fit, "cov.lv") to 
##    investigate.
# Inspect 4-factor
summary(fit4_comb,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 257 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       132
## 
##   Number of observations per group:                   
##     Dekker_2008/Van_2009                           151
##     Dos_Santos_2020                                210
##   Number of missing patterns per group:               
##     Dekker_2008/Van_2009                            18
##     Dos_Santos_2020                                  3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               608.104     572.937
##   Degrees of freedom                               328         328
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.061
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     Dekker_2008/Van_2009                       301.554     301.554
##     Dos_Santos_2020                            271.382     271.382
## 
## Model Test Baseline Model:
## 
##   Test statistic                              1390.926    1256.752
##   Degrees of freedom                               380         380
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.107
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.723       0.721
##   Tucker-Lewis Index (TLI)                       0.679       0.676
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.741
##   Robust Tucker-Lewis Index (TLI)                            0.700
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -18603.557  -18603.557
##   Scaling correction factor                                  1.083
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -18299.505  -18299.505
##   Scaling correction factor                                  1.068
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               37471.115   37471.115
##   Bayesian (BIC)                             37984.447   37984.447
##   Sample-size adjusted Bayesian (SABIC)      37565.673   37565.673
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.069       0.064
##   90 Percent confidence interval - lower         0.060       0.056
##   90 Percent confidence interval - upper         0.077       0.073
##   P-value H_0: RMSEA <= 0.050                    0.000       0.004
##   P-value H_0: RMSEA >= 0.080                    0.014       0.001
##                                                                   
##   Robust RMSEA                                               0.067
##   90 Percent confidence interval - lower                     0.057
##   90 Percent confidence interval - upper                     0.077
##   P-value H_0: Robust RMSEA <= 0.050                         0.003
##   P-value H_0: Robust RMSEA >= 0.080                         0.015
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.086       0.086
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [Dekker_2008/Van_2009]:
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.715    0.646
##     dsq_suppressin       0.600    0.196    3.064    0.002    1.630    0.420
##     dsq_sublimatin       0.769    0.221    3.487    0.000    2.088    0.565
##     dsq_anticipatn       0.712    0.163    4.376    0.000    1.932    0.634
##     dsq_rationlztn       0.559    0.128    4.364    0.000    1.516    0.510
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.487    0.394
##     dsq_idealizatn       0.940    0.738    1.273    0.203    1.398    0.365
##     dsq_psed_ltrsm       1.216    0.505    2.407    0.016    1.809    0.598
##     dsq_undoing          1.072    0.374    2.869    0.004    1.594    0.401
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               1.718    0.403
##     dsq_displacmnt       0.649    0.293    2.214    0.027    1.115    0.272
##     dsq_pssv_ggrss       0.936    0.306    3.056    0.002    1.609    0.502
##     dsq_somatizatn       0.662    0.215    3.073    0.002    1.137    0.322
##     dsq_acting_out       0.948    0.336    2.825    0.005    1.630    0.387
##     dsq_projection       1.089    0.312    3.491    0.000    1.871    0.494
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.484    0.326
##     dsq_dissociatn       1.052    0.358    2.942    0.003    1.562    0.423
##     dsq_devaluatin       1.441    0.487    2.961    0.003    2.139    0.671
##     dsq_splitting        1.477    0.600    2.459    0.014    2.191    0.575
##     dsq_denial           0.752    0.243    3.091    0.002    1.116    0.340
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.485    0.780    3.187    0.001    0.615    0.615
##     Immature         -0.047    0.917   -0.051    0.959   -0.010   -0.010
##     Image_Distrtng    0.154    0.598    0.258    0.797    0.038    0.038
##   Neurotic ~~                                                           
##     Immature          0.861    0.813    1.059    0.290    0.337    0.337
##     Image_Distrtng    0.787    0.502    1.566    0.117    0.356    0.356
##   Immature ~~                                                           
##     Image_Distrtng    2.854    1.070    2.667    0.008    1.119    1.119
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.306    0.346   26.925    0.000    9.306    2.215
##    .dsq_suppressin    8.568    0.320   26.748    0.000    8.568    2.206
##    .dsq_sublimatin   10.026    0.308   32.571    0.000   10.026    2.711
##    .dsq_anticipatn   10.123    0.253   40.053    0.000   10.123    3.320
##    .dsq_rationlztn    8.847    0.245   36.084    0.000    8.847    2.976
##    .dsq_rctn_frmtn    9.884    0.310   31.894    0.000    9.884    2.621
##    .dsq_idealizatn    7.965    0.315   25.320    0.000    7.965    2.081
##    .dsq_psed_ltrsm   12.696    0.254   50.029    0.000   12.696    4.195
##    .dsq_undoing      11.139    0.333   33.474    0.000   11.139    2.802
##    .dsq_tstc_fntsy    9.187    0.352   26.081    0.000    9.187    2.152
##    .dsq_displacmnt    8.146    0.342   23.818    0.000    8.146    1.990
##    .dsq_pssv_ggrss    7.737    0.270   28.699    0.000    7.737    2.416
##    .dsq_somatizatn   11.442    0.289   39.622    0.000   11.442    3.236
##    .dsq_acting_out    9.434    0.347   27.153    0.000    9.434    2.240
##    .dsq_projection    9.348    0.313   29.891    0.000    9.348    2.469
##    .dsq_isolation     8.592    0.377   22.759    0.000    8.592    1.887
##    .dsq_dissociatn    9.582    0.303   31.595    0.000    9.582    2.598
##    .dsq_devaluatin    9.761    0.262   37.288    0.000    9.761    3.063
##    .dsq_splitting     9.718    0.311   31.272    0.000    9.718    2.552
##    .dsq_denial        6.885    0.269   25.552    0.000    6.885    2.100
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.285    2.147    4.790    0.000   10.285    0.583
##    .dsq_suppressin   12.433    1.791    6.943    0.000   12.433    0.824
##    .dsq_sublimatin    9.315    1.620    5.748    0.000    9.315    0.681
##    .dsq_anticipatn    5.561    1.054    5.276    0.000    5.561    0.598
##    .dsq_rationlztn    6.540    0.926    7.060    0.000    6.540    0.740
##    .dsq_rctn_frmtn   12.011    1.940    6.190    0.000   12.011    0.844
##    .dsq_idealizatn   12.701    2.144    5.923    0.000   12.701    0.867
##    .dsq_psed_ltrsm    5.888    2.203    2.672    0.008    5.888    0.643
##    .dsq_undoing      13.260    2.032    6.524    0.000   13.260    0.839
##    .dsq_tstc_fntsy   15.266    1.710    8.925    0.000   15.266    0.838
##    .dsq_displacmnt   15.520    1.686    9.208    0.000   15.520    0.926
##    .dsq_pssv_ggrss    7.668    1.061    7.227    0.000    7.668    0.748
##    .dsq_somatizatn   11.205    1.089   10.293    0.000   11.205    0.896
##    .dsq_acting_out   15.088    1.751    8.616    0.000   15.088    0.850
##    .dsq_projection   10.833    1.463    7.404    0.000   10.833    0.756
##    .dsq_isolation    18.522    1.913    9.681    0.000   18.522    0.894
##    .dsq_dissociatn   11.162    1.459    7.648    0.000   11.162    0.821
##    .dsq_devaluatin    5.580    0.793    7.040    0.000    5.580    0.550
##    .dsq_splitting     9.699    1.624    5.973    0.000    9.699    0.669
##    .dsq_denial        9.504    1.060    8.967    0.000    9.504    0.884
##     Mature            7.371    2.356    3.129    0.002    1.000    1.000
##     Neurotic          2.212    1.622    1.364    0.173    1.000    1.000
##     Immature          2.953    1.281    2.305    0.021    1.000    1.000
##     Image_Distrtng    2.202    1.431    1.539    0.124    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.417
##     dsq_suppressin    0.176
##     dsq_sublimatin    0.319
##     dsq_anticipatn    0.402
##     dsq_rationlztn    0.260
##     dsq_rctn_frmtn    0.156
##     dsq_idealizatn    0.133
##     dsq_psed_ltrsm    0.357
##     dsq_undoing       0.161
##     dsq_tstc_fntsy    0.162
##     dsq_displacmnt    0.074
##     dsq_pssv_ggrss    0.252
##     dsq_somatizatn    0.104
##     dsq_acting_out    0.150
##     dsq_projection    0.244
##     dsq_isolation     0.106
##     dsq_dissociatn    0.179
##     dsq_devaluatin    0.450
##     dsq_splitting     0.331
##     dsq_denial        0.116
## 
## 
## Group 2 [Dos_Santos_2020]:
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.202    0.489
##     dsq_suppressin       0.856    0.249    3.431    0.001    1.885    0.465
##     dsq_sublimatin       0.721    0.212    3.408    0.001    1.588    0.399
##     dsq_anticipatn       0.962    0.233    4.137    0.000    2.119    0.498
##     dsq_rationlztn       1.274    0.240    5.306    0.000    2.806    0.687
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.599    0.397
##     dsq_idealizatn       1.148    0.359    3.198    0.001    1.836    0.452
##     dsq_psed_ltrsm       0.574    0.264    2.172    0.030    0.917    0.247
##     dsq_undoing          1.012    0.474    2.136    0.033    1.617    0.395
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.324    0.626
##     dsq_displacmnt       0.493    0.118    4.194    0.000    1.639    0.400
##     dsq_pssv_ggrss       0.744    0.123    6.071    0.000    2.474    0.635
##     dsq_somatizatn       0.499    0.154    3.244    0.001    1.657    0.348
##     dsq_acting_out       0.726    0.138    5.264    0.000    2.414    0.493
##     dsq_projection       0.778    0.120    6.499    0.000    2.586    0.647
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.764    0.360
##     dsq_dissociatn       0.648    0.633    1.024    0.306    1.143    0.366
##     dsq_devaluatin       0.870    0.252    3.453    0.001    1.535    0.474
##     dsq_splitting        0.763    0.330    2.313    0.021    1.346    0.327
##     dsq_denial           0.865    0.545    1.587    0.113    1.527    0.455
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          3.088    1.139    2.712    0.007    0.877    0.877
##     Immature         -1.208    0.924   -1.307    0.191   -0.165   -0.165
##     Image_Distrtng    1.628    0.877    1.857    0.063    0.419    0.419
##   Neurotic ~~                                                           
##     Immature          1.276    0.882    1.446    0.148    0.240    0.240
##     Image_Distrtng    1.252    0.590    2.123    0.034    0.444    0.444
##   Immature ~~                                                           
##     Image_Distrtng    3.983    2.770    1.438    0.150    0.679    0.679
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.815    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.488    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.646    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.076    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.290   29.133    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.327    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.125    0.000    8.100    1.996
##    .dsq_psed_ltrsm   11.032    0.264   41.786    0.000   11.032    2.968
##    .dsq_undoing       9.453    0.290   32.580    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.323    0.376   27.444    0.000   10.323    1.945
##    .dsq_displacmnt   10.040    0.291   34.522    0.000   10.040    2.450
##    .dsq_pssv_ggrss    8.765    0.276   31.700    0.000    8.765    2.250
##    .dsq_somatizatn   11.561    0.388   29.778    0.000   11.561    2.425
##    .dsq_acting_out   10.729    0.347   30.900    0.000   10.729    2.193
##    .dsq_projection    8.165    0.283   28.834    0.000    8.165    2.042
##    .dsq_isolation     9.844    0.349   28.227    0.000    9.844    2.006
##    .dsq_dissociatn    5.265    0.223   23.615    0.000    5.265    1.684
##    .dsq_devaluatin    7.181    0.230   31.232    0.000    7.181    2.217
##    .dsq_splitting    10.008    0.292   34.261    0.000   10.008    2.433
##    .dsq_denial        5.393    0.239   22.543    0.000    5.393    1.606
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        15.407    1.860    8.285    0.000   15.407    0.761
##    .dsq_suppressin   12.872    1.983    6.491    0.000   12.872    0.784
##    .dsq_sublimatin   13.313    1.510    8.815    0.000   13.313    0.841
##    .dsq_anticipatn   13.583    1.510    8.996    0.000   13.583    0.752
##    .dsq_rationlztn    8.805    1.386    6.355    0.000    8.805    0.528
##    .dsq_rctn_frmtn   13.649    1.908    7.154    0.000   13.649    0.842
##    .dsq_idealizatn   13.101    1.892    6.925    0.000   13.101    0.795
##    .dsq_psed_ltrsm   12.976    1.307    9.927    0.000   12.976    0.939
##    .dsq_undoing      14.116    1.818    7.764    0.000   14.116    0.844
##    .dsq_tstc_fntsy   17.105    2.528    6.767    0.000   17.105    0.608
##    .dsq_displacmnt   14.101    1.419    9.939    0.000   14.101    0.840
##    .dsq_pssv_ggrss    9.062    1.373    6.601    0.000    9.062    0.597
##    .dsq_somatizatn   19.989    2.221    9.000    0.000   19.989    0.879
##    .dsq_acting_out   18.106    1.946    9.306    0.000   18.106    0.757
##    .dsq_projection    9.302    1.373    6.776    0.000    9.302    0.582
##    .dsq_isolation    20.958    2.302    9.106    0.000   20.958    0.871
##    .dsq_dissociatn    8.471    1.967    4.307    0.000    8.471    0.866
##    .dsq_devaluatin    8.132    1.424    5.710    0.000    8.132    0.775
##    .dsq_splitting    15.109    1.745    8.657    0.000   15.109    0.893
##    .dsq_denial        8.947    1.878    4.765    0.000    8.947    0.793
##     Mature            4.850    1.887    2.570    0.010    1.000    1.000
##     Neurotic          2.556    1.642    1.557    0.119    1.000    1.000
##     Immature         11.047    2.577    4.287    0.000    1.000    1.000
##     Image_Distrtng    3.112    2.101    1.481    0.139    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.239
##     dsq_suppressin    0.216
##     dsq_sublimatin    0.159
##     dsq_anticipatn    0.248
##     dsq_rationlztn    0.472
##     dsq_rctn_frmtn    0.158
##     dsq_idealizatn    0.205
##     dsq_psed_ltrsm    0.061
##     dsq_undoing       0.156
##     dsq_tstc_fntsy    0.392
##     dsq_displacmnt    0.160
##     dsq_pssv_ggrss    0.403
##     dsq_somatizatn    0.121
##     dsq_acting_out    0.243
##     dsq_projection    0.418
##     dsq_isolation     0.129
##     dsq_dissociatn    0.134
##     dsq_devaluatin    0.225
##     dsq_splitting     0.107
##     dsq_denial        0.207

3.3.1 Checking Error Message

cov2cor(lavInspect(fit4_comb, "cov.lv")[[1]])  # Group 1: Dekker
##                  Mature Neurtc Immatr Img_Ds
## Mature            1.000                     
## Neurotic          0.615  1.000              
## Immature         -0.010  0.337  1.000       
## Image_Distorting  0.038  0.356  1.119  1.000
cov2cor(lavInspect(fit4_comb, "cov.lv")[[2]])  # Group 2: Dos Santos
##                  Mature Neurtc Immatr Img_Ds
## Mature            1.000                     
## Neurotic          0.877  1.000              
## Immature         -0.165  0.240  1.000       
## Image_Distorting  0.419  0.444  0.679  1.000
eigen(lavInspect(fit4_comb, "cov.lv")[[1]])$values  # For group 1
## [1]  8.4624333  5.6195531  0.9606699 -0.3042989
eigen(lavInspect(fit4_comb, "cov.lv")[[2]])$values  # For group 2
## [1] 12.9668323  7.6046000  1.1045038 -0.1094094

4 CFA per Study

4.1 Dekker

4.1.1 One Factor Solution

# Fit models for Dekker & Van subset
fit1_dekker <- cfa(model_1f, data = dekker_df, estimator = "mlr", missing = "fiml")

# Inspect 1-factor
summary(fit1_dekker,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 124 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        60
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               440.112     422.559
##   Degrees of freedom                               170         170
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.042
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.433       0.414
##   Tucker-Lewis Index (TLI)                       0.366       0.345
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.434
##   Robust Tucker-Lewis Index (TLI)                            0.368
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7836.322   -7836.322
##   Scaling correction factor                                  1.034
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15792.645   15792.645
##   Bayesian (BIC)                             15973.681   15973.681
##   Sample-size adjusted Bayesian (SABIC)      15783.788   15783.788
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.103       0.099
##   90 Percent confidence interval - lower         0.091       0.088
##   90 Percent confidence interval - upper         0.114       0.111
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.999       0.996
##                                                                   
##   Robust RMSEA                                               0.104
##   90 Percent confidence interval - lower                     0.091
##   90 Percent confidence interval - upper                     0.117
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.999
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.112       0.112
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Factor1 =~                                                            
##     dsq_sublimatin    1.000                               0.536    0.145
##     dsq_humor        -0.236    1.605   -0.147    0.883   -0.126   -0.030
##     dsq_anticipatn    0.583    0.615    0.948    0.343    0.313    0.102
##     dsq_suppressin    2.253    1.845    1.221    0.222    1.208    0.311
##     dsq_psed_ltrsm    0.734    0.563    1.304    0.192    0.394    0.130
##     dsq_idealizatn    2.333    2.323    1.004    0.315    1.251    0.327
##     dsq_rctn_frmtn    1.256    1.323    0.949    0.342    0.674    0.179
##     dsq_undoing       2.539    2.859    0.888    0.375    1.362    0.343
##     dsq_rationlztn    0.677    0.611    1.110    0.267    0.363    0.122
##     dsq_projection    3.272    4.148    0.789    0.430    1.755    0.464
##     dsq_pssv_ggrss    3.311    3.542    0.935    0.350    1.776    0.555
##     dsq_acting_out    3.287    3.532    0.931    0.352    1.763    0.418
##     dsq_isolation     2.873    3.306    0.869    0.385    1.541    0.339
##     dsq_tstc_fntsy    3.052    3.717    0.821    0.412    1.637    0.383
##     dsq_denial        2.270    2.702    0.840    0.401    1.218    0.371
##     dsq_displacmnt    2.115    2.577    0.821    0.412    1.134    0.277
##     dsq_dissociatn    2.821    3.517    0.802    0.422    1.513    0.410
##     dsq_splitting     4.228    4.705    0.899    0.369    2.268    0.596
##     dsq_devaluatin    3.935    4.604    0.855    0.393    2.111    0.663
##     dsq_somatizatn    2.309    2.594    0.890    0.373    1.239    0.350
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin   10.016    0.308   32.524    0.000   10.016    2.709
##    .dsq_humor         9.300    0.347   26.830    0.000    9.300    2.214
##    .dsq_anticipatn   10.130    0.253   39.961    0.000   10.130    3.322
##    .dsq_suppressin    8.575    0.321   26.749    0.000    8.575    2.206
##    .dsq_psed_ltrsm   12.707    0.254   50.061    0.000   12.707    4.187
##    .dsq_idealizatn    7.962    0.314   25.368    0.000    7.962    2.080
##    .dsq_rctn_frmtn    9.898    0.310   31.967    0.000    9.898    2.629
##    .dsq_undoing      11.142    0.333   33.503    0.000   11.142    2.806
##    .dsq_rationlztn    8.830    0.245   36.025    0.000    8.830    2.971
##    .dsq_projection    9.348    0.312   29.926    0.000    9.348    2.469
##    .dsq_pssv_ggrss    7.757    0.269   28.885    0.000    7.757    2.426
##    .dsq_acting_out    9.440    0.348   27.125    0.000    9.440    2.238
##    .dsq_isolation     8.587    0.378   22.738    0.000    8.587    1.887
##    .dsq_tstc_fntsy    9.194    0.352   26.093    0.000    9.194    2.153
##    .dsq_denial        6.883    0.269   25.568    0.000    6.883    2.100
##    .dsq_displacmnt    8.150    0.342   23.844    0.000    8.150    1.992
##    .dsq_dissociatn    9.579    0.304   31.540    0.000    9.579    2.596
##    .dsq_splitting     9.718    0.311   31.275    0.000    9.718    2.552
##    .dsq_devaluatin    9.754    0.262   37.273    0.000    9.754    3.064
##    .dsq_somatizatn   11.442    0.289   39.623    0.000   11.442    3.236
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin   13.382    1.465    9.138    0.000   13.382    0.979
##    .dsq_humor        17.622    1.497   11.768    0.000   17.622    0.999
##    .dsq_anticipatn    9.201    1.006    9.144    0.000    9.201    0.989
##    .dsq_suppressin   13.646    1.794    7.607    0.000   13.646    0.903
##    .dsq_psed_ltrsm    9.057    1.162    7.795    0.000    9.057    0.983
##    .dsq_idealizatn   13.083    1.611    8.119    0.000   13.083    0.893
##    .dsq_rctn_frmtn   13.725    1.531    8.964    0.000   13.725    0.968
##    .dsq_undoing      13.917    1.396    9.970    0.000   13.917    0.882
##    .dsq_rationlztn    8.701    0.939    9.267    0.000    8.701    0.985
##    .dsq_projection   11.253    1.445    7.787    0.000   11.253    0.785
##    .dsq_pssv_ggrss    7.072    0.947    7.466    0.000    7.072    0.692
##    .dsq_acting_out   14.678    1.801    8.148    0.000   14.678    0.825
##    .dsq_isolation    18.341    1.798   10.199    0.000   18.341    0.885
##    .dsq_tstc_fntsy   15.559    1.854    8.394    0.000   15.559    0.853
##    .dsq_denial        9.265    0.987    9.391    0.000    9.265    0.862
##    .dsq_displacmnt   15.453    1.670    9.256    0.000   15.453    0.923
##    .dsq_dissociatn   11.325    1.583    7.153    0.000   11.325    0.832
##    .dsq_splitting     9.358    1.671    5.601    0.000    9.358    0.645
##    .dsq_devaluatin    5.682    0.945    6.014    0.000    5.682    0.561
##    .dsq_somatizatn   10.965    1.087   10.084    0.000   10.965    0.877
##     Factor1           0.288    0.633    0.454    0.650    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_sublimatin    0.021
##     dsq_humor         0.001
##     dsq_anticipatn    0.011
##     dsq_suppressin    0.097
##     dsq_psed_ltrsm    0.017
##     dsq_idealizatn    0.107
##     dsq_rctn_frmtn    0.032
##     dsq_undoing       0.118
##     dsq_rationlztn    0.015
##     dsq_projection    0.215
##     dsq_pssv_ggrss    0.308
##     dsq_acting_out    0.175
##     dsq_isolation     0.115
##     dsq_tstc_fntsy    0.147
##     dsq_denial        0.138
##     dsq_displacmnt    0.077
##     dsq_dissociatn    0.168
##     dsq_splitting     0.355
##     dsq_devaluatin    0.439
##     dsq_somatizatn    0.123

4.1.2 Three Factor Solution

fit3_dekker <- cfa(model_3f, data = dekker_df, estimator = "mlr", missing = "fiml")

# Inspect 3-factor
summary(fit3_dekker,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 201 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        63
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               349.664     340.357
##   Degrees of freedom                               167         167
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.027
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.617       0.598
##   Tucker-Lewis Index (TLI)                       0.564       0.542
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.619
##   Robust Tucker-Lewis Index (TLI)                            0.567
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7791.099   -7791.099
##   Scaling correction factor                                  1.072
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15708.197   15708.197
##   Bayesian (BIC)                             15898.286   15898.286
##   Sample-size adjusted Bayesian (SABIC)      15698.898   15698.898
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.085       0.083
##   90 Percent confidence interval - lower         0.073       0.070
##   90 Percent confidence interval - upper         0.098       0.095
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.757       0.660
##                                                                   
##   Robust RMSEA                                               0.086
##   90 Percent confidence interval - lower                     0.073
##   90 Percent confidence interval - upper                     0.100
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.781
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.098       0.098
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               2.754    0.654
##     dsq_suppressin    0.566    0.223    2.543    0.011    1.559    0.401
##     dsq_sublimatin    0.771    0.256    3.013    0.003    2.124    0.574
##     dsq_anticipatn    0.703    0.162    4.334    0.000    1.936    0.634
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.359    0.360
##     dsq_idealizatn    1.202    1.403    0.857    0.392    1.633    0.426
##     dsq_psed_ltrsm    1.218    0.488    2.496    0.013    1.655    0.546
##     dsq_undoing       1.129    0.413    2.734    0.006    1.533    0.385
##   Immature =~                                                           
##     dsq_rationlztn    1.000                               0.201    0.068
##     dsq_isolation     7.629   13.139    0.581    0.561    1.533    0.337
##     dsq_dissociatn    7.975   14.505    0.550    0.582    1.602    0.434
##     dsq_devaluatin   10.904   19.376    0.563    0.574    2.191    0.687
##     dsq_splitting    10.954   19.035    0.575    0.565    2.201    0.578
##     dsq_denial        6.010   10.255    0.586    0.558    1.207    0.368
##     dsq_tstc_fntsy    8.501   15.480    0.549    0.583    1.708    0.400
##     dsq_displacmnt    5.617   10.006    0.561    0.575    1.128    0.276
##     dsq_pssv_ggrss    8.690   14.705    0.591    0.555    1.746    0.545
##     dsq_somatizatn    5.970   10.949    0.545    0.586    1.199    0.339
##     dsq_acting_out    8.509   14.618    0.582    0.560    1.709    0.406
##     dsq_projection    9.684   17.787    0.544    0.586    1.946    0.514
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.475    0.976    2.536    0.011    0.662    0.662
##     Immature          0.002    0.094    0.024    0.981    0.004    0.004
##   Neurotic ~~                                                           
##     Immature          0.106    0.190    0.559    0.576    0.390    0.390
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.295    0.347   26.805    0.000    9.295    2.208
##    .dsq_suppressin    8.557    0.321   26.693    0.000    8.557    2.200
##    .dsq_sublimatin   10.019    0.307   32.634    0.000   10.019    2.706
##    .dsq_anticipatn   10.120    0.253   40.019    0.000   10.120    3.313
##    .dsq_rctn_frmtn    9.887    0.311   31.838    0.000    9.887    2.623
##    .dsq_idealizatn    7.962    0.314   25.351    0.000    7.962    2.080
##    .dsq_psed_ltrsm   12.698    0.254   49.971    0.000   12.698    4.192
##    .dsq_undoing      11.136    0.334   33.377    0.000   11.136    2.800
##    .dsq_rationlztn    8.829    0.245   36.041    0.000    8.829    2.971
##    .dsq_isolation     8.588    0.378   22.737    0.000    8.588    1.886
##    .dsq_dissociatn    9.583    0.303   31.594    0.000    9.583    2.598
##    .dsq_devaluatin    9.763    0.262   37.279    0.000    9.763    3.064
##    .dsq_splitting     9.718    0.311   31.278    0.000    9.718    2.552
##    .dsq_denial        6.886    0.269   25.555    0.000    6.886    2.100
##    .dsq_tstc_fntsy    9.190    0.352   26.081    0.000    9.190    2.153
##    .dsq_displacmnt    8.152    0.342   23.834    0.000    8.152    1.992
##    .dsq_pssv_ggrss    7.752    0.269   28.835    0.000    7.752    2.421
##    .dsq_somatizatn   11.442    0.289   39.627    0.000   11.442    3.236
##    .dsq_acting_out    9.439    0.348   27.148    0.000    9.439    2.239
##    .dsq_projection    9.350    0.312   29.933    0.000    9.350    2.469
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.137    2.431    4.170    0.000   10.137    0.572
##    .dsq_suppressin   12.690    1.866    6.801    0.000   12.690    0.839
##    .dsq_sublimatin    9.193    1.722    5.338    0.000    9.193    0.671
##    .dsq_anticipatn    5.582    1.092    5.113    0.000    5.582    0.598
##    .dsq_rctn_frmtn   12.361    2.542    4.862    0.000   12.361    0.870
##    .dsq_idealizatn   11.992    3.017    3.974    0.000   11.992    0.818
##    .dsq_psed_ltrsm    6.434    2.501    2.572    0.010    6.434    0.701
##    .dsq_undoing      13.467    2.588    5.203    0.000   13.467    0.851
##    .dsq_rationlztn    8.794    0.920    9.560    0.000    8.794    0.995
##    .dsq_isolation    18.379    1.852    9.923    0.000   18.379    0.887
##    .dsq_dissociatn   11.034    1.523    7.247    0.000   11.034    0.811
##    .dsq_devaluatin    5.354    0.819    6.535    0.000    5.354    0.527
##    .dsq_splitting     9.656    1.677    5.757    0.000    9.656    0.666
##    .dsq_denial        9.292    1.029    9.033    0.000    9.292    0.864
##    .dsq_tstc_fntsy   15.310    1.775    8.624    0.000   15.310    0.840
##    .dsq_displacmnt   15.477    1.685    9.186    0.000   15.477    0.924
##    .dsq_pssv_ggrss    7.205    0.973    7.401    0.000    7.205    0.703
##    .dsq_somatizatn   11.060    1.075   10.292    0.000   11.060    0.885
##    .dsq_acting_out   14.845    1.778    8.351    0.000   14.845    0.836
##    .dsq_projection   10.552    1.281    8.238    0.000   10.552    0.736
##     Mature            7.585    2.659    2.853    0.004    1.000    1.000
##     Neurotic          1.846    2.345    0.787    0.431    1.000    1.000
##     Immature          0.040    0.141    0.286    0.775    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.428
##     dsq_suppressin    0.161
##     dsq_sublimatin    0.329
##     dsq_anticipatn    0.402
##     dsq_rctn_frmtn    0.130
##     dsq_idealizatn    0.182
##     dsq_psed_ltrsm    0.299
##     dsq_undoing       0.149
##     dsq_rationlztn    0.005
##     dsq_isolation     0.113
##     dsq_dissociatn    0.189
##     dsq_devaluatin    0.473
##     dsq_splitting     0.334
##     dsq_denial        0.136
##     dsq_tstc_fntsy    0.160
##     dsq_displacmnt    0.076
##     dsq_pssv_ggrss    0.297
##     dsq_somatizatn    0.115
##     dsq_acting_out    0.164
##     dsq_projection    0.264

4.1.3 Four Factor Solution

fit4_dekker <- cfa(model_4f, data = dekker_df, estimator = "mlr", missing = "fiml")
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite ; use lavInspect(fit, "cov.lv") to investigate.
# Inspect 4-factor for Dekker & Van
summary(fit4_dekker,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 141 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               320.064     308.506
##   Degrees of freedom                               164         164
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.037
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.672       0.665
##   Tucker-Lewis Index (TLI)                       0.620       0.611
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.680
##   Robust Tucker-Lewis Index (TLI)                            0.629
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7776.299   -7776.299
##   Scaling correction factor                                  1.045
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15684.597   15684.597
##   Bayesian (BIC)                             15883.737   15883.737
##   Sample-size adjusted Bayesian (SABIC)      15674.854   15674.854
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.079       0.076
##   90 Percent confidence interval - lower         0.066       0.063
##   90 Percent confidence interval - upper         0.092       0.089
##   P-value H_0: RMSEA <= 0.050                    0.000       0.001
##   P-value H_0: RMSEA >= 0.080                    0.480       0.331
##                                                                   
##   Robust RMSEA                                               0.080
##   90 Percent confidence interval - lower                     0.066
##   90 Percent confidence interval - upper                     0.094
##   P-value H_0: Robust RMSEA <= 0.050                         0.001
##   P-value H_0: Robust RMSEA >= 0.080                         0.500
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.089       0.089
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.715    0.646
##     dsq_suppressin       0.600    0.196    3.064    0.002    1.630    0.420
##     dsq_sublimatin       0.769    0.221    3.487    0.000    2.088    0.565
##     dsq_anticipatn       0.712    0.163    4.376    0.000    1.932    0.634
##     dsq_rationlztn       0.559    0.128    4.364    0.000    1.516    0.510
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.487    0.394
##     dsq_idealizatn       0.940    0.739    1.273    0.203    1.398    0.365
##     dsq_psed_ltrsm       1.217    0.506    2.407    0.016    1.809    0.598
##     dsq_undoing          1.072    0.374    2.868    0.004    1.594    0.401
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               1.719    0.403
##     dsq_displacmnt       0.649    0.293    2.214    0.027    1.115    0.272
##     dsq_pssv_ggrss       0.936    0.306    3.057    0.002    1.609    0.502
##     dsq_somatizatn       0.662    0.215    3.074    0.002    1.137    0.322
##     dsq_acting_out       0.948    0.336    2.826    0.005    1.630    0.387
##     dsq_projection       1.088    0.312    3.492    0.000    1.871    0.494
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.485    0.326
##     dsq_dissociatn       1.052    0.358    2.942    0.003    1.562    0.423
##     dsq_devaluatin       1.441    0.486    2.962    0.003    2.139    0.671
##     dsq_splitting        1.476    0.600    2.459    0.014    2.191    0.575
##     dsq_denial           0.752    0.243    3.091    0.002    1.116    0.340
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.484    0.779    3.186    0.001    0.615    0.615
##     Immature         -0.047    0.918   -0.052    0.959   -0.010   -0.010
##     Image_Distrtng    0.154    0.598    0.257    0.797    0.038    0.038
##   Neurotic ~~                                                           
##     Immature          0.861    0.813    1.059    0.290    0.337    0.337
##     Image_Distrtng    0.787    0.502    1.566    0.117    0.356    0.356
##   Immature ~~                                                           
##     Image_Distrtng    2.856    1.071    2.667    0.008    1.119    1.119
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.306    0.346   26.925    0.000    9.306    2.215
##    .dsq_suppressin    8.568    0.320   26.748    0.000    8.568    2.206
##    .dsq_sublimatin   10.026    0.308   32.570    0.000   10.026    2.711
##    .dsq_anticipatn   10.123    0.253   40.053    0.000   10.123    3.320
##    .dsq_rationlztn    8.847    0.245   36.084    0.000    8.847    2.976
##    .dsq_rctn_frmtn    9.884    0.310   31.894    0.000    9.884    2.621
##    .dsq_idealizatn    7.965    0.315   25.320    0.000    7.965    2.081
##    .dsq_psed_ltrsm   12.696    0.254   50.029    0.000   12.696    4.195
##    .dsq_undoing      11.139    0.333   33.474    0.000   11.139    2.802
##    .dsq_tstc_fntsy    9.187    0.352   26.081    0.000    9.187    2.152
##    .dsq_displacmnt    8.146    0.342   23.818    0.000    8.146    1.990
##    .dsq_pssv_ggrss    7.737    0.270   28.699    0.000    7.737    2.416
##    .dsq_somatizatn   11.442    0.289   39.622    0.000   11.442    3.236
##    .dsq_acting_out    9.434    0.347   27.153    0.000    9.434    2.240
##    .dsq_projection    9.348    0.313   29.891    0.000    9.348    2.469
##    .dsq_isolation     8.592    0.377   22.759    0.000    8.592    1.887
##    .dsq_dissociatn    9.582    0.303   31.595    0.000    9.582    2.598
##    .dsq_devaluatin    9.761    0.262   37.288    0.000    9.761    3.063
##    .dsq_splitting     9.718    0.311   31.272    0.000    9.718    2.552
##    .dsq_denial        6.885    0.269   25.552    0.000    6.885    2.100
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.285    2.147    4.790    0.000   10.285    0.583
##    .dsq_suppressin   12.433    1.791    6.943    0.000   12.433    0.824
##    .dsq_sublimatin    9.315    1.621    5.748    0.000    9.315    0.681
##    .dsq_anticipatn    5.561    1.054    5.275    0.000    5.561    0.598
##    .dsq_rationlztn    6.540    0.926    7.060    0.000    6.540    0.740
##    .dsq_rctn_frmtn   12.011    1.940    6.191    0.000   12.011    0.845
##    .dsq_idealizatn   12.701    2.145    5.921    0.000   12.701    0.867
##    .dsq_psed_ltrsm    5.888    2.204    2.671    0.008    5.888    0.643
##    .dsq_undoing      13.260    2.032    6.525    0.000   13.260    0.839
##    .dsq_tstc_fntsy   15.265    1.710    8.925    0.000   15.265    0.838
##    .dsq_displacmnt   15.520    1.685    9.208    0.000   15.520    0.926
##    .dsq_pssv_ggrss    7.668    1.061    7.228    0.000    7.668    0.748
##    .dsq_somatizatn   11.205    1.089   10.293    0.000   11.205    0.896
##    .dsq_acting_out   15.088    1.751    8.616    0.000   15.088    0.850
##    .dsq_projection   10.833    1.463    7.404    0.000   10.833    0.756
##    .dsq_isolation    18.522    1.913    9.681    0.000   18.522    0.894
##    .dsq_dissociatn   11.162    1.459    7.648    0.000   11.162    0.821
##    .dsq_devaluatin    5.580    0.793    7.041    0.000    5.580    0.550
##    .dsq_splitting     9.699    1.624    5.973    0.000    9.699    0.669
##    .dsq_denial        9.504    1.060    8.967    0.000    9.504    0.884
##     Mature            7.370    2.356    3.129    0.002    1.000    1.000
##     Neurotic          2.211    1.622    1.363    0.173    1.000    1.000
##     Immature          2.955    1.282    2.305    0.021    1.000    1.000
##     Image_Distrtng    2.204    1.432    1.539    0.124    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.417
##     dsq_suppressin    0.176
##     dsq_sublimatin    0.319
##     dsq_anticipatn    0.402
##     dsq_rationlztn    0.260
##     dsq_rctn_frmtn    0.155
##     dsq_idealizatn    0.133
##     dsq_psed_ltrsm    0.357
##     dsq_undoing       0.161
##     dsq_tstc_fntsy    0.162
##     dsq_displacmnt    0.074
##     dsq_pssv_ggrss    0.252
##     dsq_somatizatn    0.104
##     dsq_acting_out    0.150
##     dsq_projection    0.244
##     dsq_isolation     0.106
##     dsq_dissociatn    0.179
##     dsq_devaluatin    0.450
##     dsq_splitting     0.331
##     dsq_denial        0.116

4.1.4 Checking Error Message

cov2cor(lavInspect(fit4_dekker, "cov.lv"))
##                  Mature Neurtc Immatr Img_Ds
## Mature            1.000                     
## Neurotic          0.615  1.000              
## Immature         -0.010  0.337  1.000       
## Image_Distorting  0.038  0.356  1.119  1.000

4.1.5 Model Comparison

# Likelihood Ratio Tests (Nested)
anova(fit1_dekker, fit3_dekker)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##              Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit3_dekker 167 15708 15898 349.66                                  
## fit1_dekker 170 15793 15974 440.11      49.38       3  1.083e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(fit1_dekker, fit4_dekker)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##              Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit4_dekker 164 15685 15884 320.06                                  
## fit1_dekker 170 15793 15974 440.11     104.13       6  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# BIC (Non-Nested)
fitMeasures(fit3_dekker, "bic")
##      bic 
## 15898.29
fitMeasures(fit4_dekker, "bic")
##      bic 
## 15883.74

4.1.6 Model Comparison Winner: Four Factor Solution

modindices(fit4_dekker, sort. = TRUE, minimum.value = 3.84)
## Warning: lavaan->lav_start_check_cov():  
##    starting values imply a correlation larger than 1; variables involved are: Immature Image_Distorting
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 113               Immature =~    dsq_pseudo_altruism 20.111 -1.053  -1.810   -0.598   -0.598
## 127       Image_Distorting =~    dsq_pseudo_altruism 18.915 -1.187  -1.762   -0.582   -0.582
## 148              dsq_humor ~~         dsq_projection 15.308 -4.067  -4.067   -0.385   -0.385
## 78                  Mature =~            dsq_undoing 13.997 -0.885  -2.402   -0.604   -0.604
## 84                  Mature =~         dsq_projection 13.003 -0.486  -1.321   -0.349   -0.349
## 121       Image_Distorting =~        dsq_suppression 11.268  0.811   1.205    0.310    0.310
## 77                  Mature =~    dsq_pseudo_altruism 10.509  0.718   1.948    0.644    0.644
## 107               Immature =~        dsq_suppression  9.703  0.660   1.134    0.292    0.292
## 114               Immature =~            dsq_undoing  9.014  0.785   1.350    0.340    0.340
## 106               Immature =~              dsq_humor  8.735 -0.653  -1.123   -0.267   -0.267
## 283       dsq_displacement ~~         dsq_projection  8.495 -3.512  -3.512   -0.271   -0.271
## 282       dsq_displacement ~~         dsq_acting_out  8.383  3.970   3.970    0.259    0.259
## 128       Image_Distorting =~            dsq_undoing  8.343  0.877   1.301    0.327    0.327
## 176        dsq_sublimation ~~    dsq_pseudo_altruism  8.179  2.237   2.237    0.302    0.302
## 120       Image_Distorting =~              dsq_humor  7.498 -0.691  -1.026   -0.244   -0.244
## 318          dsq_isolation ~~             dsq_denial  7.289  3.131   3.131    0.236    0.236
## 227 dsq_reaction_formation ~~         dsq_acting_out  7.027 -3.177  -3.177   -0.236   -0.236
## 228 dsq_reaction_formation ~~         dsq_projection  6.303  2.623   2.623    0.230    0.230
## 268            dsq_undoing ~~          dsq_splitting  6.168  2.660   2.660    0.235    0.235
## 240       dsq_idealization ~~         dsq_acting_out  5.756  2.936   2.936    0.212    0.212
## 169        dsq_suppression ~~        dsq_devaluation  5.495  1.905   1.905    0.229    0.229
## 254    dsq_pseudo_altruism ~~          dsq_isolation  5.414 -2.344  -2.344   -0.224   -0.224
## 81                  Mature =~ dsq_passive_aggression  5.265  0.266   0.722    0.225    0.225
## 126       Image_Distorting =~       dsq_idealization  5.145  0.650   0.965    0.252    0.252
## 112               Immature =~       dsq_idealization  4.942  0.549   0.944    0.247    0.247
## 222 dsq_reaction_formation ~~            dsq_undoing  4.733  2.702   2.702    0.214    0.214
## 212    dsq_rationalization ~~       dsq_somatization  4.445 -1.597  -1.597   -0.187   -0.187
## 201       dsq_anticipation ~~       dsq_dissociation  4.395 -1.587  -1.587   -0.201   -0.201
## 196       dsq_anticipation ~~ dsq_passive_aggression  4.382  1.360   1.360    0.208    0.208
## 224 dsq_reaction_formation ~~       dsq_displacement  4.308 -2.503  -2.503   -0.183   -0.183
## 259            dsq_undoing ~~   dsq_autistic_fantasy  4.305  2.666   2.666    0.187    0.187
## 90                Neurotic =~              dsq_humor  4.284 -0.897  -1.334   -0.317   -0.317
## 245       dsq_idealization ~~          dsq_splitting  4.234  2.104   2.104    0.190    0.190
## 321       dsq_dissociation ~~             dsq_denial  4.109  1.861   1.861    0.181    0.181
## 151              dsq_humor ~~        dsq_devaluation  3.924 -1.610  -1.610   -0.213   -0.213
## 142              dsq_humor ~~            dsq_undoing  3.853 -2.295  -2.295   -0.197   -0.197

4.1.7 Combining factors of Immature and Image_Distorting

# New 3-factor model combining Immature + Image_Distorting
model_3f_combined <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization +
                       dsq_acting_out + dsq_projection + dsq_isolation + dsq_dissociation + dsq_devaluation +
                       dsq_splitting + dsq_denial
'

# Fit combined-factor model for Dekker
fit3_combined_dekker <- cfa(model_3f_combined, data = dekker_df, estimator = "mlr", missing = "fiml")

# Summary of results
summary(fit3_combined_dekker,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 116 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        63
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               322.096     308.665
##   Degrees of freedom                               167         167
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.044
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.674       0.671
##   Tucker-Lewis Index (TLI)                       0.630       0.626
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.682
##   Robust Tucker-Lewis Index (TLI)                            0.638
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7777.315   -7777.315
##   Scaling correction factor                                  1.029
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15680.629   15680.629
##   Bayesian (BIC)                             15870.718   15870.718
##   Sample-size adjusted Bayesian (SABIC)      15671.330   15671.330
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.078       0.075
##   90 Percent confidence interval - lower         0.065       0.062
##   90 Percent confidence interval - upper         0.091       0.088
##   P-value H_0: RMSEA <= 0.050                    0.000       0.001
##   P-value H_0: RMSEA >= 0.080                    0.431       0.265
##                                                                   
##   Robust RMSEA                                               0.079
##   90 Percent confidence interval - lower                     0.065
##   90 Percent confidence interval - upper                     0.093
##   P-value H_0: Robust RMSEA <= 0.050                         0.001
##   P-value H_0: Robust RMSEA >= 0.080                         0.452
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.089       0.089
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.705    0.644
##     dsq_suppressin        0.599    0.196    3.053    0.002    1.619    0.417
##     dsq_sublimatin        0.772    0.219    3.523    0.000    2.088    0.565
##     dsq_anticipatn        0.720    0.149    4.843    0.000    1.948    0.639
##     dsq_rationlztn        0.559    0.128    4.378    0.000    1.511    0.508
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.487    0.394
##     dsq_idealizatn        0.941    0.737    1.278    0.201    1.400    0.366
##     dsq_psed_ltrsm        1.217    0.498    2.447    0.014    1.810    0.598
##     dsq_undoing           1.068    0.367    2.908    0.004    1.588    0.400
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.708    0.400
##     dsq_displacmnt        0.670    0.300    2.233    0.026    1.144    0.279
##     dsq_pssv_ggrss        1.020    0.328    3.111    0.002    1.742    0.544
##     dsq_somatizatn        0.713    0.223    3.196    0.001    1.217    0.344
##     dsq_acting_out        0.998    0.368    2.713    0.007    1.704    0.404
##     dsq_projection        1.142    0.322    3.542    0.000    1.950    0.515
##     dsq_isolation         0.901    0.339    2.654    0.008    1.538    0.338
##     dsq_dissociatn        0.942    0.279    3.371    0.001    1.609    0.436
##     dsq_devaluatin        1.284    0.305    4.214    0.000    2.192    0.688
##     dsq_splitting         1.282    0.343    3.742    0.000    2.189    0.575
##     dsq_denial            0.702    0.273    2.573    0.010    1.198    0.366
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.479    0.767    3.231    0.001    0.616    0.616
##     Combined_Immtr    0.095    0.647    0.147    0.883    0.021    0.021
##   Neurotic ~~                                                           
##     Combined_Immtr    0.854    0.693    1.232    0.218    0.336    0.336
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.307    0.346   26.920    0.000    9.307    2.215
##    .dsq_suppressin    8.568    0.320   26.768    0.000    8.568    2.206
##    .dsq_sublimatin   10.028    0.308   32.593    0.000   10.028    2.712
##    .dsq_anticipatn   10.125    0.252   40.111    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.100    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.884    0.310   31.876    0.000    9.884    2.621
##    .dsq_idealizatn    7.966    0.314   25.332    0.000    7.966    2.081
##    .dsq_psed_ltrsm   12.697    0.253   50.105    0.000   12.697    4.195
##    .dsq_undoing      11.140    0.333   33.492    0.000   11.140    2.802
##    .dsq_tstc_fntsy    9.190    0.352   26.071    0.000    9.190    2.152
##    .dsq_displacmnt    8.152    0.342   23.836    0.000    8.152    1.992
##    .dsq_pssv_ggrss    7.751    0.269   28.824    0.000    7.751    2.420
##    .dsq_somatizatn   11.442    0.289   39.627    0.000   11.442    3.236
##    .dsq_acting_out    9.438    0.348   27.149    0.000    9.438    2.239
##    .dsq_projection    9.349    0.313   29.905    0.000    9.349    2.469
##    .dsq_isolation     8.587    0.378   22.738    0.000    8.587    1.886
##    .dsq_dissociatn    9.583    0.303   31.588    0.000    9.583    2.598
##    .dsq_devaluatin    9.762    0.262   37.271    0.000    9.762    3.063
##    .dsq_splitting     9.718    0.311   31.278    0.000    9.718    2.552
##    .dsq_denial        6.886    0.269   25.555    0.000    6.886    2.100
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.341    2.088    4.953    0.000   10.341    0.586
##    .dsq_suppressin   12.466    1.777    7.015    0.000   12.466    0.826
##    .dsq_sublimatin    9.312    1.619    5.753    0.000    9.312    0.681
##    .dsq_anticipatn    5.500    0.985    5.582    0.000    5.500    0.592
##    .dsq_rationlztn    6.558    0.925    7.087    0.000    6.558    0.742
##    .dsq_rctn_frmtn   12.011    1.930    6.224    0.000   12.011    0.845
##    .dsq_idealizatn   12.696    2.130    5.960    0.000   12.696    0.866
##    .dsq_psed_ltrsm    5.883    2.171    2.709    0.007    5.883    0.642
##    .dsq_undoing      13.278    2.028    6.547    0.000   13.278    0.840
##    .dsq_tstc_fntsy   15.314    1.773    8.636    0.000   15.314    0.840
##    .dsq_displacmnt   15.442    1.680    9.190    0.000   15.442    0.922
##    .dsq_pssv_ggrss    7.218    0.964    7.491    0.000    7.218    0.704
##    .dsq_somatizatn   11.018    1.072   10.281    0.000   11.018    0.882
##    .dsq_acting_out   14.864    1.766    8.418    0.000   14.864    0.837
##    .dsq_projection   10.535    1.267    8.312    0.000   10.535    0.735
##    .dsq_isolation    18.363    1.845    9.951    0.000   18.363    0.886
##    .dsq_dissociatn   11.013    1.498    7.352    0.000   11.013    0.810
##    .dsq_devaluatin    5.352    0.811    6.602    0.000    5.352    0.527
##    .dsq_splitting     9.706    1.681    5.774    0.000    9.706    0.669
##    .dsq_denial        9.314    1.031    9.034    0.000    9.314    0.866
##     Mature            7.315    2.292    3.192    0.001    1.000    1.000
##     Neurotic          2.211    1.616    1.369    0.171    1.000    1.000
##     Combined_Immtr    2.916    1.384    2.106    0.035    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.414
##     dsq_suppressin    0.174
##     dsq_sublimatin    0.319
##     dsq_anticipatn    0.408
##     dsq_rationlztn    0.258
##     dsq_rctn_frmtn    0.155
##     dsq_idealizatn    0.134
##     dsq_psed_ltrsm    0.358
##     dsq_undoing       0.160
##     dsq_tstc_fntsy    0.160
##     dsq_displacmnt    0.078
##     dsq_pssv_ggrss    0.296
##     dsq_somatizatn    0.118
##     dsq_acting_out    0.163
##     dsq_projection    0.265
##     dsq_isolation     0.114
##     dsq_dissociatn    0.190
##     dsq_devaluatin    0.473
##     dsq_splitting     0.331
##     dsq_denial        0.134

4.1.8 Adding correlated errors in Four Factor Solution I

model_3f_combined_adj_I <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization +
                       dsq_acting_out + dsq_projection + dsq_isolation + dsq_dissociation + dsq_devaluation +
                       dsq_splitting + dsq_denial
                       
                       dsq_displacement ~~ dsq_acting_out
'

fit3f_combined_adj_I <- cfa(model_3f_combined_adj_I, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_I,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 118 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        64
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               313.645     300.393
##   Degrees of freedom                               166         166
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.044
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.690       0.688
##   Tucker-Lewis Index (TLI)                       0.645       0.643
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.700
##   Robust Tucker-Lewis Index (TLI)                            0.656
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7773.089   -7773.089
##   Scaling correction factor                                  1.028
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15674.178   15674.178
##   Bayesian (BIC)                             15867.284   15867.284
##   Sample-size adjusted Bayesian (SABIC)      15664.730   15664.730
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.077       0.073
##   90 Percent confidence interval - lower         0.064       0.060
##   90 Percent confidence interval - upper         0.090       0.086
##   P-value H_0: RMSEA <= 0.050                    0.001       0.002
##   P-value H_0: RMSEA >= 0.080                    0.350       0.199
##                                                                   
##   Robust RMSEA                                               0.077
##   90 Percent confidence interval - lower                     0.062
##   90 Percent confidence interval - upper                     0.091
##   P-value H_0: Robust RMSEA <= 0.050                         0.002
##   P-value H_0: Robust RMSEA >= 0.080                         0.362
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.088       0.088
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.712    0.645
##     dsq_suppressin        0.595    0.195    3.047    0.002    1.613    0.415
##     dsq_sublimatin        0.769    0.217    3.545    0.000    2.085    0.564
##     dsq_anticipatn        0.719    0.149    4.840    0.000    1.951    0.640
##     dsq_rationlztn        0.556    0.127    4.367    0.000    1.508    0.507
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.497    0.397
##     dsq_idealizatn        0.942    0.730    1.290    0.197    1.410    0.368
##     dsq_psed_ltrsm        1.196    0.485    2.466    0.014    1.790    0.591
##     dsq_undoing           1.066    0.359    2.972    0.003    1.596    0.402
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.727    0.404
##     dsq_displacmnt        0.559    0.279    2.006    0.045    0.965    0.236
##     dsq_pssv_ggrss        1.005    0.323    3.108    0.002    1.736    0.542
##     dsq_somatizatn        0.710    0.222    3.203    0.001    1.225    0.347
##     dsq_acting_out        0.926    0.348    2.664    0.008    1.599    0.380
##     dsq_projection        1.164    0.329    3.538    0.000    2.009    0.531
##     dsq_isolation         0.909    0.342    2.660    0.008    1.569    0.345
##     dsq_dissociatn        0.931    0.278    3.346    0.001    1.607    0.436
##     dsq_devaluatin        1.266    0.297    4.259    0.000    2.186    0.686
##     dsq_splitting         1.257    0.332    3.791    0.000    2.170    0.570
##     dsq_denial            0.700    0.275    2.546    0.011    1.209    0.369
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_displacement ~~                                                      
##    .dsq_acting_out       3.889    1.478    2.632    0.008    3.889    0.251
##   Mature ~~                                                                
##     Neurotic             2.497    0.771    3.239    0.001    0.615    0.615
##     Combined_Immtr       0.055    0.669    0.082    0.935    0.012    0.012
##   Neurotic ~~                                                              
##     Combined_Immtr       0.903    0.690    1.308    0.191    0.349    0.349
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.307    0.346   26.920    0.000    9.307    2.215
##    .dsq_suppressin    8.568    0.320   26.767    0.000    8.568    2.206
##    .dsq_sublimatin   10.028    0.308   32.594    0.000   10.028    2.712
##    .dsq_anticipatn   10.125    0.252   40.112    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.100    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.884    0.310   31.871    0.000    9.884    2.621
##    .dsq_idealizatn    7.965    0.314   25.331    0.000    7.965    2.081
##    .dsq_psed_ltrsm   12.698    0.253   50.112    0.000   12.698    4.195
##    .dsq_undoing      11.140    0.333   33.494    0.000   11.140    2.802
##    .dsq_tstc_fntsy    9.189    0.352   26.072    0.000    9.189    2.152
##    .dsq_displacmnt    8.164    0.341   23.946    0.000    8.164    1.998
##    .dsq_pssv_ggrss    7.750    0.269   28.828    0.000    7.750    2.420
##    .dsq_somatizatn   11.442    0.289   39.629    0.000   11.442    3.236
##    .dsq_acting_out    9.419    0.349   26.989    0.000    9.419    2.236
##    .dsq_projection    9.349    0.313   29.909    0.000    9.349    2.469
##    .dsq_isolation     8.587    0.378   22.738    0.000    8.587    1.886
##    .dsq_dissociatn    9.583    0.303   31.587    0.000    9.583    2.598
##    .dsq_devaluatin    9.763    0.262   37.278    0.000    9.763    3.063
##    .dsq_splitting     9.718    0.311   31.277    0.000    9.718    2.552
##    .dsq_denial        6.886    0.269   25.555    0.000    6.886    2.100
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.302    2.086    4.939    0.000   10.302    0.583
##    .dsq_suppressin   12.486    1.777    7.026    0.000   12.486    0.828
##    .dsq_sublimatin    9.327    1.607    5.805    0.000    9.327    0.682
##    .dsq_anticipatn    5.489    0.977    5.621    0.000    5.489    0.591
##    .dsq_rationlztn    6.567    0.927    7.084    0.000    6.567    0.743
##    .dsq_rctn_frmtn   11.980    1.948    6.149    0.000   11.980    0.842
##    .dsq_idealizatn   12.667    2.104    6.020    0.000   12.667    0.864
##    .dsq_psed_ltrsm    5.956    2.071    2.876    0.004    5.956    0.650
##    .dsq_undoing      13.253    2.049    6.468    0.000   13.253    0.839
##    .dsq_tstc_fntsy   15.249    1.758    8.676    0.000   15.249    0.836
##    .dsq_displacmnt   15.769    1.661    9.495    0.000   15.769    0.944
##    .dsq_pssv_ggrss    7.242    0.978    7.403    0.000    7.242    0.706
##    .dsq_somatizatn   10.998    1.062   10.353    0.000   10.998    0.880
##    .dsq_acting_out   15.193    1.757    8.649    0.000   15.193    0.856
##    .dsq_projection   10.303    1.251    8.236    0.000   10.303    0.719
##    .dsq_isolation    18.265    1.857    9.838    0.000   18.265    0.881
##    .dsq_dissociatn   11.020    1.502    7.339    0.000   11.020    0.810
##    .dsq_devaluatin    5.382    0.816    6.596    0.000    5.382    0.530
##    .dsq_splitting     9.789    1.689    5.795    0.000    9.789    0.675
##    .dsq_denial        9.290    1.041    8.923    0.000    9.290    0.864
##     Mature            7.354    2.294    3.206    0.001    1.000    1.000
##     Neurotic          2.241    1.644    1.363    0.173    1.000    1.000
##     Combined_Immtr    2.981    1.400    2.130    0.033    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.417
##     dsq_suppressin    0.172
##     dsq_sublimatin    0.318
##     dsq_anticipatn    0.409
##     dsq_rationlztn    0.257
##     dsq_rctn_frmtn    0.158
##     dsq_idealizatn    0.136
##     dsq_psed_ltrsm    0.350
##     dsq_undoing       0.161
##     dsq_tstc_fntsy    0.164
##     dsq_displacmnt    0.056
##     dsq_pssv_ggrss    0.294
##     dsq_somatizatn    0.120
##     dsq_acting_out    0.144
##     dsq_projection    0.281
##     dsq_isolation     0.119
##     dsq_dissociatn    0.190
##     dsq_devaluatin    0.470
##     dsq_splitting     0.325
##     dsq_denial        0.136
modindices(fit3f_combined_adj_I, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 124              dsq_humor ~~         dsq_projection 15.547 -3.958  -3.958   -0.384   -0.384
## 109      Combined_Immature =~    dsq_pseudo_altruism 15.133 -0.845  -1.459   -0.482   -0.482
## 74                  Mature =~            dsq_undoing 13.672 -0.869  -2.357   -0.593   -0.593
## 80                  Mature =~         dsq_projection 13.031 -0.444  -1.204   -0.318   -0.318
## 73                  Mature =~    dsq_pseudo_altruism 10.350  0.695   1.886    0.623    0.623
## 103      Combined_Immature =~        dsq_suppression  9.955  0.638   1.102    0.284    0.284
## 152        dsq_sublimation ~~    dsq_pseudo_altruism  8.373  2.266   2.266    0.304    0.304
## 110      Combined_Immature =~            dsq_undoing  7.746  0.696   1.201    0.302    0.302
## 102      Combined_Immature =~              dsq_humor  7.677 -0.581  -1.004   -0.239   -0.239
## 293          dsq_isolation ~~             dsq_denial  7.383  3.099   3.099    0.238    0.238
## 204 dsq_reaction_formation ~~         dsq_projection  6.088  2.491   2.491    0.224    0.224
## 244            dsq_undoing ~~          dsq_splitting  6.083  2.605   2.605    0.229    0.229
## 216       dsq_idealization ~~         dsq_acting_out  6.032  2.879   2.879    0.208    0.208
## 145        dsq_suppression ~~        dsq_devaluation  5.817  1.904   1.904    0.232    0.232
## 258       dsq_displacement ~~         dsq_projection  5.543 -2.630  -2.630   -0.206   -0.206
## 230    dsq_pseudo_altruism ~~          dsq_isolation  5.221 -2.281  -2.281   -0.219   -0.219
## 172       dsq_anticipation ~~ dsq_passive_aggression  4.914  1.384   1.384    0.219    0.219
## 203 dsq_reaction_formation ~~         dsq_acting_out  4.842 -2.525  -2.525   -0.187   -0.187
## 188    dsq_rationalization ~~       dsq_somatization  4.816 -1.645  -1.645   -0.194   -0.194
## 198 dsq_reaction_formation ~~            dsq_undoing  4.703  2.696   2.696    0.214    0.214
## 177       dsq_anticipation ~~       dsq_dissociation  4.660 -1.612  -1.612   -0.207   -0.207
## 108      Combined_Immature =~       dsq_idealization  4.558  0.505   0.872    0.228    0.228
## 235            dsq_undoing ~~   dsq_autistic_fantasy  4.441  2.679   2.679    0.188    0.188
## 296       dsq_dissociation ~~             dsq_denial  4.342  1.870   1.870    0.185    0.185
## 96                Neurotic =~         dsq_projection  4.330 -0.560  -0.839   -0.222   -0.222
## 221       dsq_idealization ~~          dsq_splitting  4.296  2.091   2.091    0.188    0.188
## 77                  Mature =~ dsq_passive_aggression  4.173  0.215   0.584    0.182    0.182
## 86                Neurotic =~              dsq_humor  4.083 -0.867  -1.299   -0.309   -0.309
## 268 dsq_passive_aggression ~~       dsq_dissociation  4.043 -1.734  -1.734   -0.194   -0.194
## 278       dsq_somatization ~~             dsq_denial  4.024 -1.753  -1.753   -0.173   -0.173
## 118              dsq_humor ~~            dsq_undoing  3.925 -2.316  -2.316   -0.198   -0.198

4.1.9 Adding correlated errors in Four Factor Solution II

model_3f_combined_adj_II <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization +
                       dsq_acting_out + dsq_projection + dsq_isolation + dsq_dissociation + dsq_devaluation +
                       dsq_splitting + dsq_denial
                       
                       dsq_displacement ~~ dsq_acting_out
                       dsq_isolation ~~ dsq_denial
'

fit3f_combined_adj_II <- cfa(model_3f_combined_adj_II, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_II,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 128 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        65
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               306.066     293.549
##   Degrees of freedom                               165         165
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.043
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.704       0.702
##   Tucker-Lewis Index (TLI)                       0.659       0.656
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.714
##   Robust Tucker-Lewis Index (TLI)                            0.671
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7769.300   -7769.300
##   Scaling correction factor                                  1.032
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15668.599   15668.599
##   Bayesian (BIC)                             15864.722   15864.722
##   Sample-size adjusted Bayesian (SABIC)      15659.004   15659.004
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.075       0.072
##   90 Percent confidence interval - lower         0.062       0.059
##   90 Percent confidence interval - upper         0.088       0.085
##   P-value H_0: RMSEA <= 0.050                    0.001       0.004
##   P-value H_0: RMSEA >= 0.080                    0.283       0.155
##                                                                   
##   Robust RMSEA                                               0.075
##   90 Percent confidence interval - lower                     0.061
##   90 Percent confidence interval - upper                     0.089
##   P-value H_0: Robust RMSEA <= 0.050                         0.003
##   P-value H_0: Robust RMSEA >= 0.080                         0.294
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.087       0.087
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.718    0.647
##     dsq_suppressin        0.592    0.194    3.044    0.002    1.608    0.414
##     dsq_sublimatin        0.766    0.215    3.556    0.000    2.081    0.563
##     dsq_anticipatn        0.719    0.149    4.837    0.000    1.954    0.641
##     dsq_rationlztn        0.554    0.127    4.369    0.000    1.506    0.506
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.485    0.394
##     dsq_idealizatn        0.962    0.768    1.254    0.210    1.429    0.373
##     dsq_psed_ltrsm        1.196    0.473    2.528    0.011    1.776    0.587
##     dsq_undoing           1.077    0.366    2.941    0.003    1.599    0.402
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.746    0.409
##     dsq_displacmnt        0.566    0.282    2.008    0.045    0.989    0.242
##     dsq_pssv_ggrss        0.990    0.318    3.112    0.002    1.729    0.540
##     dsq_somatizatn        0.708    0.218    3.249    0.001    1.237    0.350
##     dsq_acting_out        0.921    0.350    2.631    0.009    1.608    0.382
##     dsq_projection        1.146    0.323    3.549    0.000    2.002    0.529
##     dsq_isolation         0.806    0.309    2.606    0.009    1.408    0.309
##     dsq_dissociatn        0.899    0.266    3.374    0.001    1.570    0.426
##     dsq_devaluatin        1.266    0.302    4.194    0.000    2.211    0.693
##     dsq_splitting         1.257    0.333    3.772    0.000    2.194    0.576
##     dsq_denial            0.638    0.256    2.492    0.013    1.114    0.340
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_displacement ~~                                                      
##    .dsq_acting_out       3.841    1.491    2.576    0.010    3.841    0.249
##  .dsq_isolation ~~                                                         
##    .dsq_denial           3.153    1.318    2.393    0.017    3.153    0.236
##   Mature ~~                                                                
##     Neurotic             2.484    0.787    3.155    0.002    0.616    0.616
##     Combined_Immtr       0.027    0.683    0.040    0.968    0.006    0.006
##   Neurotic ~~                                                              
##     Combined_Immtr       0.943    0.672    1.404    0.160    0.364    0.364
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.307    0.346   26.921    0.000    9.307    2.215
##    .dsq_suppressin    8.568    0.320   26.766    0.000    8.568    2.206
##    .dsq_sublimatin   10.029    0.308   32.595    0.000   10.029    2.712
##    .dsq_anticipatn   10.125    0.252   40.112    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.100    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.884    0.310   31.869    0.000    9.884    2.621
##    .dsq_idealizatn    7.965    0.314   25.331    0.000    7.965    2.081
##    .dsq_psed_ltrsm   12.698    0.253   50.120    0.000   12.698    4.196
##    .dsq_undoing      11.140    0.333   33.493    0.000   11.140    2.803
##    .dsq_tstc_fntsy    9.189    0.352   26.076    0.000    9.189    2.152
##    .dsq_displacmnt    8.164    0.341   23.949    0.000    8.164    1.998
##    .dsq_pssv_ggrss    7.748    0.269   28.823    0.000    7.748    2.419
##    .dsq_somatizatn   11.442    0.289   39.627    0.000   11.442    3.236
##    .dsq_acting_out    9.419    0.349   26.987    0.000    9.419    2.236
##    .dsq_projection    9.349    0.313   29.910    0.000    9.349    2.469
##    .dsq_isolation     8.586    0.377   22.758    0.000    8.586    1.887
##    .dsq_dissociatn    9.584    0.303   31.590    0.000    9.584    2.598
##    .dsq_devaluatin    9.763    0.262   37.272    0.000    9.763    3.063
##    .dsq_splitting     9.718    0.311   31.276    0.000    9.718    2.552
##    .dsq_denial        6.887    0.269   25.571    0.000    6.887    2.102
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.272    2.083    4.931    0.000   10.272    0.582
##    .dsq_suppressin   12.503    1.776    7.041    0.000   12.503    0.829
##    .dsq_sublimatin    9.343    1.602    5.833    0.000    9.343    0.683
##    .dsq_anticipatn    5.479    0.973    5.633    0.000    5.479    0.589
##    .dsq_rationlztn    6.573    0.929    7.077    0.000    6.573    0.744
##    .dsq_rctn_frmtn   12.016    1.987    6.047    0.000   12.016    0.845
##    .dsq_idealizatn   12.614    2.139    5.898    0.000   12.614    0.861
##    .dsq_psed_ltrsm    6.005    2.036    2.950    0.003    6.005    0.656
##    .dsq_undoing      13.243    2.066    6.410    0.000   13.243    0.838
##    .dsq_tstc_fntsy   15.178    1.762    8.613    0.000   15.178    0.833
##    .dsq_displacmnt   15.722    1.664    9.446    0.000   15.722    0.941
##    .dsq_pssv_ggrss    7.264    0.994    7.306    0.000    7.264    0.708
##    .dsq_somatizatn   10.969    1.074   10.213    0.000   10.969    0.878
##    .dsq_acting_out   15.163    1.779    8.522    0.000   15.163    0.854
##    .dsq_projection   10.331    1.280    8.073    0.000   10.331    0.721
##    .dsq_isolation    18.722    1.821   10.279    0.000   18.722    0.904
##    .dsq_dissociatn   11.138    1.502    7.416    0.000   11.138    0.819
##    .dsq_devaluatin    5.274    0.853    6.187    0.000    5.274    0.519
##    .dsq_splitting     9.684    1.671    5.794    0.000    9.684    0.668
##    .dsq_denial        9.500    1.048    9.061    0.000    9.500    0.884
##     Mature            7.385    2.296    3.217    0.001    1.000    1.000
##     Neurotic          2.205    1.689    1.305    0.192    1.000    1.000
##     Combined_Immtr    3.050    1.419    2.150    0.032    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.418
##     dsq_suppressin    0.171
##     dsq_sublimatin    0.317
##     dsq_anticipatn    0.411
##     dsq_rationlztn    0.256
##     dsq_rctn_frmtn    0.155
##     dsq_idealizatn    0.139
##     dsq_psed_ltrsm    0.344
##     dsq_undoing       0.162
##     dsq_tstc_fntsy    0.167
##     dsq_displacmnt    0.059
##     dsq_pssv_ggrss    0.292
##     dsq_somatizatn    0.122
##     dsq_acting_out    0.146
##     dsq_projection    0.279
##     dsq_isolation     0.096
##     dsq_dissociatn    0.181
##     dsq_devaluatin    0.481
##     dsq_splitting     0.332
##     dsq_denial        0.116
modindices(fit3f_combined_adj_II, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 125              dsq_humor ~~         dsq_projection 15.497 -3.955  -3.955   -0.384   -0.384
## 110      Combined_Immature =~    dsq_pseudo_altruism 14.718 -0.831  -1.450   -0.479   -0.479
## 75                  Mature =~            dsq_undoing 13.705 -0.862  -2.344   -0.590   -0.590
## 81                  Mature =~         dsq_projection 12.818 -0.440  -1.195   -0.316   -0.316
## 74                  Mature =~    dsq_pseudo_altruism 10.288  0.679   1.845    0.610    0.610
## 104      Combined_Immature =~        dsq_suppression  9.806  0.627   1.095    0.282    0.282
## 153        dsq_sublimation ~~    dsq_pseudo_altruism  8.306  2.257   2.257    0.301    0.301
## 111      Combined_Immature =~            dsq_undoing  7.807  0.699   1.220    0.307    0.307
## 103      Combined_Immature =~              dsq_humor  7.570 -0.572  -0.998   -0.238   -0.238
## 146        dsq_suppression ~~        dsq_devaluation  6.095  1.945   1.945    0.239    0.239
## 205 dsq_reaction_formation ~~         dsq_projection  6.077  2.495   2.495    0.224    0.224
## 217       dsq_idealization ~~         dsq_acting_out  5.995  2.867   2.867    0.207    0.207
## 245            dsq_undoing ~~          dsq_splitting  5.856  2.550   2.550    0.225    0.225
## 259       dsq_displacement ~~         dsq_projection  5.747 -2.682  -2.682   -0.210   -0.210
## 173       dsq_anticipation ~~ dsq_passive_aggression  5.018  1.400   1.400    0.222    0.222
## 204 dsq_reaction_formation ~~         dsq_acting_out  4.842 -2.526  -2.526   -0.187   -0.187
## 199 dsq_reaction_formation ~~            dsq_undoing  4.732  2.698   2.698    0.214    0.214
## 189    dsq_rationalization ~~       dsq_somatization  4.718 -1.627  -1.627   -0.192   -0.192
## 178       dsq_anticipation ~~       dsq_dissociation  4.568 -1.601  -1.601   -0.205   -0.205
## 97                Neurotic =~         dsq_projection  4.560 -0.585  -0.869   -0.229   -0.229
## 286         dsq_projection ~~          dsq_isolation  4.433  2.581   2.581    0.186    0.186
## 109      Combined_Immature =~       dsq_idealization  4.325  0.492   0.860    0.225    0.225
## 236            dsq_undoing ~~   dsq_autistic_fantasy  4.320  2.639   2.639    0.186    0.186
## 78                  Mature =~ dsq_passive_aggression  4.236  0.217   0.589    0.184    0.184
## 87                Neurotic =~              dsq_humor  4.224 -0.883  -1.311   -0.312   -0.312
## 222       dsq_idealization ~~          dsq_splitting  4.224  2.067   2.067    0.187    0.187
## 165        dsq_sublimation ~~             dsq_denial  4.139 -1.684  -1.684   -0.179   -0.179
## 285         dsq_acting_out ~~             dsq_denial  4.121  1.975   1.975    0.165    0.165
## 279       dsq_somatization ~~             dsq_denial  4.092 -1.717  -1.717   -0.168   -0.168
## 119              dsq_humor ~~            dsq_undoing  3.915 -2.312  -2.312   -0.198   -0.198

4.1.10 Adding correlated errors in Four Factor Solution III

model_3f_combined_adj_III <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization +
                       dsq_acting_out + dsq_projection + dsq_isolation + dsq_dissociation + dsq_devaluation +
                       dsq_splitting + dsq_denial
                       
                       dsq_displacement ~~ dsq_acting_out
                       dsq_isolation ~~ dsq_denial
                       dsq_displacement ~~ dsq_projection
'

fit3f_combined_adj_III <- cfa(model_3f_combined_adj_III, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_III,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 138 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               299.813     287.190
##   Degrees of freedom                               164         164
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.044
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.715       0.714
##   Tucker-Lewis Index (TLI)                       0.670       0.669
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.725
##   Robust Tucker-Lewis Index (TLI)                            0.681
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7766.173   -7766.173
##   Scaling correction factor                                  1.029
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15664.345   15664.345
##   Bayesian (BIC)                             15863.486   15863.486
##   Sample-size adjusted Bayesian (SABIC)      15654.603   15654.603
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.074       0.071
##   90 Percent confidence interval - lower         0.061       0.057
##   90 Percent confidence interval - upper         0.087       0.084
##   P-value H_0: RMSEA <= 0.050                    0.002       0.007
##   P-value H_0: RMSEA >= 0.080                    0.236       0.120
##                                                                   
##   Robust RMSEA                                               0.074
##   90 Percent confidence interval - lower                     0.059
##   90 Percent confidence interval - upper                     0.088
##   P-value H_0: Robust RMSEA <= 0.050                         0.005
##   P-value H_0: Robust RMSEA >= 0.080                         0.248
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.087       0.087
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.721    0.648
##     dsq_suppressin        0.591    0.194    3.037    0.002    1.607    0.414
##     dsq_sublimatin        0.765    0.217    3.523    0.000    2.081    0.563
##     dsq_anticipatn        0.717    0.149    4.818    0.000    1.950    0.640
##     dsq_rationlztn        0.554    0.127    4.363    0.000    1.507    0.507
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.494    0.396
##     dsq_idealizatn        0.942    0.730    1.290    0.197    1.407    0.367
##     dsq_psed_ltrsm        1.200    0.490    2.449    0.014    1.793    0.592
##     dsq_undoing           1.073    0.365    2.942    0.003    1.602    0.403
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.729    0.405
##     dsq_displacmnt        0.692    0.295    2.345    0.019    1.197    0.294
##     dsq_pssv_ggrss        1.013    0.321    3.156    0.002    1.751    0.547
##     dsq_somatizatn        0.710    0.216    3.293    0.001    1.227    0.347
##     dsq_acting_out        0.927    0.351    2.637    0.008    1.602    0.380
##     dsq_projection        1.183    0.327    3.619    0.000    2.046    0.540
##     dsq_isolation         0.821    0.313    2.626    0.009    1.420    0.312
##     dsq_dissociatn        0.905    0.265    3.412    0.001    1.565    0.424
##     dsq_devaluatin        1.278    0.305    4.186    0.000    2.210    0.693
##     dsq_splitting         1.266    0.334    3.790    0.000    2.188    0.575
##     dsq_denial            0.619    0.251    2.461    0.014    1.070    0.326
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_displacement ~~                                                      
##    .dsq_acting_out       3.133    1.441    2.174    0.030    3.133    0.207
##  .dsq_isolation ~~                                                         
##    .dsq_denial           3.201    1.325    2.416    0.016    3.201    0.239
##  .dsq_displacement ~~                                                      
##    .dsq_projection      -2.827    1.190   -2.375    0.018   -2.827   -0.228
##   Mature ~~                                                                
##     Neurotic             2.494    0.775    3.221    0.001    0.614    0.614
##     Combined_Immtr      -0.027    0.680   -0.039    0.969   -0.006   -0.006
##   Neurotic ~~                                                              
##     Combined_Immtr       0.873    0.689    1.268    0.205    0.338    0.338
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.307    0.346   26.921    0.000    9.307    2.215
##    .dsq_suppressin    8.568    0.320   26.767    0.000    8.568    2.206
##    .dsq_sublimatin   10.029    0.308   32.591    0.000   10.029    2.712
##    .dsq_anticipatn   10.125    0.252   40.111    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.100    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.884    0.310   31.869    0.000    9.884    2.621
##    .dsq_idealizatn    7.966    0.314   25.330    0.000    7.966    2.081
##    .dsq_psed_ltrsm   12.698    0.253   50.113    0.000   12.698    4.196
##    .dsq_undoing      11.139    0.333   33.490    0.000   11.139    2.802
##    .dsq_tstc_fntsy    9.189    0.352   26.074    0.000    9.189    2.152
##    .dsq_displacmnt    8.151    0.340   23.970    0.000    8.151    2.003
##    .dsq_pssv_ggrss    7.749    0.269   28.821    0.000    7.749    2.419
##    .dsq_somatizatn   11.442    0.289   39.629    0.000   11.442    3.236
##    .dsq_acting_out    9.423    0.349   27.014    0.000    9.423    2.236
##    .dsq_projection    9.360    0.313   29.930    0.000    9.360    2.472
##    .dsq_isolation     8.586    0.377   22.758    0.000    8.586    1.887
##    .dsq_dissociatn    9.584    0.303   31.595    0.000    9.584    2.599
##    .dsq_devaluatin    9.763    0.262   37.267    0.000    9.763    3.063
##    .dsq_splitting     9.718    0.311   31.276    0.000    9.718    2.552
##    .dsq_denial        6.887    0.269   25.571    0.000    6.887    2.102
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.252    2.098    4.886    0.000   10.252    0.581
##    .dsq_suppressin   12.507    1.774    7.050    0.000   12.507    0.829
##    .dsq_sublimatin    9.343    1.609    5.806    0.000    9.343    0.683
##    .dsq_anticipatn    5.491    0.967    5.678    0.000    5.491    0.591
##    .dsq_rationlztn    6.568    0.927    7.083    0.000    6.568    0.743
##    .dsq_rctn_frmtn   11.991    1.943    6.171    0.000   11.991    0.843
##    .dsq_idealizatn   12.677    2.100    6.037    0.000   12.677    0.865
##    .dsq_psed_ltrsm    5.945    2.086    2.850    0.004    5.945    0.649
##    .dsq_undoing      13.234    2.057    6.434    0.000   13.234    0.838
##    .dsq_tstc_fntsy   15.239    1.760    8.661    0.000   15.239    0.836
##    .dsq_displacmnt   15.124    1.588    9.525    0.000   15.124    0.913
##    .dsq_pssv_ggrss    7.190    0.976    7.366    0.000    7.190    0.701
##    .dsq_somatizatn   10.992    1.082   10.155    0.000   10.992    0.879
##    .dsq_acting_out   15.188    1.779    8.537    0.000   15.188    0.855
##    .dsq_projection   10.154    1.274    7.973    0.000   10.154    0.708
##    .dsq_isolation    18.687    1.815   10.296    0.000   18.687    0.903
##    .dsq_dissociatn   11.151    1.491    7.479    0.000   11.151    0.820
##    .dsq_devaluatin    5.277    0.828    6.372    0.000    5.277    0.519
##    .dsq_splitting     9.711    1.655    5.869    0.000    9.711    0.670
##    .dsq_denial        9.595    1.052    9.123    0.000    9.595    0.893
##     Mature            7.404    2.311    3.204    0.001    1.000    1.000
##     Neurotic          2.231    1.638    1.362    0.173    1.000    1.000
##     Combined_Immtr    2.989    1.391    2.149    0.032    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.419
##     dsq_suppressin    0.171
##     dsq_sublimatin    0.317
##     dsq_anticipatn    0.409
##     dsq_rationlztn    0.257
##     dsq_rctn_frmtn    0.157
##     dsq_idealizatn    0.135
##     dsq_psed_ltrsm    0.351
##     dsq_undoing       0.162
##     dsq_tstc_fntsy    0.164
##     dsq_displacmnt    0.087
##     dsq_pssv_ggrss    0.299
##     dsq_somatizatn    0.121
##     dsq_acting_out    0.145
##     dsq_projection    0.292
##     dsq_isolation     0.097
##     dsq_dissociatn    0.180
##     dsq_devaluatin    0.481
##     dsq_splitting     0.330
##     dsq_denial        0.107
modindices(fit3f_combined_adj_III, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 126              dsq_humor ~~         dsq_projection 16.994 -4.053  -4.053   -0.397   -0.397
## 111      Combined_Immature =~    dsq_pseudo_altruism 15.148 -0.834  -1.443   -0.477   -0.477
## 82                  Mature =~         dsq_projection 14.254 -0.455  -1.238   -0.327   -0.327
## 76                  Mature =~            dsq_undoing 13.915 -0.871  -2.369   -0.596   -0.596
## 75                  Mature =~    dsq_pseudo_altruism 10.414  0.692   1.884    0.623    0.623
## 105      Combined_Immature =~        dsq_suppression  9.452  0.619   1.070    0.276    0.276
## 112      Combined_Immature =~            dsq_undoing  8.267  0.710   1.227    0.309    0.309
## 154        dsq_sublimation ~~    dsq_pseudo_altruism  8.246  2.249   2.249    0.302    0.302
## 104      Combined_Immature =~              dsq_humor  8.221 -0.599  -1.035   -0.246   -0.246
## 147        dsq_suppression ~~        dsq_devaluation  6.224  1.957   1.957    0.241    0.241
## 98                Neurotic =~         dsq_projection  6.171 -0.656  -0.979   -0.259   -0.259
## 218       dsq_idealization ~~         dsq_acting_out  5.929  2.870   2.870    0.207    0.207
## 246            dsq_undoing ~~          dsq_splitting  5.733  2.518   2.518    0.222    0.222
## 205 dsq_reaction_formation ~~         dsq_acting_out  5.392 -2.679  -2.679   -0.199   -0.199
## 206 dsq_reaction_formation ~~         dsq_projection  5.091  2.235   2.235    0.203    0.203
## 174       dsq_anticipation ~~ dsq_passive_aggression  4.813  1.365   1.365    0.217    0.217
## 179       dsq_anticipation ~~       dsq_dissociation  4.780 -1.638  -1.638   -0.209   -0.209
## 200 dsq_reaction_formation ~~            dsq_undoing  4.695  2.695   2.695    0.214    0.214
## 79                  Mature =~ dsq_passive_aggression  4.632  0.225   0.612    0.191    0.191
## 286         dsq_projection ~~          dsq_isolation  4.613  2.587   2.587    0.188    0.188
## 190    dsq_rationalization ~~       dsq_somatization  4.609 -1.609  -1.609   -0.189   -0.189
## 227    dsq_pseudo_altruism ~~       dsq_displacement  4.534 -1.859  -1.859   -0.196   -0.196
## 285         dsq_acting_out ~~             dsq_denial  4.447  2.065   2.065    0.171    0.171
## 110      Combined_Immature =~       dsq_idealization  4.397  0.489   0.846    0.221    0.221
## 223       dsq_idealization ~~          dsq_splitting  4.334  2.093   2.093    0.189    0.189
## 88                Neurotic =~              dsq_humor  4.305 -0.889  -1.328   -0.316   -0.316
## 237            dsq_undoing ~~   dsq_autistic_fantasy  4.286  2.629   2.629    0.185    0.185
## 264       dsq_displacement ~~             dsq_denial  4.219 -1.997  -1.997   -0.166   -0.166
## 166        dsq_sublimation ~~             dsq_denial  4.158 -1.692  -1.692   -0.179   -0.179
## 94                Neurotic =~       dsq_displacement  3.952 -0.593  -0.886   -0.218   -0.218
## 120              dsq_humor ~~            dsq_undoing  3.880 -2.301  -2.301   -0.198   -0.198

4.1.11 Adding correlated errors in Four Factor Solution IV

model_3f_combined_adj_IV <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization +
                       dsq_acting_out + dsq_projection + dsq_isolation + dsq_dissociation + dsq_devaluation +
                       dsq_splitting + dsq_denial
                       
                       dsq_displacement ~~ dsq_acting_out
                       dsq_isolation ~~ dsq_denial
                       dsq_displacement ~~ dsq_projection
                       dsq_reaction_formation ~~ dsq_undoing
'

fit3f_combined_adj_IV <- cfa(model_3f_combined_adj_IV, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_IV,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 138 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        67
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               294.608     283.810
##   Degrees of freedom                               163         163
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.038
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.724       0.720
##   Tucker-Lewis Index (TLI)                       0.678       0.673
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.734
##   Robust Tucker-Lewis Index (TLI)                            0.690
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7763.571   -7763.571
##   Scaling correction factor                                  1.044
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15661.141   15661.141
##   Bayesian (BIC)                             15863.299   15863.299
##   Sample-size adjusted Bayesian (SABIC)      15651.251   15651.251
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.073       0.070
##   90 Percent confidence interval - lower         0.060       0.057
##   90 Percent confidence interval - upper         0.086       0.083
##   P-value H_0: RMSEA <= 0.050                    0.003       0.009
##   P-value H_0: RMSEA >= 0.080                    0.203       0.110
##                                                                   
##   Robust RMSEA                                               0.073
##   90 Percent confidence interval - lower                     0.058
##   90 Percent confidence interval - upper                     0.087
##   P-value H_0: Robust RMSEA <= 0.050                         0.007
##   P-value H_0: Robust RMSEA >= 0.080                         0.214
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.086       0.086
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.750    0.654
##     dsq_suppressin        0.581    0.194    2.997    0.003    1.596    0.411
##     dsq_sublimatin        0.757    0.221    3.420    0.001    2.082    0.563
##     dsq_anticipatn        0.712    0.146    4.882    0.000    1.959    0.643
##     dsq_rationlztn        0.536    0.131    4.093    0.000    1.475    0.496
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.115    0.296
##     dsq_idealizatn        1.483    1.353    1.096    0.273    1.654    0.432
##     dsq_psed_ltrsm        1.421    0.516    2.756    0.006    1.585    0.523
##     dsq_undoing           1.054    0.575    1.832    0.067    1.176    0.296
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.715    0.402
##     dsq_displacmnt        0.695    0.296    2.347    0.019    1.193    0.293
##     dsq_pssv_ggrss        1.021    0.324    3.150    0.002    1.751    0.547
##     dsq_somatizatn        0.709    0.217    3.263    0.001    1.215    0.344
##     dsq_acting_out        0.948    0.357    2.653    0.008    1.625    0.386
##     dsq_projection        1.193    0.334    3.576    0.000    2.047    0.541
##     dsq_isolation         0.817    0.313    2.608    0.009    1.401    0.308
##     dsq_dissociatn        0.905    0.267    3.385    0.001    1.552    0.421
##     dsq_devaluatin        1.291    0.311    4.152    0.000    2.213    0.694
##     dsq_splitting         1.280    0.344    3.725    0.000    2.196    0.577
##     dsq_denial            0.627    0.254    2.468    0.014    1.076    0.328
## 
## Covariances:
##                             Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_displacement ~~                                                            
##    .dsq_acting_out             3.098    1.441    2.150    0.032    3.098    0.205
##  .dsq_isolation ~~                                                               
##    .dsq_denial                 3.213    1.323    2.428    0.015    3.213    0.240
##  .dsq_displacement ~~                                                            
##    .dsq_projection            -2.811    1.183   -2.376    0.017   -2.811   -0.227
##  .dsq_reaction_formation ~~                                                      
##    .dsq_undoing                2.992    1.572    1.903    0.057    2.992    0.219
##   Mature ~~                                                                      
##     Neurotic                   2.262    1.050    2.154    0.031    0.737    0.737
##     Combined_Immtr            -0.041    0.683   -0.060    0.952   -0.009   -0.009
##   Neurotic ~~                                                                    
##     Combined_Immtr             0.735    0.504    1.459    0.145    0.384    0.384
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.306    0.346   26.889    0.000    9.306    2.214
##    .dsq_suppressin    8.566    0.320   26.746    0.000    8.566    2.205
##    .dsq_sublimatin   10.028    0.308   32.594    0.000   10.028    2.712
##    .dsq_anticipatn   10.126    0.252   40.112    0.000   10.126    3.321
##    .dsq_rationlztn    8.848    0.245   36.102    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.883    0.310   31.846    0.000    9.883    2.620
##    .dsq_idealizatn    7.958    0.315   25.299    0.000    7.958    2.078
##    .dsq_psed_ltrsm   12.700    0.254   50.067    0.000   12.700    4.194
##    .dsq_undoing      11.144    0.333   33.454    0.000   11.144    2.805
##    .dsq_tstc_fntsy    9.189    0.352   26.077    0.000    9.189    2.152
##    .dsq_displacmnt    8.151    0.340   23.970    0.000    8.151    2.004
##    .dsq_pssv_ggrss    7.748    0.269   28.818    0.000    7.748    2.420
##    .dsq_somatizatn   11.442    0.289   39.626    0.000   11.442    3.236
##    .dsq_acting_out    9.423    0.349   27.015    0.000    9.423    2.236
##    .dsq_projection    9.359    0.312   29.949    0.000    9.359    2.472
##    .dsq_isolation     8.586    0.377   22.760    0.000    8.586    1.887
##    .dsq_dissociatn    9.584    0.303   31.598    0.000    9.584    2.599
##    .dsq_devaluatin    9.761    0.262   37.281    0.000    9.761    3.063
##    .dsq_splitting     9.718    0.311   31.276    0.000    9.718    2.552
##    .dsq_denial        6.887    0.269   25.568    0.000    6.887    2.102
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.104    2.124    4.756    0.000   10.104    0.572
##    .dsq_suppressin   12.544    1.767    7.099    0.000   12.544    0.831
##    .dsq_sublimatin    9.339    1.644    5.681    0.000    9.339    0.683
##    .dsq_anticipatn    5.459    0.998    5.471    0.000    5.459    0.587
##    .dsq_rationlztn    6.665    0.955    6.982    0.000    6.665    0.754
##    .dsq_rctn_frmtn   12.983    1.897    6.844    0.000   12.983    0.913
##    .dsq_idealizatn   11.932    2.231    5.348    0.000   11.932    0.814
##    .dsq_psed_ltrsm    6.656    2.510    2.652    0.008    6.656    0.726
##    .dsq_undoing      14.398    1.798    8.008    0.000   14.398    0.912
##    .dsq_tstc_fntsy   15.288    1.754    8.716    0.000   15.288    0.839
##    .dsq_displacmnt   15.127    1.598    9.464    0.000   15.127    0.914
##    .dsq_pssv_ggrss    7.187    0.975    7.368    0.000    7.187    0.701
##    .dsq_somatizatn   11.021    1.084   10.170    0.000   11.021    0.882
##    .dsq_acting_out   15.117    1.788    8.457    0.000   15.117    0.851
##    .dsq_projection   10.148    1.280    7.930    0.000   10.148    0.708
##    .dsq_isolation    18.739    1.836   10.206    0.000   18.739    0.905
##    .dsq_dissociatn   11.193    1.503    7.447    0.000   11.193    0.823
##    .dsq_devaluatin    5.259    0.833    6.312    0.000    5.259    0.518
##    .dsq_splitting     9.677    1.666    5.808    0.000    9.677    0.667
##    .dsq_denial        9.583    1.050    9.123    0.000    9.583    0.892
##     Mature            7.563    2.363    3.200    0.001    1.000    1.000
##     Neurotic          1.244    1.470    0.847    0.397    1.000    1.000
##     Combined_Immtr    2.942    1.377    2.136    0.033    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.428
##     dsq_suppressin    0.169
##     dsq_sublimatin    0.317
##     dsq_anticipatn    0.413
##     dsq_rationlztn    0.246
##     dsq_rctn_frmtn    0.087
##     dsq_idealizatn    0.186
##     dsq_psed_ltrsm    0.274
##     dsq_undoing       0.088
##     dsq_tstc_fntsy    0.161
##     dsq_displacmnt    0.086
##     dsq_pssv_ggrss    0.299
##     dsq_somatizatn    0.118
##     dsq_acting_out    0.149
##     dsq_projection    0.292
##     dsq_isolation     0.095
##     dsq_dissociatn    0.177
##     dsq_devaluatin    0.482
##     dsq_splitting     0.333
##     dsq_denial        0.108
modindices(fit3f_combined_adj_IV, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 127              dsq_humor ~~         dsq_projection 17.185 -4.053  -4.053   -0.400   -0.400
## 83                  Mature =~         dsq_projection 14.008 -0.444  -1.222   -0.323   -0.323
## 112      Combined_Immature =~    dsq_pseudo_altruism 13.150 -0.825  -1.414   -0.467   -0.467
## 77                  Mature =~            dsq_undoing 10.989 -0.878  -2.416   -0.608   -0.608
## 99                Neurotic =~         dsq_projection  9.961 -1.114  -1.243   -0.328   -0.328
## 106      Combined_Immature =~        dsq_suppression  9.478  0.625   1.072    0.276    0.276
## 76                  Mature =~    dsq_pseudo_altruism  9.054  0.785   2.158    0.713    0.713
## 113      Combined_Immature =~            dsq_undoing  8.514  0.704   1.208    0.304    0.304
## 105      Combined_Immature =~              dsq_humor  8.054 -0.597  -1.023   -0.243   -0.243
## 246            dsq_undoing ~~          dsq_splitting  7.913  2.925   2.925    0.248    0.248
## 155        dsq_sublimation ~~    dsq_pseudo_altruism  7.084  2.137   2.137    0.271    0.271
## 148        dsq_suppression ~~        dsq_devaluation  6.210  1.953   1.953    0.240    0.240
## 89                Neurotic =~              dsq_humor  6.124 -1.703  -1.900   -0.452   -0.452
## 175       dsq_anticipation ~~ dsq_passive_aggression  4.819  1.360   1.360    0.217    0.217
## 286         dsq_projection ~~          dsq_isolation  4.791  2.637   2.637    0.191    0.191
## 210 dsq_reaction_formation ~~          dsq_splitting  4.775 -2.126  -2.126   -0.190   -0.190
## 90                Neurotic =~        dsq_suppression  4.764  1.426   1.590    0.409    0.409
## 227    dsq_pseudo_altruism ~~       dsq_displacement  4.683 -1.920  -1.920   -0.191   -0.191
## 218       dsq_idealization ~~         dsq_acting_out  4.640  2.495   2.495    0.186    0.186
## 80                  Mature =~ dsq_passive_aggression  4.582  0.221   0.606    0.189    0.189
## 180       dsq_anticipation ~~       dsq_dissociation  4.517 -1.588  -1.588   -0.203   -0.203
## 206 dsq_reaction_formation ~~         dsq_projection  4.485  2.075   2.075    0.181    0.181
## 185    dsq_rationalization ~~       dsq_idealization  4.364 -1.736  -1.736   -0.195   -0.195
## 285         dsq_acting_out ~~             dsq_denial  4.315  2.030   2.030    0.169    0.169
## 167        dsq_sublimation ~~             dsq_denial  4.289 -1.715  -1.715   -0.181   -0.181
## 191    dsq_rationalization ~~       dsq_somatization  4.273 -1.555  -1.555   -0.181   -0.181
## 264       dsq_displacement ~~             dsq_denial  4.221 -1.997  -1.997   -0.166   -0.166
## 240            dsq_undoing ~~       dsq_somatization  3.843  2.073   2.073    0.165    0.165

4.1.12 Removing weakest loading defense (displacement) com. 3 factor solution V

model_3f_combined_adj_V <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_passive_aggression + dsq_somatization +
                       dsq_acting_out + dsq_projection + dsq_isolation + dsq_dissociation + dsq_devaluation +
                       dsq_splitting + dsq_denial
'

fit3f_combined_adj_V <- cfa(model_3f_combined_adj_V, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_V,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 115 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        60
## 
##   Number of observations                           151
##   Number of missing patterns                        17
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               279.772     268.317
##   Degrees of freedom                               149         149
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.043
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               615.607     573.004
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.074
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.706       0.703
##   Tucker-Lewis Index (TLI)                       0.662       0.659
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.715
##   Robust Tucker-Lewis Index (TLI)                            0.673
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7377.131   -7377.131
##   Scaling correction factor                                  1.033
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7237.245   -7237.245
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               14874.262   14874.262
##   Bayesian (BIC)                             15055.299   15055.299
##   Sample-size adjusted Bayesian (SABIC)      14865.405   14865.405
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.076       0.073
##   90 Percent confidence interval - lower         0.062       0.059
##   90 Percent confidence interval - upper         0.090       0.086
##   P-value H_0: RMSEA <= 0.050                    0.001       0.004
##   P-value H_0: RMSEA >= 0.080                    0.336       0.199
##                                                                   
##   Robust RMSEA                                               0.076
##   90 Percent confidence interval - lower                     0.061
##   90 Percent confidence interval - upper                     0.091
##   P-value H_0: Robust RMSEA <= 0.050                         0.003
##   P-value H_0: Robust RMSEA >= 0.080                         0.346
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.089       0.089
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.716    0.646
##     dsq_suppressin        0.593    0.195    3.041    0.002    1.611    0.415
##     dsq_sublimatin        0.767    0.216    3.560    0.000    2.084    0.563
##     dsq_anticipatn        0.719    0.149    4.841    0.000    1.952    0.640
##     dsq_rationlztn        0.554    0.127    4.351    0.000    1.505    0.506
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.497    0.397
##     dsq_idealizatn        0.953    0.751    1.269    0.204    1.427    0.373
##     dsq_psed_ltrsm        1.186    0.473    2.509    0.012    1.776    0.587
##     dsq_undoing           1.062    0.352    3.015    0.003    1.589    0.400
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.720    0.403
##     dsq_pssv_ggrss        1.001    0.324    3.090    0.002    1.721    0.537
##     dsq_somatizatn        0.716    0.225    3.182    0.001    1.231    0.348
##     dsq_acting_out        0.933    0.350    2.664    0.008    1.605    0.381
##     dsq_projection        1.190    0.332    3.581    0.000    2.046    0.540
##     dsq_isolation         0.918    0.347    2.649    0.008    1.580    0.347
##     dsq_dissociatn        0.929    0.281    3.312    0.001    1.598    0.433
##     dsq_devaluatin        1.266    0.298    4.253    0.000    2.178    0.683
##     dsq_splitting         1.248    0.329    3.792    0.000    2.146    0.564
##     dsq_denial            0.713    0.279    2.553    0.011    1.226    0.374
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.505    0.776    3.230    0.001    0.616    0.616
##     Combined_Immtr    0.045    0.674    0.067    0.947    0.010    0.010
##   Neurotic ~~                                                           
##     Combined_Immtr    0.931    0.675    1.379    0.168    0.361    0.361
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.307    0.346   26.921    0.000    9.307    2.215
##    .dsq_suppressin    8.568    0.320   26.766    0.000    8.568    2.206
##    .dsq_sublimatin   10.028    0.308   32.596    0.000   10.028    2.712
##    .dsq_anticipatn   10.125    0.252   40.113    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.101    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.884    0.310   31.870    0.000    9.884    2.621
##    .dsq_idealizatn    7.965    0.314   25.331    0.000    7.965    2.081
##    .dsq_psed_ltrsm   12.698    0.253   50.111    0.000   12.698    4.195
##    .dsq_undoing      11.140    0.332   33.510    0.000   11.140    2.803
##    .dsq_tstc_fntsy    9.191    0.352   26.081    0.000    9.191    2.153
##    .dsq_pssv_ggrss    7.752    0.269   28.819    0.000    7.752    2.420
##    .dsq_somatizatn   11.442    0.289   39.629    0.000   11.442    3.236
##    .dsq_acting_out    9.441    0.348   27.143    0.000    9.441    2.240
##    .dsq_projection    9.352    0.313   29.924    0.000    9.352    2.470
##    .dsq_isolation     8.588    0.378   22.739    0.000    8.588    1.886
##    .dsq_dissociatn    9.583    0.303   31.592    0.000    9.583    2.598
##    .dsq_devaluatin    9.764    0.262   37.279    0.000    9.764    3.064
##    .dsq_splitting     9.718    0.311   31.277    0.000    9.718    2.552
##    .dsq_denial        6.886    0.269   25.556    0.000    6.886    2.100
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.282    2.085    4.931    0.000   10.282    0.582
##    .dsq_suppressin   12.495    1.778    7.028    0.000   12.495    0.828
##    .dsq_sublimatin    9.333    1.599    5.836    0.000    9.333    0.683
##    .dsq_anticipatn    5.483    0.973    5.634    0.000    5.483    0.590
##    .dsq_rationlztn    6.574    0.929    7.074    0.000    6.574    0.744
##    .dsq_rctn_frmtn   11.980    1.980    6.051    0.000   11.980    0.842
##    .dsq_idealizatn   12.619    2.131    5.922    0.000   12.619    0.861
##    .dsq_psed_ltrsm    6.007    2.035    2.953    0.003    6.007    0.656
##    .dsq_undoing      13.273    2.056    6.456    0.000   13.273    0.840
##    .dsq_tstc_fntsy   15.270    1.746    8.745    0.000   15.270    0.838
##    .dsq_pssv_ggrss    7.295    0.982    7.430    0.000    7.295    0.711
##    .dsq_somatizatn   10.983    1.058   10.384    0.000   10.983    0.879
##    .dsq_acting_out   15.194    1.759    8.639    0.000   15.194    0.855
##    .dsq_projection   10.152    1.245    8.155    0.000   10.152    0.708
##    .dsq_isolation    18.232    1.859    9.807    0.000   18.232    0.880
##    .dsq_dissociatn   11.050    1.491    7.408    0.000   11.050    0.812
##    .dsq_devaluatin    5.413    0.814    6.647    0.000    5.413    0.533
##    .dsq_splitting     9.894    1.673    5.914    0.000    9.894    0.682
##    .dsq_denial        9.246    1.039    8.894    0.000    9.246    0.860
##     Mature            7.375    2.297    3.211    0.001    1.000    1.000
##     Neurotic          2.242    1.686    1.330    0.184    1.000    1.000
##     Combined_Immtr    2.958    1.397    2.117    0.034    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.418
##     dsq_suppressin    0.172
##     dsq_sublimatin    0.317
##     dsq_anticipatn    0.410
##     dsq_rationlztn    0.256
##     dsq_rctn_frmtn    0.158
##     dsq_idealizatn    0.139
##     dsq_psed_ltrsm    0.344
##     dsq_undoing       0.160
##     dsq_tstc_fntsy    0.162
##     dsq_pssv_ggrss    0.289
##     dsq_somatizatn    0.121
##     dsq_acting_out    0.145
##     dsq_projection    0.292
##     dsq_isolation     0.120
##     dsq_dissociatn    0.188
##     dsq_devaluatin    0.467
##     dsq_splitting     0.318
##     dsq_denial        0.140
modindices(fit3f_combined_adj_V, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 117              dsq_humor ~~         dsq_projection 15.612 -3.948  -3.948   -0.386   -0.386
## 103      Combined_Immature =~    dsq_pseudo_altruism 15.001 -0.849  -1.461   -0.483   -0.483
## 70                  Mature =~            dsq_undoing 13.408 -0.856  -2.324   -0.585   -0.585
## 75                  Mature =~         dsq_projection 13.353 -0.447  -1.215   -0.321   -0.321
## 69                  Mature =~    dsq_pseudo_altruism 10.358  0.685   1.860    0.615    0.615
## 97       Combined_Immature =~        dsq_suppression  9.988  0.642   1.105    0.284    0.284
## 144        dsq_sublimation ~~    dsq_pseudo_altruism  8.389  2.269   2.269    0.303    0.303
## 96       Combined_Immature =~              dsq_humor  7.624 -0.582  -1.001   -0.238   -0.238
## 104      Combined_Immature =~            dsq_undoing  7.262  0.682   1.174    0.295    0.295
## 269          dsq_isolation ~~             dsq_denial  7.236  3.064   3.064    0.236    0.236
## 191 dsq_reaction_formation ~~         dsq_acting_out  7.063 -3.162  -3.162   -0.234   -0.234
## 229            dsq_undoing ~~          dsq_splitting  6.248  2.651   2.651    0.231    0.231
## 192 dsq_reaction_formation ~~         dsq_projection  5.920  2.447   2.447    0.222    0.222
## 137        dsq_suppression ~~        dsq_devaluation  5.887  1.920   1.920    0.233    0.233
## 203       dsq_idealization ~~         dsq_acting_out  5.763  2.915   2.915    0.211    0.211
## 216    dsq_pseudo_altruism ~~          dsq_isolation  5.348 -2.310  -2.310   -0.221   -0.221
## 162       dsq_anticipation ~~ dsq_passive_aggression  4.914  1.387   1.387    0.219    0.219
## 177    dsq_rationalization ~~       dsq_somatization  4.851 -1.651  -1.651   -0.194   -0.194
## 90                Neurotic =~         dsq_projection  4.792 -0.592  -0.886   -0.234   -0.234
## 187 dsq_reaction_formation ~~            dsq_undoing  4.727  2.699   2.699    0.214    0.214
## 167       dsq_anticipation ~~       dsq_dissociation  4.588 -1.601  -1.601   -0.206   -0.206
## 221            dsq_undoing ~~   dsq_autistic_fantasy  4.535  2.710   2.710    0.190    0.190
## 102      Combined_Immature =~       dsq_idealization  4.487  0.508   0.874    0.228    0.228
## 272       dsq_dissociation ~~             dsq_denial  4.282  1.857   1.857    0.184    0.184
## 208       dsq_idealization ~~          dsq_splitting  4.232  2.081   2.081    0.186    0.186
## 254       dsq_somatization ~~             dsq_denial  4.213 -1.791  -1.791   -0.178   -0.178
## 81                Neurotic =~              dsq_humor  4.186 -0.875  -1.310   -0.312   -0.312
## 72                  Mature =~ dsq_passive_aggression  4.165  0.215   0.585    0.183    0.183
## 112              dsq_humor ~~            dsq_undoing  3.921 -2.315  -2.315   -0.198   -0.198

4.1.13 Removing weakest loading defense (somatization) com. 3 factor solution VI

model_3f_combined_adj_VI <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_passive_aggression +
                       dsq_acting_out + dsq_projection + dsq_isolation + dsq_dissociation + dsq_devaluation +
                       dsq_splitting + dsq_denial
'

fit3f_combined_adj_VI <- cfa(model_3f_combined_adj_VI, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_VI,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 113 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        57
## 
##   Number of observations                           151
##   Number of missing patterns                        17
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               256.577     245.258
##   Degrees of freedom                               132         132
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.046
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               578.118     534.354
##   Degrees of freedom                               153         153
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.082
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.707       0.703
##   Tucker-Lewis Index (TLI)                       0.660       0.656
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.715
##   Robust Tucker-Lewis Index (TLI)                            0.670
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -6982.004   -6982.004
##   Scaling correction factor                                  1.042
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -6853.716   -6853.716
##   Scaling correction factor                                  1.045
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               14078.009   14078.009
##   Bayesian (BIC)                             14249.994   14249.994
##   Sample-size adjusted Bayesian (SABIC)      14069.595   14069.595
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.079       0.075
##   90 Percent confidence interval - lower         0.065       0.061
##   90 Percent confidence interval - upper         0.093       0.090
##   P-value H_0: RMSEA <= 0.050                    0.001       0.003
##   P-value H_0: RMSEA >= 0.080                    0.470       0.307
##                                                                   
##   Robust RMSEA                                               0.079
##   90 Percent confidence interval - lower                     0.063
##   90 Percent confidence interval - upper                     0.095
##   P-value H_0: Robust RMSEA <= 0.050                         0.002
##   P-value H_0: Robust RMSEA >= 0.080                         0.482
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.090       0.090
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.717    0.647
##     dsq_suppressin        0.593    0.195    3.039    0.002    1.610    0.415
##     dsq_sublimatin        0.767    0.218    3.524    0.000    2.085    0.564
##     dsq_anticipatn        0.719    0.148    4.846    0.000    1.955    0.641
##     dsq_rationlztn        0.552    0.130    4.253    0.000    1.501    0.505
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.487    0.394
##     dsq_idealizatn        0.976    0.835    1.168    0.243    1.451    0.379
##     dsq_psed_ltrsm        1.195    0.473    2.529    0.011    1.776    0.587
##     dsq_undoing           1.043    0.344    3.034    0.002    1.551    0.390
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.698    0.398
##     dsq_pssv_ggrss        1.021    0.336    3.039    0.002    1.734    0.542
##     dsq_acting_out        0.942    0.362    2.604    0.009    1.599    0.379
##     dsq_projection        1.200    0.346    3.467    0.001    2.037    0.538
##     dsq_isolation         0.920    0.350    2.630    0.009    1.562    0.343
##     dsq_dissociatn        0.917    0.285    3.219    0.001    1.558    0.422
##     dsq_devaluatin        1.292    0.311    4.149    0.000    2.193    0.688
##     dsq_splitting         1.257    0.336    3.734    0.000    2.133    0.560
##     dsq_denial            0.759    0.288    2.631    0.009    1.289    0.393
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.512    0.780    3.220    0.001    0.622    0.622
##     Combined_Immtr    0.016    0.667    0.024    0.981    0.003    0.003
##   Neurotic ~~                                                           
##     Combined_Immtr    0.885    0.676    1.308    0.191    0.351    0.351
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.307    0.346   26.915    0.000    9.307    2.215
##    .dsq_suppressin    8.568    0.320   26.766    0.000    8.568    2.206
##    .dsq_sublimatin   10.029    0.308   32.597    0.000   10.029    2.712
##    .dsq_anticipatn   10.125    0.252   40.114    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.102    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.884    0.310   31.877    0.000    9.884    2.621
##    .dsq_idealizatn    7.964    0.314   25.327    0.000    7.964    2.080
##    .dsq_psed_ltrsm   12.698    0.254   50.088    0.000   12.698    4.195
##    .dsq_undoing      11.140    0.333   33.492    0.000   11.140    2.803
##    .dsq_tstc_fntsy    9.187    0.353   26.053    0.000    9.187    2.151
##    .dsq_pssv_ggrss    7.747    0.269   28.849    0.000    7.747    2.420
##    .dsq_acting_out    9.438    0.348   27.149    0.000    9.438    2.239
##    .dsq_projection    9.347    0.313   29.904    0.000    9.347    2.469
##    .dsq_isolation     8.587    0.378   22.739    0.000    8.587    1.886
##    .dsq_dissociatn    9.581    0.304   31.544    0.000    9.581    2.597
##    .dsq_devaluatin    9.763    0.262   37.267    0.000    9.763    3.063
##    .dsq_splitting     9.718    0.311   31.284    0.000    9.718    2.552
##    .dsq_denial        6.885    0.269   25.558    0.000    6.885    2.100
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.277    2.102    4.890    0.000   10.277    0.582
##    .dsq_suppressin   12.496    1.779    7.022    0.000   12.496    0.828
##    .dsq_sublimatin    9.328    1.607    5.805    0.000    9.328    0.682
##    .dsq_anticipatn    5.475    0.984    5.563    0.000    5.475    0.589
##    .dsq_rationlztn    6.588    0.940    7.007    0.000    6.588    0.745
##    .dsq_rctn_frmtn   12.009    2.036    5.898    0.000   12.009    0.845
##    .dsq_idealizatn   12.551    2.337    5.371    0.000   12.551    0.856
##    .dsq_psed_ltrsm    6.005    2.224    2.700    0.007    6.005    0.656
##    .dsq_undoing      13.394    2.062    6.494    0.000   13.394    0.848
##    .dsq_tstc_fntsy   15.351    1.745    8.798    0.000   15.351    0.842
##    .dsq_pssv_ggrss    7.242    0.974    7.438    0.000    7.242    0.707
##    .dsq_acting_out   15.209    1.756    8.662    0.000   15.209    0.856
##    .dsq_projection   10.185    1.273    8.003    0.000   10.185    0.710
##    .dsq_isolation    18.284    1.833    9.973    0.000   18.284    0.882
##    .dsq_dissociatn   11.181    1.493    7.489    0.000   11.181    0.822
##    .dsq_devaluatin    5.347    0.826    6.471    0.000    5.347    0.526
##    .dsq_splitting     9.948    1.626    6.117    0.000    9.948    0.686
##    .dsq_denial        9.090    1.026    8.862    0.000    9.090    0.846
##     Mature            7.381    2.315    3.188    0.001    1.000    1.000
##     Neurotic          2.210    1.756    1.259    0.208    1.000    1.000
##     Combined_Immtr    2.883    1.396    2.065    0.039    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.418
##     dsq_suppressin    0.172
##     dsq_sublimatin    0.318
##     dsq_anticipatn    0.411
##     dsq_rationlztn    0.255
##     dsq_rctn_frmtn    0.155
##     dsq_idealizatn    0.144
##     dsq_psed_ltrsm    0.344
##     dsq_undoing       0.152
##     dsq_tstc_fntsy    0.158
##     dsq_pssv_ggrss    0.293
##     dsq_acting_out    0.144
##     dsq_projection    0.290
##     dsq_isolation     0.118
##     dsq_dissociatn    0.178
##     dsq_devaluatin    0.474
##     dsq_splitting     0.314
##     dsq_denial        0.154
modindices(fit3f_combined_adj_VI, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 111              dsq_humor ~~         dsq_projection 15.983 -4.005  -4.005   -0.391   -0.391
## 98       Combined_Immature =~    dsq_pseudo_altruism 15.211 -0.865  -1.469   -0.485   -0.485
## 71                  Mature =~         dsq_projection 12.913 -0.441  -1.198   -0.316   -0.316
## 67                  Mature =~            dsq_undoing 12.706 -0.841  -2.285   -0.575   -0.575
## 66                  Mature =~    dsq_pseudo_altruism 10.176  0.693   1.883    0.622    0.622
## 92       Combined_Immature =~        dsq_suppression  9.484  0.637   1.081    0.278    0.278
## 137        dsq_sublimation ~~    dsq_pseudo_altruism  8.379  2.270   2.270    0.303    0.303
## 91       Combined_Immature =~              dsq_humor  7.204 -0.576  -0.978   -0.233   -0.233
## 180 dsq_reaction_formation ~~         dsq_acting_out  7.104 -3.177  -3.177   -0.235   -0.235
## 246          dsq_isolation ~~             dsq_denial  6.988  3.007   3.007    0.233    0.233
## 215            dsq_undoing ~~          dsq_splitting  6.985  2.819   2.819    0.244    0.244
## 130        dsq_suppression ~~        dsq_devaluation  6.427  2.009   2.009    0.246    0.246
## 99       Combined_Immature =~            dsq_undoing  6.158  0.633   1.075    0.270    0.270
## 181 dsq_reaction_formation ~~         dsq_projection  5.863  2.443   2.443    0.221    0.221
## 97       Combined_Immature =~       dsq_idealization  5.427  0.565   0.960    0.251    0.251
## 154       dsq_anticipation ~~ dsq_passive_aggression  5.424  1.456   1.456    0.231    0.231
## 191       dsq_idealization ~~         dsq_acting_out  5.419  2.827   2.827    0.205    0.205
## 203    dsq_pseudo_altruism ~~          dsq_isolation  5.241 -2.291  -2.291   -0.219   -0.219
## 208            dsq_undoing ~~   dsq_autistic_fantasy  4.991  2.858   2.858    0.199    0.199
## 177 dsq_reaction_formation ~~            dsq_undoing  4.945  2.757   2.757    0.217    0.217
## 85                Neurotic =~         dsq_projection  4.488 -0.575  -0.855   -0.226   -0.226
## 69                  Mature =~ dsq_passive_aggression  4.389  0.221   0.601    0.188    0.188
## 158       dsq_anticipation ~~       dsq_dissociation  4.296 -1.556  -1.556   -0.199   -0.199
## 249       dsq_dissociation ~~             dsq_denial  4.089  1.819   1.819    0.180    0.180
## 77                Neurotic =~              dsq_humor  4.002 -0.873  -1.298   -0.309   -0.309
## 107              dsq_humor ~~            dsq_undoing  3.970 -2.333  -2.333   -0.199   -0.199
## 196       dsq_idealization ~~          dsq_splitting  3.844  1.989   1.989    0.178    0.178

4.1.14 Removing weakest loading defense (isolation) com. 3 factor solution VII

model_3f_combined_adj_VII <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_passive_aggression +
                       dsq_acting_out + dsq_projection + dsq_dissociation + dsq_devaluation +
                       dsq_splitting + dsq_denial
'

fit3f_combined_adj_VII <- cfa(model_3f_combined_adj_VII, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_VII,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 115 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        54
## 
##   Number of observations                           151
##   Number of missing patterns                        17
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               221.355     214.641
##   Degrees of freedom                               116         116
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.031
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               529.913     491.040
##   Degrees of freedom                               136         136
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.079
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.733       0.722
##   Tucker-Lewis Index (TLI)                       0.686       0.674
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.740
##   Robust Tucker-Lewis Index (TLI)                            0.695
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -6562.933   -6562.933
##   Scaling correction factor                                  1.067
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -6452.255   -6452.255
##   Scaling correction factor                                  1.043
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               13233.866   13233.866
##   Bayesian (BIC)                             13396.799   13396.799
##   Sample-size adjusted Bayesian (SABIC)      13225.895   13225.895
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.078       0.075
##   90 Percent confidence interval - lower         0.062       0.059
##   90 Percent confidence interval - upper         0.093       0.090
##   P-value H_0: RMSEA <= 0.050                    0.003       0.005
##   P-value H_0: RMSEA >= 0.080                    0.410       0.309
##                                                                   
##   Robust RMSEA                                               0.078
##   90 Percent confidence interval - lower                     0.061
##   90 Percent confidence interval - upper                     0.094
##   P-value H_0: Robust RMSEA <= 0.050                         0.005
##   P-value H_0: Robust RMSEA >= 0.080                         0.427
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.088       0.088
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.729    0.649
##     dsq_suppressin        0.586    0.193    3.042    0.002    1.600    0.412
##     dsq_sublimatin        0.761    0.215    3.547    0.000    2.078    0.562
##     dsq_anticipatn        0.719    0.148    4.845    0.000    1.963    0.644
##     dsq_rationlztn        0.547    0.130    4.199    0.000    1.492    0.502
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.429    0.379
##     dsq_idealizatn        1.076    1.080    0.997    0.319    1.538    0.402
##     dsq_psed_ltrsm        1.204    0.450    2.677    0.007    1.721    0.569
##     dsq_undoing           1.067    0.370    2.881    0.004    1.525    0.384
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.706    0.400
##     dsq_pssv_ggrss        1.009    0.339    2.976    0.003    1.721    0.538
##     dsq_acting_out        0.974    0.378    2.574    0.010    1.662    0.394
##     dsq_projection        1.157    0.341    3.398    0.001    1.975    0.522
##     dsq_dissociatn        0.868    0.269    3.232    0.001    1.482    0.402
##     dsq_devaluatin        1.309    0.329    3.973    0.000    2.233    0.700
##     dsq_splitting         1.285    0.355    3.614    0.000    2.192    0.576
##     dsq_denial            0.700    0.272    2.574    0.010    1.194    0.364
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.461    0.872    2.823    0.005    0.631    0.631
##     Combined_Immtr   -0.032    0.672   -0.048    0.962   -0.007   -0.007
##   Neurotic ~~                                                           
##     Combined_Immtr    0.968    0.605    1.601    0.109    0.397    0.397
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.308    0.346   26.913    0.000    9.308    2.215
##    .dsq_suppressin    8.568    0.320   26.763    0.000    8.568    2.206
##    .dsq_sublimatin   10.029    0.308   32.600    0.000   10.029    2.712
##    .dsq_anticipatn   10.125    0.252   40.114    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.103    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.885    0.310   31.868    0.000    9.885    2.622
##    .dsq_idealizatn    7.963    0.314   25.325    0.000    7.963    2.080
##    .dsq_psed_ltrsm   12.699    0.253   50.096    0.000   12.699    4.196
##    .dsq_undoing      11.140    0.333   33.475    0.000   11.140    2.803
##    .dsq_tstc_fntsy    9.184    0.352   26.056    0.000    9.184    2.151
##    .dsq_pssv_ggrss    7.741    0.268   28.855    0.000    7.741    2.419
##    .dsq_acting_out    9.436    0.347   27.160    0.000    9.436    2.239
##    .dsq_projection    9.345    0.313   29.900    0.000    9.345    2.468
##    .dsq_dissociatn    9.583    0.304   31.548    0.000    9.583    2.598
##    .dsq_devaluatin    9.762    0.262   37.240    0.000    9.762    3.062
##    .dsq_splitting     9.719    0.311   31.285    0.000    9.719    2.552
##    .dsq_denial        6.884    0.269   25.560    0.000    6.884    2.100
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.211    2.101    4.859    0.000   10.211    0.578
##    .dsq_suppressin   12.531    1.775    7.061    0.000   12.531    0.830
##    .dsq_sublimatin    9.359    1.595    5.867    0.000    9.359    0.684
##    .dsq_anticipatn    5.443    0.981    5.549    0.000    5.443    0.585
##    .dsq_rationlztn    6.615    0.952    6.947    0.000    6.615    0.748
##    .dsq_rctn_frmtn   12.170    2.281    5.337    0.000   12.170    0.856
##    .dsq_idealizatn   12.290    2.644    4.648    0.000   12.290    0.839
##    .dsq_psed_ltrsm    6.199    2.328    2.662    0.008    6.199    0.677
##    .dsq_undoing      13.472    2.244    6.004    0.000   13.472    0.853
##    .dsq_tstc_fntsy   15.326    1.767    8.675    0.000   15.326    0.840
##    .dsq_pssv_ggrss    7.281    1.008    7.227    0.000    7.281    0.711
##    .dsq_acting_out   15.002    1.781    8.424    0.000   15.002    0.845
##    .dsq_projection   10.437    1.343    7.773    0.000   10.437    0.728
##    .dsq_dissociatn   11.414    1.477    7.729    0.000   11.414    0.839
##    .dsq_devaluatin    5.177    0.946    5.474    0.000    5.177    0.509
##    .dsq_splitting     9.694    1.592    6.089    0.000    9.694    0.669
##    .dsq_denial        9.322    1.032    9.035    0.000    9.322    0.867
##     Mature            7.450    2.326    3.203    0.001    1.000    1.000
##     Neurotic          2.042    2.045    0.998    0.318    1.000    1.000
##     Combined_Immtr    2.911    1.431    2.035    0.042    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.422
##     dsq_suppressin    0.170
##     dsq_sublimatin    0.316
##     dsq_anticipatn    0.415
##     dsq_rationlztn    0.252
##     dsq_rctn_frmtn    0.144
##     dsq_idealizatn    0.161
##     dsq_psed_ltrsm    0.323
##     dsq_undoing       0.147
##     dsq_tstc_fntsy    0.160
##     dsq_pssv_ggrss    0.289
##     dsq_acting_out    0.155
##     dsq_projection    0.272
##     dsq_dissociatn    0.161
##     dsq_devaluatin    0.491
##     dsq_splitting     0.331
##     dsq_denial        0.133
modindices(fit3f_combined_adj_VII, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 106              dsq_humor ~~         dsq_projection 16.190 -4.059  -4.059   -0.393   -0.393
## 93       Combined_Immature =~    dsq_pseudo_altruism 14.203 -0.852  -1.454   -0.480   -0.480
## 64                  Mature =~            dsq_undoing 12.180 -0.810  -2.212   -0.556   -0.556
## 68                  Mature =~         dsq_projection 12.158 -0.429  -1.171   -0.309   -0.309
## 63                  Mature =~    dsq_pseudo_altruism  9.955  0.653   1.782    0.589    0.589
## 87       Combined_Immature =~        dsq_suppression  8.838  0.614   1.048    0.270    0.270
## 130        dsq_sublimation ~~    dsq_pseudo_altruism  8.283  2.262   2.262    0.297    0.297
## 123        dsq_suppression ~~        dsq_devaluation  7.458  2.160   2.160    0.268    0.268
## 170 dsq_reaction_formation ~~         dsq_acting_out  7.246 -3.205  -3.205   -0.237   -0.237
## 201            dsq_undoing ~~          dsq_splitting  6.601  2.732   2.732    0.239    0.239
## 86       Combined_Immature =~              dsq_humor  6.498 -0.546  -0.931   -0.222   -0.222
## 94       Combined_Immature =~            dsq_undoing  5.839  0.636   1.085    0.273    0.273
## 171 dsq_reaction_formation ~~         dsq_projection  5.748  2.448   2.448    0.217    0.217
## 146       dsq_anticipation ~~ dsq_passive_aggression  5.577  1.478   1.478    0.235    0.235
## 167 dsq_reaction_formation ~~            dsq_undoing  5.260  2.823   2.823    0.220    0.220
## 92       Combined_Immature =~       dsq_idealization  5.117  0.570   0.973    0.254    0.254
## 81                Neurotic =~         dsq_projection  5.107 -0.659  -0.941   -0.249   -0.249
## 227       dsq_dissociation ~~             dsq_denial  5.046  2.048   2.048    0.199    0.199
## 180       dsq_idealization ~~         dsq_acting_out  4.900  2.663   2.663    0.196    0.196
## 195            dsq_undoing ~~   dsq_autistic_fantasy  4.884  2.831   2.831    0.197    0.197
## 66                  Mature =~ dsq_passive_aggression  4.483  0.223   0.609    0.190    0.190
## 73                Neurotic =~              dsq_humor  4.201 -0.918  -1.311   -0.312   -0.312
## 149       dsq_anticipation ~~       dsq_dissociation  4.164 -1.541  -1.541   -0.195   -0.195
## 102              dsq_humor ~~            dsq_undoing  3.995 -2.342  -2.342   -0.200   -0.200

4.1.15 Removing weakest loading defense (denial) com. 3 factor solution VIII

model_3f_combined_adj_VIII <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_passive_aggression +
                       dsq_acting_out + dsq_projection + dsq_dissociation + dsq_devaluation +
                       dsq_splitting
'

fit3f_combined_adj_VIII <- cfa(model_3f_combined_adj_VIII, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_VIII,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 113 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        51
## 
##   Number of observations                           151
##   Number of missing patterns                        17
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               198.749     190.891
##   Degrees of freedom                               101         101
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.041
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               492.475     451.360
##   Degrees of freedom                               120         120
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.091
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.738       0.729
##   Tucker-Lewis Index (TLI)                       0.688       0.678
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.747
##   Robust Tucker-Lewis Index (TLI)                            0.699
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -6184.694   -6184.694
##   Scaling correction factor                                  1.067
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -6085.319   -6085.319
##   Scaling correction factor                                  1.050
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               12471.387   12471.387
##   Bayesian (BIC)                             12625.268   12625.268
##   Sample-size adjusted Bayesian (SABIC)      12463.859   12463.859
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.080       0.077
##   90 Percent confidence interval - lower         0.064       0.060
##   90 Percent confidence interval - upper         0.096       0.093
##   P-value H_0: RMSEA <= 0.050                    0.002       0.005
##   P-value H_0: RMSEA >= 0.080                    0.517       0.385
##                                                                   
##   Robust RMSEA                                               0.080
##   90 Percent confidence interval - lower                     0.062
##   90 Percent confidence interval - upper                     0.098
##   P-value H_0: Robust RMSEA <= 0.050                         0.005
##   P-value H_0: Robust RMSEA >= 0.080                         0.515
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.089       0.089
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.740    0.652
##     dsq_suppressin        0.580    0.192    3.021    0.003    1.588    0.409
##     dsq_sublimatin        0.756    0.214    3.534    0.000    2.071    0.560
##     dsq_anticipatn        0.718    0.149    4.819    0.000    1.967    0.645
##     dsq_rationlztn        0.544    0.128    4.237    0.000    1.492    0.502
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.439    0.382
##     dsq_idealizatn        1.053    0.966    1.090    0.276    1.515    0.396
##     dsq_psed_ltrsm        1.206    0.450    2.683    0.007    1.735    0.573
##     dsq_undoing           1.071    0.363    2.949    0.003    1.541    0.388
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.771    0.415
##     dsq_pssv_ggrss        0.949    0.311    3.054    0.002    1.680    0.525
##     dsq_acting_out        0.901    0.357    2.522    0.012    1.595    0.379
##     dsq_projection        1.142    0.334    3.422    0.001    2.022    0.534
##     dsq_dissociatn        0.787    0.244    3.228    0.001    1.393    0.378
##     dsq_devaluatin        1.285    0.332    3.868    0.000    2.276    0.714
##     dsq_splitting         1.228    0.328    3.744    0.000    2.175    0.571
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.468    0.841    2.935    0.003    0.626    0.626
##     Combined_Immtr   -0.133    0.725   -0.183    0.855   -0.027   -0.027
##   Neurotic ~~                                                           
##     Combined_Immtr    1.016    0.614    1.656    0.098    0.399    0.399
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.308    0.346   26.917    0.000    9.308    2.215
##    .dsq_suppressin    8.568    0.320   26.764    0.000    8.568    2.206
##    .dsq_sublimatin   10.029    0.308   32.596    0.000   10.029    2.712
##    .dsq_anticipatn   10.125    0.252   40.111    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.099    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.886    0.310   31.864    0.000    9.886    2.622
##    .dsq_idealizatn    7.964    0.314   25.335    0.000    7.964    2.081
##    .dsq_psed_ltrsm   12.699    0.253   50.151    0.000   12.699    4.196
##    .dsq_undoing      11.140    0.333   33.487    0.000   11.140    2.803
##    .dsq_tstc_fntsy    9.185    0.352   26.068    0.000    9.185    2.151
##    .dsq_pssv_ggrss    7.738    0.269   28.813    0.000    7.738    2.415
##    .dsq_acting_out    9.437    0.348   27.153    0.000    9.437    2.239
##    .dsq_projection    9.347    0.312   29.915    0.000    9.347    2.469
##    .dsq_dissociatn    9.584    0.304   31.552    0.000    9.584    2.598
##    .dsq_devaluatin    9.763    0.262   37.232    0.000    9.763    3.061
##    .dsq_splitting     9.719    0.311   31.280    0.000    9.719    2.553
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.152    2.110    4.812    0.000   10.152    0.575
##    .dsq_suppressin   12.567    1.775    7.081    0.000   12.567    0.833
##    .dsq_sublimatin    9.392    1.596    5.883    0.000    9.392    0.687
##    .dsq_anticipatn    5.428    0.968    5.605    0.000    5.428    0.584
##    .dsq_rationlztn    6.616    0.944    7.007    0.000    6.616    0.748
##    .dsq_rctn_frmtn   12.144    2.171    5.594    0.000   12.144    0.854
##    .dsq_idealizatn   12.360    2.390    5.171    0.000   12.360    0.843
##    .dsq_psed_ltrsm    6.146    2.102    2.923    0.003    6.146    0.671
##    .dsq_undoing      13.421    2.169    6.187    0.000   13.421    0.850
##    .dsq_tstc_fntsy   15.097    1.773    8.514    0.000   15.097    0.828
##    .dsq_pssv_ggrss    7.439    1.051    7.075    0.000    7.439    0.725
##    .dsq_acting_out   15.222    1.812    8.399    0.000   15.222    0.857
##    .dsq_projection   10.247    1.378    7.438    0.000   10.247    0.715
##    .dsq_dissociatn   11.667    1.476    7.906    0.000   11.667    0.857
##    .dsq_devaluatin    4.988    0.996    5.007    0.000    4.988    0.491
##    .dsq_splitting     9.764    1.588    6.150    0.000    9.764    0.674
##     Mature            7.508    2.336    3.214    0.001    1.000    1.000
##     Neurotic          2.070    1.916    1.080    0.280    1.000    1.000
##     Combined_Immtr    3.136    1.485    2.112    0.035    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.425
##     dsq_suppressin    0.167
##     dsq_sublimatin    0.313
##     dsq_anticipatn    0.416
##     dsq_rationlztn    0.252
##     dsq_rctn_frmtn    0.146
##     dsq_idealizatn    0.157
##     dsq_psed_ltrsm    0.329
##     dsq_undoing       0.150
##     dsq_tstc_fntsy    0.172
##     dsq_pssv_ggrss    0.275
##     dsq_acting_out    0.143
##     dsq_projection    0.285
##     dsq_dissociatn    0.143
##     dsq_devaluatin    0.509
##     dsq_splitting     0.326
modindices(fit3f_combined_adj_VIII, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 101              dsq_humor ~~         dsq_projection 15.654 -3.971  -3.971   -0.389   -0.389
## 88       Combined_Immature =~    dsq_pseudo_altruism 13.119 -0.792  -1.403   -0.464   -0.464
## 61                  Mature =~            dsq_undoing 12.234 -0.795  -2.177   -0.548   -0.548
## 65                  Mature =~         dsq_projection 11.817 -0.421  -1.153   -0.305   -0.305
## 60                  Mature =~    dsq_pseudo_altruism  9.567  0.625   1.714    0.566    0.566
## 82       Combined_Immature =~        dsq_suppression  8.665  0.589   1.043    0.268    0.268
## 117        dsq_suppression ~~        dsq_devaluation  8.168  2.261   2.261    0.286    0.286
## 123        dsq_sublimation ~~    dsq_pseudo_altruism  8.053  2.227   2.227    0.293    0.293
## 160 dsq_reaction_formation ~~         dsq_acting_out  7.103 -3.190  -3.190   -0.235   -0.235
## 81       Combined_Immature =~              dsq_humor  6.862 -0.543  -0.961   -0.229   -0.229
## 188            dsq_undoing ~~          dsq_splitting  6.327  2.684   2.684    0.234    0.234
## 89       Combined_Immature =~            dsq_undoing  6.225  0.634   1.124    0.283    0.283
## 138       dsq_anticipation ~~ dsq_passive_aggression  5.843  1.525   1.525    0.240    0.240
## 161 dsq_reaction_formation ~~         dsq_projection  5.722  2.434   2.434    0.218    0.218
## 169       dsq_idealization ~~         dsq_acting_out  5.375  2.808   2.808    0.205    0.205
## 77                Neurotic =~         dsq_projection  5.300 -0.665  -0.956   -0.253   -0.253
## 157 dsq_reaction_formation ~~            dsq_undoing  5.149  2.790   2.790    0.219    0.219
## 63                  Mature =~ dsq_passive_aggression  4.696  0.229   0.628    0.196    0.196
## 182            dsq_undoing ~~   dsq_autistic_fantasy  4.602  2.735   2.735    0.192    0.192
## 69                Neurotic =~              dsq_humor  4.469 -0.922  -1.326   -0.316   -0.316
## 199 dsq_passive_aggression ~~          dsq_splitting  4.382  1.881   1.881    0.221    0.221
## 87       Combined_Immature =~       dsq_idealization  4.093  0.491   0.870    0.227    0.227
## 141       dsq_anticipation ~~       dsq_dissociation  3.981 -1.518  -1.518   -0.191   -0.191
## 97               dsq_humor ~~            dsq_undoing  3.948 -2.324  -2.324   -0.199   -0.199
## 164 dsq_reaction_formation ~~          dsq_splitting  3.883 -1.968  -1.968   -0.181   -0.181
## 134       dsq_anticipation ~~       dsq_idealization  3.853  1.597   1.597    0.195    0.195

4.1.16 Removing weakest loading defense (dissociation) com. 3 factor solution IX

model_3f_combined_adj_IX <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_passive_aggression +
                       dsq_acting_out + dsq_projection + dsq_devaluation + dsq_splitting
'

fit3f_combined_adj_IX <- cfa(model_3f_combined_adj_IX, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_IX,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 98 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        48
## 
##   Number of observations                           151
##   Number of missing patterns                        16
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               181.018     178.639
##   Degrees of freedom                                87          87
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.013
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               458.731     423.499
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.083
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.734       0.712
##   Tucker-Lewis Index (TLI)                       0.679       0.653
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.741
##   Robust Tucker-Lewis Index (TLI)                            0.688
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -5789.446   -5789.446
##   Scaling correction factor                                  1.094
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -5698.938   -5698.938
##   Scaling correction factor                                  1.042
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               11674.893   11674.893
##   Bayesian (BIC)                             11819.722   11819.722
##   Sample-size adjusted Bayesian (SABIC)      11667.807   11667.807
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.085       0.084
##   90 Percent confidence interval - lower         0.067       0.066
##   90 Percent confidence interval - upper         0.102       0.101
##   P-value H_0: RMSEA <= 0.050                    0.001       0.001
##   P-value H_0: RMSEA >= 0.080                    0.681       0.645
##                                                                   
##   Robust RMSEA                                               0.085
##   90 Percent confidence interval - lower                     0.066
##   90 Percent confidence interval - upper                     0.104
##   P-value H_0: Robust RMSEA <= 0.050                         0.002
##   P-value H_0: Robust RMSEA >= 0.080                         0.683
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.090       0.090
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.742    0.652
##     dsq_suppressin        0.582    0.196    2.974    0.003    1.597    0.411
##     dsq_sublimatin        0.755    0.220    3.436    0.001    2.070    0.560
##     dsq_anticipatn        0.716    0.150    4.785    0.000    1.964    0.644
##     dsq_rationlztn        0.543    0.134    4.062    0.000    1.490    0.501
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.397    0.371
##     dsq_idealizatn        1.136    1.270    0.894    0.371    1.587    0.415
##     dsq_psed_ltrsm        1.211    0.456    2.656    0.008    1.691    0.559
##     dsq_undoing           1.070    0.384    2.785    0.005    1.494    0.376
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.693    0.396
##     dsq_pssv_ggrss        1.035    0.340    3.047    0.002    1.753    0.547
##     dsq_acting_out        0.919    0.393    2.336    0.019    1.556    0.369
##     dsq_projection        1.187    0.371    3.201    0.001    2.009    0.531
##     dsq_devaluatin        1.316    0.368    3.571    0.000    2.228    0.699
##     dsq_splitting         1.321    0.367    3.604    0.000    2.237    0.588
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.439    0.954    2.557    0.011    0.637    0.637
##     Combined_Immtr   -0.055    0.710   -0.077    0.938   -0.012   -0.012
##   Neurotic ~~                                                           
##     Combined_Immtr    0.994    0.595    1.669    0.095    0.420    0.420
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.308    0.346   26.908    0.000    9.308    2.215
##    .dsq_suppressin    8.568    0.320   26.762    0.000    8.568    2.206
##    .dsq_sublimatin   10.029    0.308   32.596    0.000   10.029    2.712
##    .dsq_anticipatn   10.125    0.252   40.110    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.094    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.888    0.310   31.888    0.000    9.888    2.623
##    .dsq_idealizatn    7.965    0.314   25.350    0.000    7.965    2.081
##    .dsq_psed_ltrsm   12.701    0.253   50.138    0.000   12.701    4.197
##    .dsq_undoing      11.142    0.333   33.508    0.000   11.142    2.803
##    .dsq_tstc_fntsy    9.191    0.353   26.072    0.000    9.191    2.152
##    .dsq_pssv_ggrss    7.735    0.268   28.823    0.000    7.735    2.416
##    .dsq_acting_out    9.445    0.348   27.160    0.000    9.445    2.240
##    .dsq_projection    9.351    0.312   29.975    0.000    9.351    2.471
##    .dsq_devaluatin    9.753    0.262   37.296    0.000    9.753    3.062
##    .dsq_splitting     9.724    0.311   31.300    0.000    9.724    2.555
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.144    2.184    4.645    0.000   10.144    0.574
##    .dsq_suppressin   12.540    1.781    7.041    0.000   12.540    0.831
##    .dsq_sublimatin    9.395    1.616    5.815    0.000    9.395    0.687
##    .dsq_anticipatn    5.439    0.984    5.525    0.000    5.439    0.585
##    .dsq_rationlztn    6.622    0.964    6.869    0.000    6.622    0.749
##    .dsq_rctn_frmtn   12.256    2.449    5.005    0.000   12.256    0.863
##    .dsq_idealizatn   12.135    2.931    4.140    0.000   12.135    0.828
##    .dsq_psed_ltrsm    6.298    2.506    2.513    0.012    6.298    0.688
##    .dsq_undoing      13.562    2.389    5.677    0.000   13.562    0.859
##    .dsq_tstc_fntsy   15.369    1.742    8.821    0.000   15.369    0.843
##    .dsq_pssv_ggrss    7.181    1.067    6.732    0.000    7.181    0.700
##    .dsq_acting_out   15.358    1.846    8.320    0.000   15.358    0.864
##    .dsq_projection   10.282    1.447    7.105    0.000   10.282    0.718
##    .dsq_devaluatin    5.182    1.038    4.990    0.000    5.182    0.511
##    .dsq_splitting     9.487    1.644    5.772    0.000    9.487    0.655
##     Mature            7.518    2.412    3.118    0.002    1.000    1.000
##     Neurotic          1.952    2.260    0.863    0.388    1.000    1.000
##     Combined_Immtr    2.866    1.449    1.978    0.048    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.426
##     dsq_suppressin    0.169
##     dsq_sublimatin    0.313
##     dsq_anticipatn    0.415
##     dsq_rationlztn    0.251
##     dsq_rctn_frmtn    0.137
##     dsq_idealizatn    0.172
##     dsq_psed_ltrsm    0.312
##     dsq_undoing       0.141
##     dsq_tstc_fntsy    0.157
##     dsq_pssv_ggrss    0.300
##     dsq_acting_out    0.136
##     dsq_projection    0.282
##     dsq_devaluatin    0.489
##     dsq_splitting     0.345
modindices(fit3f_combined_adj_IX, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 96               dsq_humor ~~         dsq_projection 15.640 -3.984  -3.984   -0.390   -0.390
## 83       Combined_Immature =~    dsq_pseudo_altruism 13.846 -0.867  -1.468   -0.485   -0.485
## 62                  Mature =~         dsq_projection 12.570 -0.437  -1.197   -0.316   -0.316
## 58                  Mature =~            dsq_undoing 11.574 -0.784  -2.149   -0.541   -0.541
## 57                  Mature =~    dsq_pseudo_altruism  9.814  0.636   1.744    0.576    0.576
## 110        dsq_suppression ~~        dsq_devaluation  8.531  2.340   2.340    0.290    0.290
## 77       Combined_Immature =~        dsq_suppression  8.072  0.600   1.015    0.261    0.261
## 116        dsq_sublimation ~~    dsq_pseudo_altruism  8.025  2.230   2.230    0.290    0.290
## 76       Combined_Immature =~              dsq_humor  7.403 -0.595  -1.007   -0.240   -0.240
## 150 dsq_reaction_formation ~~         dsq_acting_out  6.884 -3.161  -3.161   -0.230   -0.230
## 174            dsq_undoing ~~          dsq_splitting  6.711  2.767   2.767    0.244    0.244
## 73                Neurotic =~         dsq_projection  5.996 -0.744  -1.039   -0.275   -0.275
## 151 dsq_reaction_formation ~~         dsq_projection  5.769  2.461   2.461    0.219    0.219
## 147 dsq_reaction_formation ~~            dsq_undoing  5.526  2.884   2.884    0.224    0.224
## 84       Combined_Immature =~            dsq_undoing  5.460  0.637   1.079    0.271    0.271
## 130       dsq_anticipation ~~ dsq_passive_aggression  5.388  1.455   1.455    0.233    0.233
## 82       Combined_Immature =~       dsq_idealization  5.104  0.594   1.006    0.263    0.263
## 158       dsq_idealization ~~         dsq_acting_out  4.996  2.708   2.708    0.198    0.198
## 169            dsq_undoing ~~   dsq_autistic_fantasy  4.987  2.876   2.876    0.199    0.199
## 65                Neurotic =~              dsq_humor  4.793 -0.999  -1.395   -0.332   -0.332
## 60                  Mature =~ dsq_passive_aggression  4.404  0.222   0.607    0.190    0.190
## 188         dsq_projection ~~          dsq_splitting  4.281 -2.225  -2.225   -0.225   -0.225
## 153 dsq_reaction_formation ~~          dsq_splitting  4.079 -2.018  -2.018   -0.187   -0.187
## 92               dsq_humor ~~            dsq_undoing  3.940 -2.327  -2.327   -0.198   -0.198

4.1.17 Removing weakest loading defense (acting out) com. 3 factor solution X

model_3f_combined_adj_X <- '
  Mature           =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic         =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Combined_Immature =~ dsq_autistic_fantasy + dsq_passive_aggression +
                       dsq_projection + dsq_devaluation + dsq_splitting
'

fit3f_combined_adj_X <- cfa(model_3f_combined_adj_X, data = dekker_df, estimator = "mlr", missing = "fiml")

summary(fit3f_combined_adj_X,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 114 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        45
## 
##   Number of observations                           151
##   Number of missing patterns                        15
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               162.035     158.697
##   Degrees of freedom                                74          74
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.021
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               425.192     392.362
##   Degrees of freedom                                91          91
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.084
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.737       0.719
##   Tucker-Lewis Index (TLI)                       0.676       0.654
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.741
##   Robust Tucker-Lewis Index (TLI)                            0.682
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -5376.701   -5376.701
##   Scaling correction factor                                  1.076
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -5295.683   -5295.683
##   Scaling correction factor                                  1.042
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               10843.401   10843.401
##   Bayesian (BIC)                             10979.179   10979.179
##   Sample-size adjusted Bayesian (SABIC)      10836.759   10836.759
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.089       0.087
##   90 Percent confidence interval - lower         0.070       0.069
##   90 Percent confidence interval - upper         0.107       0.106
##   P-value H_0: RMSEA <= 0.050                    0.001       0.001
##   P-value H_0: RMSEA >= 0.080                    0.791       0.747
##                                                                   
##   Robust RMSEA                                               0.090
##   90 Percent confidence interval - lower                     0.070
##   90 Percent confidence interval - upper                     0.110
##   P-value H_0: Robust RMSEA <= 0.050                         0.001
##   P-value H_0: Robust RMSEA >= 0.080                         0.796
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.089       0.089
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                 
##     dsq_humor             1.000                               2.754    0.655
##     dsq_suppressin        0.576    0.192    3.000    0.003    1.586    0.408
##     dsq_sublimatin        0.752    0.214    3.506    0.000    2.070    0.560
##     dsq_anticipatn        0.712    0.150    4.744    0.000    1.962    0.643
##     dsq_rationlztn        0.541    0.129    4.195    0.000    1.489    0.501
##   Neurotic =~                                                               
##     dsq_rctn_frmtn        1.000                               1.470    0.390
##     dsq_idealizatn        1.044    0.947    1.103    0.270    1.535    0.401
##     dsq_psed_ltrsm        1.150    0.445    2.582    0.010    1.691    0.559
##     dsq_undoing           1.055    0.346    3.046    0.002    1.550    0.390
##   Combined_Immature =~                                                      
##     dsq_tstc_fntsy        1.000                               1.774    0.415
##     dsq_pssv_ggrss        0.992    0.328    3.026    0.002    1.760    0.549
##     dsq_projection        1.183    0.369    3.207    0.001    2.098    0.554
##     dsq_devaluatin        1.218    0.329    3.707    0.000    2.161    0.678
##     dsq_splitting         1.239    0.324    3.820    0.000    2.197    0.577
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.522    0.849    2.972    0.003    0.623    0.623
##     Combined_Immtr   -0.229    0.780   -0.293    0.769   -0.047   -0.047
##   Neurotic ~~                                                           
##     Combined_Immtr    1.070    0.661    1.620    0.105    0.411    0.411
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.309    0.346   26.909    0.000    9.309    2.215
##    .dsq_suppressin    8.568    0.320   26.765    0.000    8.568    2.206
##    .dsq_sublimatin   10.029    0.308   32.598    0.000   10.029    2.712
##    .dsq_anticipatn   10.125    0.252   40.108    0.000   10.125    3.321
##    .dsq_rationlztn    8.848    0.245   36.091    0.000    8.848    2.976
##    .dsq_rctn_frmtn    9.887    0.310   31.887    0.000    9.887    2.623
##    .dsq_idealizatn    7.965    0.314   25.340    0.000    7.965    2.081
##    .dsq_psed_ltrsm   12.701    0.253   50.173    0.000   12.701    4.196
##    .dsq_undoing      11.141    0.333   33.487    0.000   11.141    2.803
##    .dsq_tstc_fntsy    9.188    0.353   26.059    0.000    9.188    2.151
##    .dsq_pssv_ggrss    7.729    0.268   28.854    0.000    7.729    2.413
##    .dsq_projection    9.347    0.312   29.949    0.000    9.347    2.471
##    .dsq_devaluatin    9.753    0.262   37.275    0.000    9.753    3.061
##    .dsq_splitting     9.724    0.311   31.299    0.000    9.724    2.554
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.080    2.162    4.662    0.000   10.080    0.571
##    .dsq_suppressin   12.574    1.777    7.076    0.000   12.574    0.833
##    .dsq_sublimatin    9.396    1.595    5.889    0.000    9.396    0.687
##    .dsq_anticipatn    5.450    0.953    5.719    0.000    5.450    0.586
##    .dsq_rationlztn    6.624    0.948    6.990    0.000    6.624    0.749
##    .dsq_rctn_frmtn   12.051    2.208    5.458    0.000   12.051    0.848
##    .dsq_idealizatn   12.299    2.414    5.096    0.000   12.299    0.839
##    .dsq_psed_ltrsm    6.302    2.039    3.091    0.002    6.302    0.688
##    .dsq_undoing      13.393    2.218    6.039    0.000   13.393    0.848
##    .dsq_tstc_fntsy   15.091    1.707    8.840    0.000   15.091    0.827
##    .dsq_pssv_ggrss    7.163    1.117    6.415    0.000    7.163    0.698
##    .dsq_projection    9.913    1.494    6.637    0.000    9.913    0.693
##    .dsq_devaluatin    5.482    0.992    5.528    0.000    5.482    0.540
##    .dsq_splitting     9.663    1.600    6.040    0.000    9.663    0.667
##     Mature            7.582    2.386    3.177    0.001    1.000    1.000
##     Neurotic          2.161    1.987    1.087    0.277    1.000    1.000
##     Combined_Immtr    3.146    1.511    2.083    0.037    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.429
##     dsq_suppressin    0.167
##     dsq_sublimatin    0.313
##     dsq_anticipatn    0.414
##     dsq_rationlztn    0.251
##     dsq_rctn_frmtn    0.152
##     dsq_idealizatn    0.161
##     dsq_psed_ltrsm    0.312
##     dsq_undoing       0.152
##     dsq_tstc_fntsy    0.173
##     dsq_pssv_ggrss    0.302
##     dsq_projection    0.307
##     dsq_devaluatin    0.460
##     dsq_splitting     0.333
modindices(fit3f_combined_adj_X, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 90               dsq_humor ~~         dsq_projection 15.532 -3.946  -3.946   -0.395   -0.395
## 78       Combined_Immature =~    dsq_pseudo_altruism 15.004 -0.853  -1.513   -0.500   -0.500
## 55                  Mature =~            dsq_undoing 12.185 -0.780  -2.147   -0.540   -0.540
## 58                  Mature =~         dsq_projection 11.917 -0.424  -1.169   -0.309   -0.309
## 54                  Mature =~    dsq_pseudo_altruism 10.662  0.634   1.747    0.577    0.577
## 103        dsq_suppression ~~        dsq_devaluation  9.102  2.464   2.464    0.297    0.297
## 109        dsq_sublimation ~~    dsq_pseudo_altruism  8.276  2.264   2.264    0.294    0.294
## 72       Combined_Immature =~        dsq_suppression  7.739  0.567   1.006    0.259    0.259
## 71       Combined_Immature =~              dsq_humor  7.245 -0.568  -1.007   -0.240   -0.240
## 79       Combined_Immature =~            dsq_undoing  6.450  0.662   1.174    0.295    0.295
## 160            dsq_undoing ~~          dsq_splitting  6.058  2.650   2.650    0.233    0.233
## 169         dsq_projection ~~          dsq_splitting  5.836 -2.709  -2.709   -0.277   -0.277
## 68                Neurotic =~         dsq_projection  5.754 -0.689  -1.012   -0.268   -0.268
## 57                  Mature =~ dsq_passive_aggression  5.500  0.249   0.685    0.214    0.214
## 122       dsq_anticipation ~~ dsq_passive_aggression  5.411  1.464   1.464    0.234    0.234
## 142 dsq_reaction_formation ~~          dsq_splitting  5.329 -2.324  -2.324   -0.215   -0.215
## 140 dsq_reaction_formation ~~         dsq_projection  4.963  2.265   2.265    0.207    0.207
## 137 dsq_reaction_formation ~~            dsq_undoing  4.958  2.744   2.744    0.216    0.216
## 61                Neurotic =~              dsq_humor  4.727 -0.916  -1.346   -0.320   -0.320
## 156            dsq_undoing ~~   dsq_autistic_fantasy  4.483  2.710   2.710    0.191    0.191
## 135 dsq_reaction_formation ~~       dsq_idealization  4.051 -2.364  -2.364   -0.194   -0.194
## 87               dsq_humor ~~            dsq_undoing  3.899 -2.308  -2.308   -0.199   -0.199
## 149       dsq_idealization ~~          dsq_splitting  3.847  2.001   2.001    0.184    0.184

4.2 Dos Santos

4.2.1 One Factor Solution

fit1_ds <- cfa(model_1f, data = ds_df, estimator = "mlr", missing = "fiml")

summary(fit1_ds,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 72 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        60
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               495.165     477.113
##   Degrees of freedom                               170         170
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.038
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               724.594     635.432
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.140
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.392       0.311
##   Tucker-Lewis Index (TLI)                       0.320       0.229
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.402
##   Robust Tucker-Lewis Index (TLI)                            0.332
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10930.821  -10930.821
##   Scaling correction factor                                  1.259
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10683.239  -10683.239
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21981.642   21981.642
##   Bayesian (BIC)                             22182.469   22182.469
##   Sample-size adjusted Bayesian (SABIC)      21992.354   21992.354
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.095       0.093
##   90 Percent confidence interval - lower         0.086       0.083
##   90 Percent confidence interval - upper         0.105       0.102
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.995       0.985
##                                                                   
##   Robust RMSEA                                               0.096
##   90 Percent confidence interval - lower                     0.084
##   90 Percent confidence interval - upper                     0.107
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.988
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.121       0.121
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Factor1 =~                                                            
##     dsq_sublimatin    1.000                               1.627    0.409
##     dsq_humor         1.409    0.658    2.141    0.032    2.293    0.510
##     dsq_anticipatn    1.259    0.319    3.942    0.000    2.049    0.482
##     dsq_suppressin    1.108    0.368    3.014    0.003    1.803    0.445
##     dsq_psed_ltrsm    0.430    0.219    1.963    0.050    0.700    0.188
##     dsq_idealizatn    1.058    0.334    3.163    0.002    1.721    0.424
##     dsq_rctn_frmtn    1.019    0.457    2.227    0.026    1.657    0.412
##     dsq_undoing       0.698    0.392    1.781    0.075    1.136    0.278
##     dsq_rationlztn    1.675    0.725    2.311    0.021    2.726    0.667
##     dsq_projection   -0.127    0.890   -0.143    0.886   -0.207   -0.052
##     dsq_pssv_ggrss   -0.064    0.796   -0.081    0.935   -0.105   -0.027
##     dsq_acting_out    0.048    0.842    0.057    0.954    0.078    0.016
##     dsq_isolation     0.083    0.705    0.118    0.906    0.135    0.028
##     dsq_tstc_fntsy    0.136    1.065    0.128    0.898    0.221    0.042
##     dsq_denial        0.666    0.347    1.923    0.055    1.084    0.323
##     dsq_displacmnt   -0.110    0.551   -0.200    0.841   -0.180   -0.044
##     dsq_dissociatn    1.018    0.274    3.718    0.000    1.657    0.530
##     dsq_splitting     0.335    0.540    0.621    0.535    0.545    0.133
##     dsq_devaluatin    0.142    0.529    0.268    0.789    0.231    0.071
##     dsq_somatizatn   -0.451    0.712   -0.634    0.526   -0.735   -0.154
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin    9.796    0.283   34.584    0.000    9.796    2.462
##    .dsq_humor         8.238    0.319   25.833    0.000    8.238    1.830
##    .dsq_anticipatn   11.805    0.304   38.891    0.000   11.805    2.777
##    .dsq_suppressin    6.755    0.289   23.402    0.000    6.755    1.667
##    .dsq_psed_ltrsm   11.027    0.264   41.736    0.000   11.027    2.967
##    .dsq_idealizatn    8.089    0.289   28.012    0.000    8.089    1.993
##    .dsq_rctn_frmtn    8.948    0.286   31.249    0.000    8.948    2.223
##    .dsq_undoing       9.445    0.291   32.462    0.000    9.445    2.309
##    .dsq_rationlztn    8.428    0.290   29.028    0.000    8.428    2.064
##    .dsq_projection    8.142    0.283   28.732    0.000    8.142    2.037
##    .dsq_pssv_ggrss    8.743    0.277   31.579    0.000    8.743    2.245
##    .dsq_acting_out   10.707    0.348   30.788    0.000   10.707    2.189
##    .dsq_isolation     9.833    0.348   28.215    0.000    9.833    2.004
##    .dsq_tstc_fntsy   10.292    0.377   27.295    0.000   10.292    1.940
##    .dsq_denial        5.379    0.239   22.479    0.000    5.379    1.602
##    .dsq_displacmnt   10.026    0.291   34.492    0.000   10.026    2.447
##    .dsq_dissociatn    5.251    0.223   23.515    0.000    5.251    1.679
##    .dsq_splitting     9.998    0.292   34.183    0.000    9.998    2.431
##    .dsq_devaluatin    7.171    0.230   31.166    0.000    7.171    2.214
##    .dsq_somatizatn   11.506    0.389   29.568    0.000   11.506    2.412
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin   13.188    1.647    8.007    0.000   13.188    0.833
##    .dsq_humor        14.998    2.721    5.513    0.000   14.998    0.740
##    .dsq_anticipatn   13.875    1.674    8.290    0.000   13.875    0.768
##    .dsq_suppressin   13.174    1.906    6.913    0.000   13.174    0.802
##    .dsq_psed_ltrsm   13.328    1.320   10.097    0.000   13.328    0.965
##    .dsq_idealizatn   13.509    2.406    5.615    0.000   13.509    0.820
##    .dsq_rctn_frmtn   13.459    1.796    7.493    0.000   13.459    0.830
##    .dsq_undoing      15.443    2.260    6.834    0.000   15.443    0.923
##    .dsq_rationlztn    9.254    3.360    2.754    0.006    9.254    0.555
##    .dsq_projection   15.937    1.390   11.466    0.000   15.937    0.997
##    .dsq_pssv_ggrss   15.160    1.440   10.531    0.000   15.160    0.999
##    .dsq_acting_out   23.918    1.747   13.695    0.000   23.918    1.000
##    .dsq_isolation    24.050    1.813   13.262    0.000   24.050    0.999
##    .dsq_tstc_fntsy   28.087    2.042   13.752    0.000   28.087    0.998
##    .dsq_denial       10.102    1.422    7.102    0.000   10.102    0.896
##    .dsq_displacmnt   16.750    1.485   11.281    0.000   16.750    0.998
##    .dsq_dissociatn    7.031    1.131    6.214    0.000    7.031    0.719
##    .dsq_splitting    16.622    1.819    9.140    0.000   16.622    0.982
##    .dsq_devaluatin   10.432    1.083    9.637    0.000   10.432    0.995
##    .dsq_somatizatn   22.225    2.313    9.610    0.000   22.225    0.976
##     Factor1           2.648    1.383    1.915    0.055    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_sublimatin    0.167
##     dsq_humor         0.260
##     dsq_anticipatn    0.232
##     dsq_suppressin    0.198
##     dsq_psed_ltrsm    0.035
##     dsq_idealizatn    0.180
##     dsq_rctn_frmtn    0.170
##     dsq_undoing       0.077
##     dsq_rationlztn    0.445
##     dsq_projection    0.003
##     dsq_pssv_ggrss    0.001
##     dsq_acting_out    0.000
##     dsq_isolation     0.001
##     dsq_tstc_fntsy    0.002
##     dsq_denial        0.104
##     dsq_displacmnt    0.002
##     dsq_dissociatn    0.281
##     dsq_splitting     0.018
##     dsq_devaluatin    0.005
##     dsq_somatizatn    0.024

4.2.2 Three Factor Solution

fit3_ds <- cfa(model_3f, data = ds_df, estimator = "mlr", missing = "fiml")

summary(fit3_ds,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 178 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        63
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               374.566     335.018
##   Degrees of freedom                               167         167
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.118
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               724.594     635.432
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.140
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.612       0.623
##   Tucker-Lewis Index (TLI)                       0.558       0.571
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.638
##   Robust Tucker-Lewis Index (TLI)                            0.589
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10870.522  -10870.522
##   Scaling correction factor                                  1.036
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10683.239  -10683.239
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21867.044   21867.044
##   Bayesian (BIC)                             22077.911   22077.911
##   Sample-size adjusted Bayesian (SABIC)      21878.291   21878.291
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.077       0.069
##   90 Percent confidence interval - lower         0.067       0.059
##   90 Percent confidence interval - upper         0.087       0.079
##   P-value H_0: RMSEA <= 0.050                    0.000       0.001
##   P-value H_0: RMSEA >= 0.080                    0.322       0.040
##                                                                   
##   Robust RMSEA                                               0.075
##   90 Percent confidence interval - lower                     0.063
##   90 Percent confidence interval - upper                     0.087
##   P-value H_0: Robust RMSEA <= 0.050                         0.001
##   P-value H_0: Robust RMSEA >= 0.080                         0.262
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.103       0.103
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               2.003    0.445
##     dsq_suppressin    0.912    0.256    3.559    0.000    1.826    0.451
##     dsq_sublimatin    0.711    0.282    2.522    0.012    1.424    0.358
##     dsq_anticipatn    1.169    0.313    3.736    0.000    2.343    0.551
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.492    0.371
##     dsq_idealizatn    1.286    0.460    2.796    0.005    1.918    0.473
##     dsq_psed_ltrsm    0.543    0.278    1.954    0.051    0.810    0.218
##     dsq_undoing       1.115    0.602    1.851    0.064    1.663    0.407
##   Immature =~                                                           
##     dsq_rationlztn    1.000                               0.483    0.118
##     dsq_isolation    -3.517    3.719   -0.946    0.344   -1.697   -0.346
##     dsq_dissociatn   -0.414    1.026   -0.403    0.687   -0.200   -0.064
##     dsq_devaluatin   -3.160    3.359   -0.941    0.347   -1.525   -0.471
##     dsq_splitting    -2.905    3.305   -0.879    0.379   -1.402   -0.341
##     dsq_denial       -1.658    2.105   -0.788    0.431   -0.800   -0.238
##     dsq_tstc_fntsy   -7.033    7.302   -0.963    0.335   -3.394   -0.640
##     dsq_displacmnt   -3.223    3.242   -0.994    0.320   -1.555   -0.380
##     dsq_pssv_ggrss   -5.152    5.236   -0.984    0.325   -2.486   -0.638
##     dsq_somatizatn   -3.369    3.386   -0.995    0.320   -1.626   -0.341
##     dsq_acting_out   -5.167    5.476   -0.944    0.345   -2.493   -0.510
##     dsq_projection   -5.163    5.228   -0.987    0.323   -2.491   -0.623
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          2.841    1.258    2.258    0.024    0.950    0.950
##     Immature          0.009    0.167    0.054    0.957    0.009    0.009
##   Neurotic ~~                                                           
##     Immature         -0.194    0.150   -1.299    0.194   -0.270   -0.270
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.247    0.319   25.813    0.000    8.247    1.832
##    .dsq_suppressin    6.762    0.288   23.479    0.000    6.762    1.669
##    .dsq_sublimatin    9.803    0.283   34.666    0.000    9.803    2.463
##    .dsq_anticipatn   11.813    0.302   39.081    0.000   11.813    2.779
##    .dsq_rctn_frmtn    8.958    0.286   31.312    0.000    8.958    2.225
##    .dsq_idealizatn    8.101    0.288   28.128    0.000    8.101    1.996
##    .dsq_psed_ltrsm   11.032    0.264   41.790    0.000   11.032    2.968
##    .dsq_undoing       9.453    0.290   32.580    0.000    9.453    2.311
##    .dsq_rationlztn    8.435    0.289   29.152    0.000    8.435    2.065
##    .dsq_isolation     9.848    0.349   28.228    0.000    9.848    2.007
##    .dsq_dissociatn    5.259    0.222   23.650    0.000    5.259    1.682
##    .dsq_devaluatin    7.185    0.230   31.224    0.000    7.185    2.219
##    .dsq_splitting    10.012    0.292   34.286    0.000   10.012    2.434
##    .dsq_denial        5.391    0.239   22.516    0.000    5.391    1.605
##    .dsq_tstc_fntsy   10.323    0.376   27.429    0.000   10.323    1.946
##    .dsq_displacmnt   10.039    0.291   34.539    0.000   10.039    2.450
##    .dsq_pssv_ggrss    8.764    0.277   31.694    0.000    8.764    2.249
##    .dsq_somatizatn   11.555    0.387   29.840    0.000   11.555    2.423
##    .dsq_acting_out   10.729    0.348   30.873    0.000   10.729    2.193
##    .dsq_projection    8.163    0.283   28.859    0.000    8.163    2.042
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        16.243    1.886    8.613    0.000   16.243    0.802
##    .dsq_suppressin   13.088    2.015    6.494    0.000   13.088    0.797
##    .dsq_sublimatin   13.807    1.628    8.484    0.000   13.807    0.872
##    .dsq_anticipatn   12.584    1.779    7.073    0.000   12.584    0.696
##    .dsq_rctn_frmtn   13.979    2.052    6.813    0.000   13.979    0.863
##    .dsq_idealizatn   12.791    1.754    7.294    0.000   12.791    0.777
##    .dsq_psed_ltrsm   13.161    1.355    9.716    0.000   13.161    0.953
##    .dsq_undoing      13.966    1.832    7.623    0.000   13.966    0.835
##    .dsq_rationlztn   16.448    1.470   11.192    0.000   16.448    0.986
##    .dsq_isolation    21.193    1.878   11.284    0.000   21.193    0.880
##    .dsq_dissociatn    9.737    0.941   10.347    0.000    9.737    0.996
##    .dsq_devaluatin    8.165    0.893    9.143    0.000    8.165    0.778
##    .dsq_splitting    14.957    1.620    9.235    0.000   14.957    0.884
##    .dsq_denial       10.638    0.971   10.954    0.000   10.638    0.943
##    .dsq_tstc_fntsy   16.636    2.314    7.188    0.000   16.636    0.591
##    .dsq_displacmnt   14.367    1.355   10.604    0.000   14.367    0.856
##    .dsq_pssv_ggrss    9.000    1.362    6.605    0.000    9.000    0.593
##    .dsq_somatizatn   20.110    2.234    9.001    0.000   20.110    0.884
##    .dsq_acting_out   17.718    1.826    9.705    0.000   17.718    0.740
##    .dsq_projection    9.783    1.345    7.274    0.000    9.783    0.612
##     Mature            4.014    1.805    2.223    0.026    1.000    1.000
##     Neurotic          2.226    1.761    1.264    0.206    1.000    1.000
##     Immature          0.233    0.481    0.484    0.629    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.198
##     dsq_suppressin    0.203
##     dsq_sublimatin    0.128
##     dsq_anticipatn    0.304
##     dsq_rctn_frmtn    0.137
##     dsq_idealizatn    0.223
##     dsq_psed_ltrsm    0.047
##     dsq_undoing       0.165
##     dsq_rationlztn    0.014
##     dsq_isolation     0.120
##     dsq_dissociatn    0.004
##     dsq_devaluatin    0.222
##     dsq_splitting     0.116
##     dsq_denial        0.057
##     dsq_tstc_fntsy    0.409
##     dsq_displacmnt    0.144
##     dsq_pssv_ggrss    0.407
##     dsq_somatizatn    0.116
##     dsq_acting_out    0.260
##     dsq_projection    0.388

4.2.3 Four Factor Solution

fit4_ds <- cfa(model_4f, data = ds_df, estimator = "mlr", missing = "fiml")
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite ; use lavInspect(fit, "cov.lv") to investigate.
summary(fit4_ds,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 159 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               288.040     265.405
##   Degrees of freedom                               164         164
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.085
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               724.594     635.432
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.140
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.768       0.772
##   Tucker-Lewis Index (TLI)                       0.731       0.736
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.797
##   Robust Tucker-Lewis Index (TLI)                            0.765
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10827.259  -10827.259
##   Scaling correction factor                                  1.121
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10683.239  -10683.239
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21786.518   21786.518
##   Bayesian (BIC)                             22007.427   22007.427
##   Sample-size adjusted Bayesian (SABIC)      21798.301   21798.301
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.060       0.054
##   90 Percent confidence interval - lower         0.048       0.043
##   90 Percent confidence interval - upper         0.071       0.066
##   P-value H_0: RMSEA <= 0.050                    0.076       0.263
##   P-value H_0: RMSEA >= 0.080                    0.001       0.000
##                                                                   
##   Robust RMSEA                                               0.057
##   90 Percent confidence interval - lower                     0.042
##   90 Percent confidence interval - upper                     0.070
##   P-value H_0: Robust RMSEA <= 0.050                         0.207
##   P-value H_0: Robust RMSEA >= 0.080                         0.002
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.084       0.084
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.202    0.489
##     dsq_suppressin       0.856    0.249    3.431    0.001    1.885    0.465
##     dsq_sublimatin       0.721    0.212    3.408    0.001    1.588    0.399
##     dsq_anticipatn       0.962    0.233    4.137    0.000    2.119    0.498
##     dsq_rationlztn       1.274    0.240    5.306    0.000    2.806    0.687
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.599    0.397
##     dsq_idealizatn       1.148    0.359    3.198    0.001    1.836    0.452
##     dsq_psed_ltrsm       0.574    0.264    2.172    0.030    0.917    0.247
##     dsq_undoing          1.012    0.474    2.136    0.033    1.617    0.395
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.324    0.626
##     dsq_displacmnt       0.493    0.118    4.194    0.000    1.639    0.400
##     dsq_pssv_ggrss       0.744    0.123    6.071    0.000    2.474    0.635
##     dsq_somatizatn       0.499    0.154    3.244    0.001    1.657    0.348
##     dsq_acting_out       0.726    0.138    5.264    0.000    2.414    0.493
##     dsq_projection       0.778    0.120    6.498    0.000    2.586    0.647
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.764    0.360
##     dsq_dissociatn       0.648    0.633    1.024    0.306    1.143    0.366
##     dsq_devaluatin       0.870    0.252    3.452    0.001    1.535    0.474
##     dsq_splitting        0.763    0.330    2.313    0.021    1.346    0.327
##     dsq_denial           0.865    0.546    1.586    0.113    1.527    0.455
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          3.088    1.139    2.712    0.007    0.877    0.877
##     Immature         -1.208    0.924   -1.307    0.191   -0.165   -0.165
##     Image_Distrtng    1.628    0.877    1.857    0.063    0.419    0.419
##   Neurotic ~~                                                           
##     Immature          1.276    0.883    1.446    0.148    0.240    0.240
##     Image_Distrtng    1.252    0.590    2.123    0.034    0.444    0.444
##   Immature ~~                                                           
##     Image_Distrtng    3.982    2.770    1.438    0.150    0.679    0.679
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.815    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.488    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.646    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.076    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.290   29.133    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.327    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.125    0.000    8.100    1.996
##    .dsq_psed_ltrsm   11.032    0.264   41.786    0.000   11.032    2.968
##    .dsq_undoing       9.453    0.290   32.580    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.323    0.376   27.444    0.000   10.323    1.945
##    .dsq_displacmnt   10.040    0.291   34.522    0.000   10.040    2.450
##    .dsq_pssv_ggrss    8.765    0.276   31.700    0.000    8.765    2.250
##    .dsq_somatizatn   11.561    0.388   29.778    0.000   11.561    2.425
##    .dsq_acting_out   10.729    0.347   30.900    0.000   10.729    2.193
##    .dsq_projection    8.165    0.283   28.834    0.000    8.165    2.042
##    .dsq_isolation     9.844    0.349   28.227    0.000    9.844    2.006
##    .dsq_dissociatn    5.265    0.223   23.615    0.000    5.265    1.684
##    .dsq_devaluatin    7.181    0.230   31.232    0.000    7.181    2.217
##    .dsq_splitting    10.008    0.292   34.261    0.000   10.008    2.433
##    .dsq_denial        5.393    0.239   22.543    0.000    5.393    1.606
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        15.407    1.860    8.285    0.000   15.407    0.761
##    .dsq_suppressin   12.872    1.983    6.491    0.000   12.872    0.784
##    .dsq_sublimatin   13.313    1.510    8.815    0.000   13.313    0.841
##    .dsq_anticipatn   13.583    1.510    8.996    0.000   13.583    0.752
##    .dsq_rationlztn    8.805    1.386    6.355    0.000    8.805    0.528
##    .dsq_rctn_frmtn   13.649    1.908    7.154    0.000   13.649    0.842
##    .dsq_idealizatn   13.101    1.892    6.925    0.000   13.101    0.795
##    .dsq_psed_ltrsm   12.976    1.307    9.927    0.000   12.976    0.939
##    .dsq_undoing      14.116    1.818    7.764    0.000   14.116    0.844
##    .dsq_tstc_fntsy   17.106    2.528    6.767    0.000   17.106    0.608
##    .dsq_displacmnt   14.101    1.419    9.939    0.000   14.101    0.840
##    .dsq_pssv_ggrss    9.061    1.373    6.601    0.000    9.061    0.597
##    .dsq_somatizatn   19.989    2.221    8.999    0.000   19.989    0.879
##    .dsq_acting_out   18.106    1.946    9.305    0.000   18.106    0.757
##    .dsq_projection    9.302    1.373    6.776    0.000    9.302    0.582
##    .dsq_isolation    20.958    2.302    9.105    0.000   20.958    0.871
##    .dsq_dissociatn    8.471    1.967    4.306    0.000    8.471    0.866
##    .dsq_devaluatin    8.132    1.424    5.709    0.000    8.132    0.775
##    .dsq_splitting    15.109    1.745    8.657    0.000   15.109    0.893
##    .dsq_denial        8.947    1.878    4.764    0.000    8.947    0.793
##     Mature            4.850    1.887    2.570    0.010    1.000    1.000
##     Neurotic          2.556    1.642    1.557    0.119    1.000    1.000
##     Immature         11.048    2.577    4.287    0.000    1.000    1.000
##     Image_Distrtng    3.113    2.102    1.481    0.139    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.239
##     dsq_suppressin    0.216
##     dsq_sublimatin    0.159
##     dsq_anticipatn    0.248
##     dsq_rationlztn    0.472
##     dsq_rctn_frmtn    0.158
##     dsq_idealizatn    0.205
##     dsq_psed_ltrsm    0.061
##     dsq_undoing       0.156
##     dsq_tstc_fntsy    0.392
##     dsq_displacmnt    0.160
##     dsq_pssv_ggrss    0.403
##     dsq_somatizatn    0.121
##     dsq_acting_out    0.243
##     dsq_projection    0.418
##     dsq_isolation     0.129
##     dsq_dissociatn    0.134
##     dsq_devaluatin    0.225
##     dsq_splitting     0.107
##     dsq_denial        0.207

4.2.4 Checking Error Message

cov2cor(lavInspect(fit4_ds, "cov.lv"))
##                  Mature Neurtc Immatr Img_Ds
## Mature            1.000                     
## Neurotic          0.877  1.000              
## Immature         -0.165  0.240  1.000       
## Image_Distorting  0.419  0.444  0.679  1.000

4.2.5 Model Comparison

# Likelihood Ratio Tests (Nested)
anova(fit1_ds, fit3_ds)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():  
##    scaling factor is negative
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit3_ds 167 21867 22078 374.57                              
## fit1_ds 170 21982 22183 495.16                  3
anova(fit1_ds, fit4_ds)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():  
##    scaling factor is negative
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit4_ds 164 21787 22007 288.04                              
## fit1_ds 170 21982 22183 495.16                  6
# BIC (Non-Nested)
fitMeasures(fit3_ds, "bic")
##      bic 
## 22077.91
fitMeasures(fit4_ds, "bic")
##      bic 
## 22007.43

4.2.6 Model Comparison Winner: Four Factor Solution

modindices(fit4_ds, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 86                  Mature =~       dsq_dissociation 28.530  0.709   1.561    0.499    0.499
## 116               Immature =~       dsq_dissociation 26.190 -0.627  -2.085   -0.667   -0.667
## 102               Neurotic =~       dsq_dissociation 19.875  1.014   1.621    0.518    0.518
## 321       dsq_dissociation ~~             dsq_denial 18.808  3.126   3.126    0.359    0.359
## 125       Image_Distorting =~ dsq_reaction_formation 14.406 -1.081  -1.907   -0.474   -0.474
## 111               Immature =~ dsq_reaction_formation 13.789 -0.405  -1.348   -0.335   -0.335
## 245       dsq_idealization ~~          dsq_splitting 10.814  3.550   3.550    0.252    0.252
## 227 dsq_reaction_formation ~~         dsq_acting_out 10.608 -3.939  -3.939   -0.251   -0.251
## 117               Immature =~        dsq_devaluation  9.521  0.410   1.362    0.420    0.420
## 319       dsq_dissociation ~~        dsq_devaluation  9.473 -2.147  -2.147   -0.259   -0.259
## 87                  Mature =~        dsq_devaluation  8.578 -0.417  -0.918   -0.284   -0.284
## 114               Immature =~            dsq_undoing  8.275  0.319   1.060    0.259    0.259
## 101               Neurotic =~          dsq_isolation  8.091 -1.013  -1.619   -0.330   -0.330
## 231 dsq_reaction_formation ~~        dsq_devaluation  7.941 -2.348  -2.348   -0.223   -0.223
## 75                  Mature =~ dsq_reaction_formation  7.154  1.003   2.209    0.549    0.549
## 150              dsq_humor ~~       dsq_dissociation  7.130  2.353   2.353    0.206    0.206
## 85                  Mature =~          dsq_isolation  7.034 -0.552  -1.215   -0.248   -0.248
## 78                  Mature =~            dsq_undoing  6.871 -0.998  -2.197   -0.537   -0.537
## 253    dsq_pseudo_altruism ~~         dsq_projection  6.855  2.293   2.293    0.209    0.209
## 213    dsq_rationalization ~~         dsq_acting_out  6.831  2.829   2.829    0.224    0.224
## 196       dsq_anticipation ~~ dsq_passive_aggression  6.191  2.268   2.268    0.204    0.204
## 128       Image_Distorting =~            dsq_undoing  5.685  0.689   1.216    0.297    0.297
## 149              dsq_humor ~~          dsq_isolation  5.558 -3.263  -3.263   -0.182   -0.182
## 118               Immature =~          dsq_splitting  5.401  0.372   1.236    0.300    0.300
## 119               Immature =~             dsq_denial  4.902 -0.301  -1.002   -0.298   -0.298
## 159        dsq_suppression ~~    dsq_pseudo_altruism  4.886 -2.179  -2.179   -0.169   -0.169
## 164        dsq_suppression ~~       dsq_somatization  4.814 -3.191  -3.191   -0.199   -0.199
## 280       dsq_displacement ~~ dsq_passive_aggression  4.650  2.085   2.085    0.184    0.184
## 176        dsq_sublimation ~~    dsq_pseudo_altruism  4.542  2.096   2.096    0.160    0.160
## 136              dsq_humor ~~        dsq_sublimation  4.493 -2.413  -2.413   -0.169   -0.169
## 103               Neurotic =~        dsq_devaluation  4.477 -0.525  -0.840   -0.259   -0.259
## 284       dsq_displacement ~~          dsq_isolation  4.308 -2.686  -2.686   -0.156   -0.156
## 93                Neurotic =~       dsq_anticipation  4.119  1.010   1.614    0.380    0.380
## 204       dsq_anticipation ~~             dsq_denial  4.089 -1.770  -1.770   -0.161   -0.161
## 302       dsq_somatization ~~          dsq_splitting  4.009  3.110   3.110    0.179    0.179
## 308         dsq_acting_out ~~          dsq_splitting  3.971  2.519   2.519    0.152    0.152
## 126       Image_Distorting =~       dsq_idealization  3.913  0.597   1.054    0.260    0.260
## 316          dsq_isolation ~~        dsq_devaluation  3.901  2.159   2.159    0.165    0.165
## 230 dsq_reaction_formation ~~       dsq_dissociation  3.897  1.617   1.617    0.150    0.150

4.2.7 Adding correlated errors in Four Factor Solution I

model_4f_adj_ds_I <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_isolation + dsq_dissociation + dsq_devaluation + dsq_splitting + dsq_denial

  # Add residual correlation within Image-Distorting factor
  dsq_dissociation ~~ dsq_denial
'
fit4_adjds_I <- cfa(model_4f_adj_ds_I, data = ds_df, estimator = "mlr", missing = "fiml")
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite ; use lavInspect(fit, "cov.lv") to investigate.
summary(fit4_adjds_I,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 167 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        67
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               266.855     242.912
##   Degrees of freedom                               163         163
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.099
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               724.594     635.432
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.140
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.806       0.821
##   Tucker-Lewis Index (TLI)                       0.774       0.791
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.836
##   Robust Tucker-Lewis Index (TLI)                            0.809
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10816.666  -10816.666
##   Scaling correction factor                                  1.088
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10683.239  -10683.239
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21767.332   21767.332
##   Bayesian (BIC)                             21991.589   21991.589
##   Sample-size adjusted Bayesian (SABIC)      21779.294   21779.294
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.055       0.048
##   90 Percent confidence interval - lower         0.043       0.036
##   90 Percent confidence interval - upper         0.067       0.060
##   P-value H_0: RMSEA <= 0.050                    0.235       0.579
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.051
##   90 Percent confidence interval - lower                     0.036
##   90 Percent confidence interval - upper                     0.065
##   P-value H_0: Robust RMSEA <= 0.050                         0.434
##   P-value H_0: Robust RMSEA >= 0.080                         0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.082       0.082
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.185    0.486
##     dsq_suppressin       0.854    0.265    3.229    0.001    1.867    0.461
##     dsq_sublimatin       0.720    0.219    3.293    0.001    1.572    0.395
##     dsq_anticipatn       0.988    0.243    4.065    0.000    2.160    0.508
##     dsq_rationlztn       1.287    0.250    5.152    0.000    2.812    0.688
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.618    0.402
##     dsq_idealizatn       1.121    0.378    2.964    0.003    1.814    0.447
##     dsq_psed_ltrsm       0.579    0.254    2.276    0.023    0.937    0.252
##     dsq_undoing          0.996    0.486    2.050    0.040    1.612    0.394
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.367    0.635
##     dsq_displacmnt       0.475    0.110    4.310    0.000    1.600    0.391
##     dsq_pssv_ggrss       0.736    0.119    6.171    0.000    2.477    0.636
##     dsq_somatizatn       0.496    0.152    3.274    0.001    1.672    0.351
##     dsq_acting_out       0.721    0.133    5.411    0.000    2.427    0.496
##     dsq_projection       0.760    0.117    6.517    0.000    2.559    0.640
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.872    0.382
##     dsq_dissociatn       0.308    0.340    0.906    0.365    0.576    0.184
##     dsq_devaluatin       0.922    0.233    3.962    0.000    1.726    0.533
##     dsq_splitting        0.747    0.407    1.836    0.066    1.399    0.340
##     dsq_denial           0.612    0.251    2.441    0.015    1.145    0.341
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_dissociation ~~                                                      
##    .dsq_denial           3.389    0.923    3.669    0.000    3.389    0.349
##   Mature ~~                                                                
##     Neurotic             3.103    1.167    2.660    0.008    0.878    0.878
##     Immature            -1.189    0.940   -1.265    0.206   -0.162   -0.162
##     Image_Distrtng       0.914    0.894    1.022    0.307    0.223    0.223
##   Neurotic ~~                                                              
##     Immature             1.289    0.923    1.396    0.163    0.236    0.236
##     Image_Distrtng       0.972    0.808    1.203    0.229    0.321    0.321
##   Immature ~~                                                              
##     Image_Distrtng       5.224    1.616    3.232    0.001    0.829    0.829
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.817    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.487    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.649    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.076    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.289   29.138    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.326    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.119    0.000    8.100    1.996
##    .dsq_psed_ltrsm   11.032    0.264   41.786    0.000   11.032    2.968
##    .dsq_undoing       9.453    0.290   32.581    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.323    0.376   27.439    0.000   10.323    1.946
##    .dsq_displacmnt   10.040    0.291   34.535    0.000   10.040    2.450
##    .dsq_pssv_ggrss    8.765    0.276   31.702    0.000    8.765    2.250
##    .dsq_somatizatn   11.559    0.388   29.825    0.000   11.559    2.424
##    .dsq_acting_out   10.729    0.347   30.891    0.000   10.729    2.193
##    .dsq_projection    8.165    0.283   28.840    0.000    8.165    2.042
##    .dsq_isolation     9.847    0.349   28.246    0.000    9.847    2.007
##    .dsq_dissociatn    5.262    0.223   23.627    0.000    5.262    1.683
##    .dsq_devaluatin    7.185    0.230   31.225    0.000    7.185    2.218
##    .dsq_splitting    10.010    0.292   34.266    0.000   10.010    2.434
##    .dsq_denial        5.392    0.239   22.527    0.000    5.392    1.606
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        15.482    1.870    8.277    0.000   15.482    0.764
##    .dsq_suppressin   12.937    2.014    6.423    0.000   12.937    0.788
##    .dsq_sublimatin   13.362    1.506    8.875    0.000   13.362    0.844
##    .dsq_anticipatn   13.407    1.526    8.785    0.000   13.407    0.742
##    .dsq_rationlztn    8.776    1.489    5.895    0.000    8.776    0.526
##    .dsq_rctn_frmtn   13.586    1.944    6.990    0.000   13.586    0.838
##    .dsq_idealizatn   13.181    1.841    7.161    0.000   13.181    0.800
##    .dsq_psed_ltrsm   12.939    1.305    9.913    0.000   12.939    0.936
##    .dsq_undoing      14.133    1.841    7.679    0.000   14.133    0.845
##    .dsq_tstc_fntsy   16.817    2.451    6.861    0.000   16.817    0.597
##    .dsq_displacmnt   14.226    1.377   10.329    0.000   14.226    0.847
##    .dsq_pssv_ggrss    9.043    1.375    6.578    0.000    9.043    0.596
##    .dsq_somatizatn   19.935    2.234    8.923    0.000   19.935    0.877
##    .dsq_acting_out   18.044    1.894    9.527    0.000   18.044    0.754
##    .dsq_projection    9.443    1.369    6.898    0.000    9.443    0.591
##    .dsq_isolation    20.568    2.402    8.563    0.000   20.568    0.854
##    .dsq_dissociatn    9.446    1.046    9.028    0.000    9.446    0.966
##    .dsq_devaluatin    7.511    1.392    5.395    0.000    7.511    0.716
##    .dsq_splitting    14.964    1.747    8.568    0.000   14.964    0.884
##    .dsq_denial        9.966    1.019    9.782    0.000    9.966    0.884
##     Mature            4.775    1.909    2.501    0.012    1.000    1.000
##     Neurotic          2.619    1.731    1.513    0.130    1.000    1.000
##     Immature         11.337    2.487    4.558    0.000    1.000    1.000
##     Image_Distrtng    3.504    2.279    1.537    0.124    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.236
##     dsq_suppressin    0.212
##     dsq_sublimatin    0.156
##     dsq_anticipatn    0.258
##     dsq_rationlztn    0.474
##     dsq_rctn_frmtn    0.162
##     dsq_idealizatn    0.200
##     dsq_psed_ltrsm    0.064
##     dsq_undoing       0.155
##     dsq_tstc_fntsy    0.403
##     dsq_displacmnt    0.153
##     dsq_pssv_ggrss    0.404
##     dsq_somatizatn    0.123
##     dsq_acting_out    0.246
##     dsq_projection    0.409
##     dsq_isolation     0.146
##     dsq_dissociatn    0.034
##     dsq_devaluatin    0.284
##     dsq_splitting     0.116
##     dsq_denial        0.116
modindices(fit4_adjds_I, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 87                  Mature =~       dsq_dissociation 24.586  0.557   1.218    0.389    0.389
## 103               Neurotic =~       dsq_dissociation 23.807  0.858   1.389    0.444    0.444
## 126       Image_Distorting =~ dsq_reaction_formation 17.976 -0.978  -1.831   -0.455   -0.455
## 117               Immature =~       dsq_dissociation 15.165 -0.641  -2.158   -0.690   -0.690
## 112               Immature =~ dsq_reaction_formation 15.063 -0.416  -1.402   -0.348   -0.348
## 246       dsq_idealization ~~          dsq_splitting 11.539  3.676   3.676    0.262    0.262
## 228 dsq_reaction_formation ~~         dsq_acting_out 10.099 -3.832  -3.832   -0.245   -0.245
## 129       Image_Distorting =~            dsq_undoing  9.204  0.707   1.324    0.324    0.324
## 115               Immature =~            dsq_undoing  9.149  0.328   1.105    0.270    0.270
## 214    dsq_rationalization ~~         dsq_acting_out  7.108  2.891   2.891    0.230    0.230
## 76                  Mature =~ dsq_reaction_formation  7.056  1.041   2.276    0.565    0.565
## 254    dsq_pseudo_altruism ~~         dsq_projection  6.725  2.271   2.271    0.205    0.205
## 79                  Mature =~            dsq_undoing  6.251 -0.991  -2.165   -0.529   -0.529
## 151              dsq_humor ~~       dsq_dissociation  6.053  2.076   2.076    0.172    0.172
## 232 dsq_reaction_formation ~~        dsq_devaluation  5.563 -1.962  -1.962   -0.194   -0.194
## 197       dsq_anticipation ~~ dsq_passive_aggression  5.493  2.122   2.122    0.193    0.193
## 165        dsq_suppression ~~       dsq_somatization  5.211 -3.324  -3.324   -0.207   -0.207
## 160        dsq_suppression ~~    dsq_pseudo_altruism  5.152 -2.243  -2.243   -0.173   -0.173
## 285       dsq_displacement ~~          dsq_isolation  5.122 -2.932  -2.932   -0.171   -0.171
## 281       dsq_displacement ~~ dsq_passive_aggression  5.070  2.155   2.155    0.190    0.190
## 322        dsq_devaluation ~~          dsq_splitting  4.807 -2.091  -2.091   -0.197   -0.197
## 110               Immature =~       dsq_anticipation  4.389  0.206   0.693    0.163    0.163
## 177        dsq_sublimation ~~    dsq_pseudo_altruism  4.309  2.045   2.045    0.156    0.156
## 217    dsq_rationalization ~~       dsq_dissociation  4.213  1.444   1.444    0.159    0.159
## 137              dsq_humor ~~        dsq_sublimation  4.213 -2.357  -2.357   -0.164   -0.164
## 170        dsq_suppression ~~        dsq_devaluation  4.167  1.621   1.621    0.164    0.164
## 124       Image_Distorting =~       dsq_anticipation  4.129  0.384   0.719    0.169    0.169
## 150              dsq_humor ~~          dsq_isolation  4.120 -2.794  -2.794   -0.157   -0.157
## 102               Neurotic =~          dsq_isolation  4.035 -0.628  -1.017   -0.207   -0.207
## 188        dsq_sublimation ~~          dsq_splitting  3.918  2.096   2.096    0.148    0.148
## 183        dsq_sublimation ~~         dsq_acting_out  3.877  2.326   2.326    0.150    0.150

4.2.8 Adding correlated errors in Four Factor Solution II

model_4f_adj_ds_II <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_isolation + dsq_dissociation + dsq_devaluation + dsq_splitting + dsq_denial

  # Add residual correlation within Image-Distorting factor
  dsq_dissociation ~~ dsq_denial
  
  # Add residual correlation within Immature factor
  dsq_displacement ~~ dsq_passive_aggression
'
fit4_adjds_II <- cfa(model_4f_adj_ds_II, data = ds_df, estimator = "mlr", missing = "fiml")
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite ; use lavInspect(fit, "cov.lv") to investigate.
summary(fit4_adjds_II,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 177 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        68
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               261.769     238.209
##   Degrees of freedom                               162         162
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.099
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               724.594     635.432
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.140
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.813       0.829
##   Tucker-Lewis Index (TLI)                       0.781       0.799
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.842
##   Robust Tucker-Lewis Index (TLI)                            0.815
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10814.123  -10814.123
##   Scaling correction factor                                  1.087
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10683.239  -10683.239
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21764.247   21764.247
##   Bayesian (BIC)                             21991.850   21991.850
##   Sample-size adjusted Bayesian (SABIC)      21776.387   21776.387
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.054       0.047
##   90 Percent confidence interval - lower         0.042       0.034
##   90 Percent confidence interval - upper         0.066       0.059
##   P-value H_0: RMSEA <= 0.050                    0.277       0.630
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.050
##   90 Percent confidence interval - lower                     0.034
##   90 Percent confidence interval - upper                     0.065
##   P-value H_0: Robust RMSEA <= 0.050                         0.472
##   P-value H_0: Robust RMSEA >= 0.080                         0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.082       0.082
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.191    0.487
##     dsq_suppressin       0.851    0.262    3.251    0.001    1.864    0.460
##     dsq_sublimatin       0.716    0.217    3.299    0.001    1.568    0.394
##     dsq_anticipatn       0.990    0.243    4.081    0.000    2.169    0.510
##     dsq_rationlztn       1.281    0.247    5.175    0.000    2.805    0.687
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.607    0.399
##     dsq_idealizatn       1.126    0.378    2.983    0.003    1.810    0.446
##     dsq_psed_ltrsm       0.594    0.264    2.250    0.024    0.954    0.257
##     dsq_undoing          1.003    0.482    2.080    0.037    1.612    0.394
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.383    0.638
##     dsq_displacmnt       0.412    0.107    3.839    0.000    1.394    0.340
##     dsq_pssv_ggrss       0.699    0.116    6.041    0.000    2.366    0.607
##     dsq_somatizatn       0.488    0.153    3.189    0.001    1.650    0.346
##     dsq_acting_out       0.715    0.133    5.368    0.000    2.419    0.494
##     dsq_projection       0.771    0.122    6.339    0.000    2.608    0.652
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.865    0.380
##     dsq_dissociatn       0.317    0.333    0.950    0.342    0.591    0.189
##     dsq_devaluatin       0.909    0.228    3.996    0.000    1.695    0.524
##     dsq_splitting        0.775    0.402    1.929    0.054    1.446    0.352
##     dsq_denial           0.598    0.243    2.460    0.014    1.115    0.332
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_dissociation ~~                                                      
##    .dsq_denial           3.390    0.906    3.741    0.000    3.390    0.348
##  .dsq_displacement ~~                                                      
##    .dsq_pssv_ggrss       2.193    1.228    1.785    0.074    2.193    0.184
##   Mature ~~                                                                
##     Neurotic             3.093    1.160    2.667    0.008    0.879    0.879
##     Immature            -1.212    0.972   -1.247    0.212   -0.164   -0.164
##     Image_Distrtng       0.936    0.880    1.063    0.288    0.229    0.229
##   Neurotic ~~                                                              
##     Immature             1.335    0.915    1.459    0.144    0.245    0.245
##     Image_Distrtng       0.997    0.780    1.278    0.201    0.333    0.333
##   Immature ~~                                                              
##     Image_Distrtng       5.426    1.663    3.263    0.001    0.860    0.860
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.819    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.486    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.650    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.073    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.289   29.138    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.322    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.116    0.000    8.100    1.996
##    .dsq_psed_ltrsm   11.032    0.264   41.788    0.000   11.032    2.968
##    .dsq_undoing       9.453    0.290   32.577    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.323    0.376   27.441    0.000   10.323    1.946
##    .dsq_displacmnt   10.038    0.291   34.541    0.000   10.038    2.450
##    .dsq_pssv_ggrss    8.764    0.276   31.710    0.000    8.764    2.249
##    .dsq_somatizatn   11.553    0.388   29.804    0.000   11.553    2.422
##    .dsq_acting_out   10.729    0.347   30.893    0.000   10.729    2.193
##    .dsq_projection    8.165    0.283   28.841    0.000    8.165    2.042
##    .dsq_isolation     9.848    0.349   28.246    0.000    9.848    2.007
##    .dsq_dissociatn    5.262    0.223   23.625    0.000    5.262    1.683
##    .dsq_devaluatin    7.185    0.230   31.227    0.000    7.185    2.218
##    .dsq_splitting    10.011    0.292   34.266    0.000   10.011    2.434
##    .dsq_denial        5.392    0.239   22.527    0.000    5.392    1.606
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        15.458    1.866    8.286    0.000   15.458    0.763
##    .dsq_suppressin   12.948    2.007    6.453    0.000   12.948    0.788
##    .dsq_sublimatin   13.376    1.506    8.885    0.000   13.376    0.845
##    .dsq_anticipatn   13.365    1.520    8.790    0.000   13.365    0.740
##    .dsq_rationlztn    8.811    1.481    5.948    0.000    8.811    0.528
##    .dsq_rctn_frmtn   13.623    1.931    7.054    0.000   13.623    0.841
##    .dsq_idealizatn   13.196    1.851    7.131    0.000   13.196    0.801
##    .dsq_psed_ltrsm   12.907    1.301    9.922    0.000   12.907    0.934
##    .dsq_undoing      14.135    1.818    7.774    0.000   14.135    0.845
##    .dsq_tstc_fntsy   16.706    2.450    6.820    0.000   16.706    0.593
##    .dsq_displacmnt   14.842    1.453   10.214    0.000   14.842    0.884
##    .dsq_pssv_ggrss    9.582    1.473    6.503    0.000    9.582    0.631
##    .dsq_somatizatn   20.024    2.240    8.939    0.000   20.024    0.880
##    .dsq_acting_out   18.082    1.913    9.453    0.000   18.082    0.756
##    .dsq_projection    9.187    1.374    6.685    0.000    9.187    0.575
##    .dsq_isolation    20.594    2.396    8.596    0.000   20.594    0.855
##    .dsq_dissociatn    9.428    1.041    9.061    0.000    9.428    0.964
##    .dsq_devaluatin    7.614    1.320    5.770    0.000    7.614    0.726
##    .dsq_splitting    14.831    1.705    8.698    0.000   14.831    0.876
##    .dsq_denial       10.036    1.019    9.850    0.000   10.036    0.890
##     Mature            4.800    1.906    2.518    0.012    1.000    1.000
##     Neurotic          2.582    1.706    1.513    0.130    1.000    1.000
##     Immature         11.447    2.503    4.573    0.000    1.000    1.000
##     Image_Distrtng    3.478    2.273    1.530    0.126    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.237
##     dsq_suppressin    0.212
##     dsq_sublimatin    0.155
##     dsq_anticipatn    0.260
##     dsq_rationlztn    0.472
##     dsq_rctn_frmtn    0.159
##     dsq_idealizatn    0.199
##     dsq_psed_ltrsm    0.066
##     dsq_undoing       0.155
##     dsq_tstc_fntsy    0.407
##     dsq_displacmnt    0.116
##     dsq_pssv_ggrss    0.369
##     dsq_somatizatn    0.120
##     dsq_acting_out    0.244
##     dsq_projection    0.425
##     dsq_isolation     0.145
##     dsq_dissociatn    0.036
##     dsq_devaluatin    0.274
##     dsq_splitting     0.124
##     dsq_denial        0.110
modindices(fit4_adjds_II, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 88                  Mature =~       dsq_dissociation 24.290  0.552   1.210    0.387    0.387
## 104               Neurotic =~       dsq_dissociation 23.770  0.869   1.397    0.447    0.447
## 127       Image_Distorting =~ dsq_reaction_formation 18.078 -0.980  -1.828   -0.454   -0.454
## 118               Immature =~       dsq_dissociation 17.015 -0.703  -2.377   -0.760   -0.760
## 113               Immature =~ dsq_reaction_formation 15.329 -0.420  -1.420   -0.353   -0.353
## 247       dsq_idealization ~~          dsq_splitting 11.504  3.665   3.665    0.262    0.262
## 229 dsq_reaction_formation ~~         dsq_acting_out 10.214 -3.868  -3.868   -0.246   -0.246
## 130       Image_Distorting =~            dsq_undoing  8.875  0.695   1.297    0.317    0.317
## 116               Immature =~            dsq_undoing  8.634  0.319   1.079    0.264    0.264
## 77                  Mature =~ dsq_reaction_formation  7.284  1.038   2.274    0.565    0.565
## 215    dsq_rationalization ~~         dsq_acting_out  7.189  2.919   2.919    0.231    0.231
## 255    dsq_pseudo_altruism ~~         dsq_projection  6.365  2.204   2.204    0.202    0.202
## 152              dsq_humor ~~       dsq_dissociation  6.128  2.087   2.087    0.173    0.173
## 80                  Mature =~            dsq_undoing  5.991 -0.953  -2.089   -0.511   -0.511
## 233 dsq_reaction_formation ~~        dsq_devaluation  5.500 -1.949  -1.949   -0.191   -0.191
## 166        dsq_suppression ~~       dsq_somatization  5.298 -3.360  -3.360   -0.209   -0.209
## 161        dsq_suppression ~~    dsq_pseudo_altruism  5.141 -2.240  -2.240   -0.173   -0.173
## 322        dsq_devaluation ~~          dsq_splitting  5.004 -2.126  -2.126   -0.200   -0.200
## 198       dsq_anticipation ~~ dsq_passive_aggression  4.636  1.926   1.926    0.170    0.170
## 291 dsq_passive_aggression ~~         dsq_acting_out  4.508  2.349   2.349    0.178    0.178
## 178        dsq_sublimation ~~    dsq_pseudo_altruism  4.296  2.042   2.042    0.155    0.155
## 218    dsq_rationalization ~~       dsq_dissociation  4.285  1.458   1.458    0.160    0.160
## 138              dsq_humor ~~        dsq_sublimation  4.210 -2.356  -2.356   -0.164   -0.164
## 103               Neurotic =~          dsq_isolation  4.172 -0.648  -1.041   -0.212   -0.212
## 171        dsq_suppression ~~        dsq_devaluation  4.145  1.617   1.617    0.163    0.163
## 285       dsq_displacement ~~          dsq_isolation  4.069 -2.576  -2.576   -0.147   -0.147
## 151              dsq_humor ~~          dsq_isolation  4.055 -2.770  -2.770   -0.155   -0.155
## 111               Immature =~       dsq_anticipation  3.977  0.196   0.662    0.156    0.156

4.2.9 Adding correlated errors in Four Factor Solution III

model_4f_adj_ds_III <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_isolation + dsq_dissociation + dsq_devaluation + dsq_splitting + dsq_denial

  # Add residual correlation within Image-Distorting factor
  dsq_dissociation ~~ dsq_denial
  dsq_devaluation ~~ dsq_splitting
  
  # Add residual correlation within Immature factor
  dsq_displacement ~~ dsq_passive_aggression
'
fit4_adjds_III <- cfa(model_4f_adj_ds_III, data = ds_df, estimator = "mlr", missing = "fiml")
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite ; use lavInspect(fit, "cov.lv") to investigate.
summary(fit4_adjds_III,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 175 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        69
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               256.620     231.721
##   Degrees of freedom                               161         161
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.107
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               724.594     635.432
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.140
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.821       0.841
##   Tucker-Lewis Index (TLI)                       0.789       0.813
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.850
##   Robust Tucker-Lewis Index (TLI)                            0.824
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10811.549  -10811.549
##   Scaling correction factor                                  1.068
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10683.239  -10683.239
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21761.097   21761.097
##   Bayesian (BIC)                             21992.048   21992.048
##   Sample-size adjusted Bayesian (SABIC)      21773.416   21773.416
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.053       0.046
##   90 Percent confidence interval - lower         0.041       0.033
##   90 Percent confidence interval - upper         0.065       0.058
##   P-value H_0: RMSEA <= 0.050                    0.323       0.707
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.049
##   90 Percent confidence interval - lower                     0.033
##   90 Percent confidence interval - upper                     0.064
##   P-value H_0: Robust RMSEA <= 0.050                         0.523
##   P-value H_0: Robust RMSEA >= 0.080                         0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.082       0.082
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.194    0.488
##     dsq_suppressin       0.844    0.260    3.250    0.001    1.851    0.457
##     dsq_sublimatin       0.716    0.216    3.310    0.001    1.572    0.395
##     dsq_anticipatn       0.991    0.245    4.043    0.000    2.174    0.511
##     dsq_rationlztn       1.279    0.249    5.147    0.000    2.808    0.687
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.596    0.397
##     dsq_idealizatn       1.140    0.396    2.878    0.004    1.820    0.448
##     dsq_psed_ltrsm       0.592    0.265    2.236    0.025    0.946    0.254
##     dsq_undoing          1.011    0.495    2.043    0.041    1.614    0.395
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.401    0.641
##     dsq_displacmnt       0.407    0.104    3.921    0.000    1.384    0.338
##     dsq_pssv_ggrss       0.693    0.114    6.098    0.000    2.358    0.605
##     dsq_somatizatn       0.494    0.152    3.251    0.001    1.679    0.352
##     dsq_acting_out       0.721    0.132    5.464    0.000    2.451    0.501
##     dsq_projection       0.757    0.120    6.335    0.000    2.576    0.644
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.955    0.398
##     dsq_dissociatn       0.266    0.241    1.102    0.270    0.520    0.166
##     dsq_devaluatin       0.978    0.247    3.965    0.000    1.913    0.591
##     dsq_splitting        0.874    0.300    2.914    0.004    1.708    0.415
##     dsq_denial           0.553    0.198    2.791    0.005    1.081    0.322
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_dissociation ~~                                                      
##    .dsq_denial           3.486    0.873    3.991    0.000    3.486    0.356
##  .dsq_devaluation ~~                                                       
##    .dsq_splitting       -2.157    0.992   -2.174    0.030   -2.157   -0.221
##  .dsq_displacement ~~                                                      
##    .dsq_pssv_ggrss       2.229    1.218    1.830    0.067    2.229    0.186
##   Mature ~~                                                                
##     Neurotic             3.075    1.178    2.610    0.009    0.878    0.878
##     Immature            -1.207    0.977   -1.235    0.217   -0.162   -0.162
##     Image_Distrtng       0.752    0.726    1.036    0.300    0.175    0.175
##   Neurotic ~~                                                              
##     Immature             1.340    0.910    1.472    0.141    0.247    0.247
##     Image_Distrtng       0.953    0.666    1.431    0.152    0.305    0.305
##   Immature ~~                                                              
##     Image_Distrtng       5.333    1.386    3.847    0.000    0.802    0.802
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.820    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.486    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.650    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.073    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.289   29.140    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.323    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.120    0.000    8.100    1.996
##    .dsq_psed_ltrsm   11.032    0.264   41.788    0.000   11.032    2.968
##    .dsq_undoing       9.453    0.290   32.579    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.324    0.376   27.436    0.000   10.324    1.946
##    .dsq_displacmnt   10.038    0.291   34.541    0.000   10.038    2.450
##    .dsq_pssv_ggrss    8.764    0.276   31.707    0.000    8.764    2.249
##    .dsq_somatizatn   11.551    0.387   29.833    0.000   11.551    2.423
##    .dsq_acting_out   10.729    0.347   30.895    0.000   10.729    2.193
##    .dsq_projection    8.165    0.283   28.843    0.000    8.165    2.042
##    .dsq_isolation     9.848    0.349   28.238    0.000    9.848    2.007
##    .dsq_dissociatn    5.261    0.223   23.635    0.000    5.261    1.683
##    .dsq_devaluatin    7.186    0.230   31.221    0.000    7.186    2.219
##    .dsq_splitting    10.012    0.292   34.284    0.000   10.012    2.434
##    .dsq_denial        5.392    0.239   22.527    0.000    5.392    1.606
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        15.442    1.879    8.219    0.000   15.442    0.762
##    .dsq_suppressin   12.997    2.004    6.486    0.000   12.997    0.791
##    .dsq_sublimatin   13.365    1.502    8.899    0.000   13.365    0.844
##    .dsq_anticipatn   13.345    1.534    8.702    0.000   13.345    0.738
##    .dsq_rationlztn    8.799    1.481    5.939    0.000    8.799    0.527
##    .dsq_rctn_frmtn   13.658    1.952    6.998    0.000   13.658    0.843
##    .dsq_idealizatn   13.158    1.864    7.059    0.000   13.158    0.799
##    .dsq_psed_ltrsm   12.923    1.303    9.916    0.000   12.923    0.935
##    .dsq_undoing      14.126    1.812    7.796    0.000   14.126    0.844
##    .dsq_tstc_fntsy   16.588    2.403    6.902    0.000   16.588    0.589
##    .dsq_displacmnt   14.870    1.443   10.303    0.000   14.870    0.886
##    .dsq_pssv_ggrss    9.620    1.452    6.623    0.000    9.620    0.634
##    .dsq_somatizatn   19.909    2.259    8.812    0.000   19.909    0.876
##    .dsq_acting_out   17.924    1.892    9.476    0.000   17.924    0.749
##    .dsq_projection    9.354    1.383    6.765    0.000    9.354    0.585
##    .dsq_isolation    20.252    1.917   10.564    0.000   20.252    0.841
##    .dsq_dissociatn    9.507    0.979    9.712    0.000    9.507    0.972
##    .dsq_devaluatin    6.831    1.346    5.073    0.000    6.831    0.651
##    .dsq_splitting    14.005    1.749    8.010    0.000   14.005    0.828
##    .dsq_denial       10.110    0.979   10.325    0.000   10.110    0.896
##     Mature            4.815    1.914    2.515    0.012    1.000    1.000
##     Neurotic          2.548    1.737    1.467    0.142    1.000    1.000
##     Immature         11.566    2.473    4.678    0.000    1.000    1.000
##     Image_Distrtng    3.821    1.624    2.352    0.019    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.238
##     dsq_suppressin    0.209
##     dsq_sublimatin    0.156
##     dsq_anticipatn    0.262
##     dsq_rationlztn    0.473
##     dsq_rctn_frmtn    0.157
##     dsq_idealizatn    0.201
##     dsq_psed_ltrsm    0.065
##     dsq_undoing       0.156
##     dsq_tstc_fntsy    0.411
##     dsq_displacmnt    0.114
##     dsq_pssv_ggrss    0.366
##     dsq_somatizatn    0.124
##     dsq_acting_out    0.251
##     dsq_projection    0.415
##     dsq_isolation     0.159
##     dsq_dissociatn    0.028
##     dsq_devaluatin    0.349
##     dsq_splitting     0.172
##     dsq_denial        0.104
modindices(fit4_adjds_III, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 89                  Mature =~       dsq_dissociation 24.626  0.552   1.211    0.387    0.387
## 105               Neurotic =~       dsq_dissociation 23.443  0.839   1.339    0.428    0.428
## 128       Image_Distorting =~ dsq_reaction_formation 19.442 -0.935  -1.828   -0.454   -0.454
## 114               Immature =~ dsq_reaction_formation 16.190 -0.428  -1.456   -0.362   -0.362
## 248       dsq_idealization ~~          dsq_splitting 11.441  3.673   3.673    0.271    0.271
## 119               Immature =~       dsq_dissociation 10.440 -0.512  -1.743   -0.557   -0.557
## 230 dsq_reaction_formation ~~         dsq_acting_out  9.816 -3.783  -3.783   -0.242   -0.242
## 117               Immature =~            dsq_undoing  8.720  0.319   1.085    0.265    0.265
## 131       Image_Distorting =~            dsq_undoing  8.064  0.611   1.195    0.292    0.292
## 78                  Mature =~ dsq_reaction_formation  7.726  1.083   2.376    0.590    0.590
## 216    dsq_rationalization ~~         dsq_acting_out  7.208  2.917   2.917    0.232    0.232
## 81                  Mature =~            dsq_undoing  6.343 -0.996  -2.185   -0.534   -0.534
## 234 dsq_reaction_formation ~~        dsq_devaluation  6.316 -2.079  -2.079   -0.215   -0.215
## 256    dsq_pseudo_altruism ~~         dsq_projection  6.099  2.164   2.164    0.197    0.197
## 153              dsq_humor ~~       dsq_dissociation  6.038  2.071   2.071    0.171    0.171
## 167        dsq_suppression ~~       dsq_somatization  5.415 -3.394  -3.394   -0.211   -0.211
## 162        dsq_suppression ~~    dsq_pseudo_altruism  5.178 -2.251  -2.251   -0.174   -0.174
## 199       dsq_anticipation ~~ dsq_passive_aggression  4.504  1.897   1.897    0.167    0.167
## 139              dsq_humor ~~        dsq_sublimation  4.296 -2.382  -2.382   -0.166   -0.166
## 179        dsq_sublimation ~~    dsq_pseudo_altruism  4.234  2.027   2.027    0.154    0.154
## 219    dsq_rationalization ~~       dsq_dissociation  4.231  1.444   1.444    0.158    0.158
## 292 dsq_passive_aggression ~~         dsq_acting_out  4.230  2.267   2.267    0.173    0.173
## 112               Immature =~       dsq_anticipation  4.134  0.198   0.674    0.158    0.158
## 126       Image_Distorting =~       dsq_anticipation  3.974  0.355   0.694    0.163    0.163

4.2.10 Adding correlated errors in Four Factor Solution IV

model_4f_adj_ds_IV <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_isolation + dsq_dissociation + dsq_devaluation + dsq_splitting + dsq_denial

  # Add residual correlation within Image-Distorting factor
  dsq_dissociation ~~ dsq_denial
  dsq_devaluation ~~ dsq_splitting
  
  # Add residual correlation within Immature factor
  dsq_displacement ~~ dsq_passive_aggression
  
  # Add residual correlation within Mature factor
  dsq_humor ~~ dsq_sublimation
'
fit4_adjds_IV <- cfa(model_4f_adj_ds_IV, data = ds_df, estimator = "mlr", missing = "fiml")

summary(fit4_adjds_IV,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 188 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        70
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               252.083     228.153
##   Degrees of freedom                               160         160
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.105
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               724.594     635.432
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.140
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.828       0.847
##   Tucker-Lewis Index (TLI)                       0.795       0.818
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.857
##   Robust Tucker-Lewis Index (TLI)                            0.831
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10809.280  -10809.280
##   Scaling correction factor                                  1.074
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10683.239  -10683.239
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21758.561   21758.561
##   Bayesian (BIC)                             21992.858   21992.858
##   Sample-size adjusted Bayesian (SABIC)      21771.058   21771.058
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.052       0.045
##   90 Percent confidence interval - lower         0.040       0.032
##   90 Percent confidence interval - upper         0.064       0.057
##   P-value H_0: RMSEA <= 0.050                    0.365       0.736
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.048
##   90 Percent confidence interval - lower                     0.032
##   90 Percent confidence interval - upper                     0.063
##   P-value H_0: Robust RMSEA <= 0.050                         0.566
##   P-value H_0: Robust RMSEA >= 0.080                         0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.081       0.081
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.328    0.517
##     dsq_suppressin       0.767    0.250    3.069    0.002    1.786    0.441
##     dsq_sublimatin       0.739    0.191    3.870    0.000    1.720    0.432
##     dsq_anticipatn       0.928    0.230    4.037    0.000    2.160    0.508
##     dsq_rationlztn       1.208    0.238    5.082    0.000    2.813    0.689
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.565    0.389
##     dsq_idealizatn       1.179    0.416    2.832    0.005    1.844    0.454
##     dsq_psed_ltrsm       0.613    0.273    2.244    0.025    0.960    0.258
##     dsq_undoing          1.022    0.504    2.028    0.043    1.600    0.391
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.401    0.641
##     dsq_displacmnt       0.406    0.104    3.916    0.000    1.382    0.337
##     dsq_pssv_ggrss       0.695    0.114    6.100    0.000    2.364    0.607
##     dsq_somatizatn       0.491    0.152    3.234    0.001    1.672    0.351
##     dsq_acting_out       0.722    0.132    5.462    0.000    2.455    0.502
##     dsq_projection       0.756    0.119    6.344    0.000    2.572    0.643
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.951    0.398
##     dsq_dissociatn       0.266    0.245    1.087    0.277    0.519    0.166
##     dsq_devaluatin       0.977    0.248    3.939    0.000    1.906    0.589
##     dsq_splitting        0.885    0.305    2.900    0.004    1.726    0.420
##     dsq_denial           0.552    0.200    2.766    0.006    1.077    0.321
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_dissociation ~~                                                      
##    .dsq_denial           3.489    0.876    3.981    0.000    3.489    0.356
##  .dsq_devaluation ~~                                                       
##    .dsq_splitting       -2.182    0.996   -2.190    0.029   -2.182   -0.223
##  .dsq_displacement ~~                                                      
##    .dsq_pssv_ggrss       2.226    1.218    1.828    0.068    2.226    0.186
##  .dsq_humor ~~                                                             
##    .dsq_sublimatin      -2.436    1.336   -1.823    0.068   -2.436   -0.176
##   Mature ~~                                                                
##     Neurotic             3.160    1.204    2.624    0.009    0.867    0.867
##     Immature            -1.228    0.994   -1.234    0.217   -0.155   -0.155
##     Image_Distrtng       0.753    0.760    0.991    0.322    0.166    0.166
##   Neurotic ~~                                                              
##     Immature             1.330    0.884    1.505    0.132    0.250    0.250
##     Image_Distrtng       0.955    0.643    1.485    0.137    0.313    0.313
##   Immature ~~                                                              
##     Image_Distrtng       5.325    1.388    3.836    0.000    0.802    0.802
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.821    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.488    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.653    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.073    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.289   29.139    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.321    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.122    0.000    8.100    1.996
##    .dsq_psed_ltrsm   11.032    0.264   41.788    0.000   11.032    2.968
##    .dsq_undoing       9.453    0.290   32.578    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.324    0.376   27.436    0.000   10.324    1.946
##    .dsq_displacmnt   10.038    0.291   34.542    0.000   10.038    2.450
##    .dsq_pssv_ggrss    8.764    0.276   31.707    0.000    8.764    2.249
##    .dsq_somatizatn   11.551    0.387   29.830    0.000   11.551    2.423
##    .dsq_acting_out   10.729    0.347   30.894    0.000   10.729    2.193
##    .dsq_projection    8.165    0.283   28.844    0.000    8.165    2.042
##    .dsq_isolation     9.848    0.349   28.237    0.000    9.848    2.007
##    .dsq_dissociatn    5.261    0.223   23.635    0.000    5.261    1.683
##    .dsq_devaluatin    7.186    0.230   31.220    0.000    7.186    2.219
##    .dsq_splitting    10.013    0.292   34.285    0.000   10.013    2.434
##    .dsq_denial        5.392    0.239   22.528    0.000    5.392    1.605
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        14.836    2.036    7.286    0.000   14.836    0.732
##    .dsq_suppressin   13.233    1.980    6.685    0.000   13.233    0.806
##    .dsq_sublimatin   12.876    1.553    8.290    0.000   12.876    0.813
##    .dsq_anticipatn   13.407    1.495    8.966    0.000   13.407    0.742
##    .dsq_rationlztn    8.769    1.378    6.364    0.000    8.769    0.526
##    .dsq_rctn_frmtn   13.757    1.939    7.094    0.000   13.757    0.849
##    .dsq_idealizatn   13.070    1.871    6.984    0.000   13.070    0.793
##    .dsq_psed_ltrsm   12.896    1.303    9.894    0.000   12.896    0.933
##    .dsq_undoing      14.173    1.803    7.859    0.000   14.173    0.847
##    .dsq_tstc_fntsy   16.585    2.402    6.906    0.000   16.585    0.589
##    .dsq_displacmnt   14.876    1.442   10.318    0.000   14.876    0.886
##    .dsq_pssv_ggrss    9.593    1.452    6.607    0.000    9.593    0.632
##    .dsq_somatizatn   19.936    2.260    8.820    0.000   19.936    0.877
##    .dsq_acting_out   17.906    1.894    9.453    0.000   17.906    0.748
##    .dsq_projection    9.375    1.379    6.798    0.000    9.375    0.586
##    .dsq_isolation    20.266    1.923   10.536    0.000   20.266    0.842
##    .dsq_dissociatn    9.508    0.979    9.709    0.000    9.508    0.972
##    .dsq_devaluatin    6.855    1.363    5.030    0.000    6.855    0.654
##    .dsq_splitting    13.942    1.756    7.940    0.000   13.942    0.824
##    .dsq_denial       10.118    0.980   10.322    0.000   10.118    0.897
##     Mature            5.421    2.103    2.578    0.010    1.000    1.000
##     Neurotic          2.448    1.712    1.430    0.153    1.000    1.000
##     Immature         11.569    2.471    4.681    0.000    1.000    1.000
##     Image_Distrtng    3.806    1.630    2.334    0.020    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.268
##     dsq_suppressin    0.194
##     dsq_sublimatin    0.187
##     dsq_anticipatn    0.258
##     dsq_rationlztn    0.474
##     dsq_rctn_frmtn    0.151
##     dsq_idealizatn    0.207
##     dsq_psed_ltrsm    0.067
##     dsq_undoing       0.153
##     dsq_tstc_fntsy    0.411
##     dsq_displacmnt    0.114
##     dsq_pssv_ggrss    0.368
##     dsq_somatizatn    0.123
##     dsq_acting_out    0.252
##     dsq_projection    0.414
##     dsq_isolation     0.158
##     dsq_dissociatn    0.028
##     dsq_devaluatin    0.346
##     dsq_splitting     0.176
##     dsq_denial        0.103
modindices(fit4_adjds_IV, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 90                  Mature =~       dsq_dissociation 25.913  0.529   1.232    0.394    0.394
## 106               Neurotic =~       dsq_dissociation 24.392  0.873   1.366    0.437    0.437
## 129       Image_Distorting =~ dsq_reaction_formation 19.060 -0.925  -1.805   -0.448   -0.448
## 115               Immature =~ dsq_reaction_formation 15.758 -0.421  -1.433   -0.356   -0.356
## 248       dsq_idealization ~~          dsq_splitting 11.111  3.617   3.617    0.268    0.268
## 120               Immature =~       dsq_dissociation 10.775 -0.528  -1.795   -0.574   -0.574
## 230 dsq_reaction_formation ~~         dsq_acting_out  9.770 -3.779  -3.779   -0.241   -0.241
## 118               Immature =~            dsq_undoing  8.620  0.317   1.078    0.264    0.264
## 132       Image_Distorting =~            dsq_undoing  7.856  0.604   1.179    0.288    0.288
## 79                  Mature =~ dsq_reaction_formation  7.809  1.026   2.388    0.593    0.593
## 153              dsq_humor ~~       dsq_dissociation  6.735  2.162   2.162    0.182    0.182
## 216    dsq_rationalization ~~         dsq_acting_out  6.476  2.738   2.738    0.218    0.218
## 82                  Mature =~            dsq_undoing  6.427 -0.947  -2.205   -0.539   -0.539
## 234 dsq_reaction_formation ~~        dsq_devaluation  6.185 -2.058  -2.058   -0.212   -0.212
## 256    dsq_pseudo_altruism ~~         dsq_projection  6.150  2.173   2.173    0.198    0.198
## 167        dsq_suppression ~~       dsq_somatization  5.575 -3.459  -3.459   -0.213   -0.213
## 162        dsq_suppression ~~    dsq_pseudo_altruism  4.913 -2.189  -2.189   -0.168   -0.168
## 157        dsq_suppression ~~        dsq_sublimation  4.410 -2.228  -2.228   -0.171   -0.171
## 199       dsq_anticipation ~~ dsq_passive_aggression  4.370  1.863   1.863    0.164    0.164
## 292 dsq_passive_aggression ~~         dsq_acting_out  4.142  2.244   2.244    0.171    0.171
## 113               Immature =~       dsq_anticipation  3.988  0.193   0.656    0.154    0.154
## 127       Image_Distorting =~       dsq_anticipation  3.913  0.350   0.683    0.161    0.161

4.2.11 Removing weakest loading defense (pseudo altruism) Four Factor Solution V

model_4f_adj_ds_V <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_isolation + dsq_dissociation + dsq_devaluation + dsq_splitting + dsq_denial
'
fit4_adjds_V <- cfa(model_4f_adj_ds_V, data = ds_df, estimator = "mlr", missing = "fiml")

summary(fit4_adjds_V,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 156 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        63
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               254.087     235.533
##   Degrees of freedom                               146         146
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.079
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               682.859     596.718
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.144
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.789       0.790
##   Tucker-Lewis Index (TLI)                       0.753       0.754
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.816
##   Robust Tucker-Lewis Index (TLI)                            0.785
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10290.234  -10290.234
##   Scaling correction factor                                  1.135
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10163.191  -10163.191
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               20706.468   20706.468
##   Bayesian (BIC)                             20917.336   20917.336
##   Sample-size adjusted Bayesian (SABIC)      20717.716   20717.716
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.059       0.054
##   90 Percent confidence interval - lower         0.047       0.041
##   90 Percent confidence interval - upper         0.071       0.066
##   P-value H_0: RMSEA <= 0.050                    0.103       0.284
##   P-value H_0: RMSEA >= 0.080                    0.002       0.000
##                                                                   
##   Robust RMSEA                                               0.056
##   90 Percent confidence interval - lower                     0.041
##   90 Percent confidence interval - upper                     0.070
##   P-value H_0: Robust RMSEA <= 0.050                         0.245
##   P-value H_0: Robust RMSEA >= 0.080                         0.002
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.084       0.084
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.239    0.497
##     dsq_suppressin       0.865    0.255    3.391    0.001    1.936    0.478
##     dsq_sublimatin       0.685    0.205    3.348    0.001    1.533    0.385
##     dsq_anticipatn       0.938    0.230    4.080    0.000    2.100    0.494
##     dsq_rationlztn       1.245    0.237    5.244    0.000    2.788    0.683
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.555    0.386
##     dsq_idealizatn       1.257    0.406    3.093    0.002    1.954    0.482
##     dsq_undoing          1.019    0.549    1.856    0.063    1.584    0.387
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.305    0.623
##     dsq_displacmnt       0.501    0.119    4.222    0.000    1.654    0.404
##     dsq_pssv_ggrss       0.756    0.124    6.099    0.000    2.498    0.641
##     dsq_somatizatn       0.499    0.155    3.211    0.001    1.650    0.346
##     dsq_acting_out       0.739    0.139    5.329    0.000    2.444    0.500
##     dsq_projection       0.774    0.118    6.565    0.000    2.559    0.640
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.742    0.355
##     dsq_dissociatn       0.672    0.654    1.028    0.304    1.171    0.375
##     dsq_devaluatin       0.864    0.255    3.390    0.001    1.505    0.465
##     dsq_splitting        0.784    0.336    2.335    0.020    1.365    0.332
##     dsq_denial           0.882    0.563    1.566    0.117    1.536    0.457
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          3.002    1.230    2.441    0.015    0.862    0.862
##     Immature         -1.224    0.933   -1.312    0.190   -0.165   -0.165
##     Image_Distrtng    1.669    0.860    1.941    0.052    0.428    0.428
##   Neurotic ~~                                                           
##     Immature          1.220    0.893    1.367    0.172    0.237    0.237
##     Image_Distrtng    1.411    0.560    2.520    0.012    0.521    0.521
##   Immature ~~                                                           
##     Image_Distrtng    3.867    2.817    1.373    0.170    0.672    0.672
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.815    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.487    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.647    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.076    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.290   29.132    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.338    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.140    0.000    8.100    1.996
##    .dsq_undoing       9.453    0.290   32.582    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.322    0.376   27.443    0.000   10.322    1.945
##    .dsq_displacmnt   10.040    0.291   34.522    0.000   10.040    2.450
##    .dsq_pssv_ggrss    8.765    0.277   31.698    0.000    8.765    2.250
##    .dsq_somatizatn   11.563    0.388   29.769    0.000   11.563    2.425
##    .dsq_acting_out   10.729    0.347   30.900    0.000   10.729    2.193
##    .dsq_projection    8.164    0.283   28.840    0.000    8.164    2.042
##    .dsq_isolation     9.844    0.349   28.225    0.000    9.844    2.006
##    .dsq_dissociatn    5.265    0.223   23.616    0.000    5.265    1.684
##    .dsq_devaluatin    7.181    0.230   31.229    0.000    7.181    2.217
##    .dsq_splitting    10.008    0.292   34.262    0.000   10.008    2.433
##    .dsq_denial        5.393    0.239   22.543    0.000    5.393    1.606
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        15.244    1.901    8.018    0.000   15.244    0.753
##    .dsq_suppressin   12.677    2.025    6.259    0.000   12.677    0.772
##    .dsq_sublimatin   13.485    1.517    8.891    0.000   13.485    0.852
##    .dsq_anticipatn   13.662    1.514    9.022    0.000   13.662    0.756
##    .dsq_rationlztn    8.911    1.475    6.039    0.000    8.911    0.534
##    .dsq_rctn_frmtn   13.786    2.008    6.865    0.000   13.786    0.851
##    .dsq_idealizatn   12.651    2.057    6.149    0.000   12.651    0.768
##    .dsq_undoing      14.222    1.822    7.806    0.000   14.222    0.850
##    .dsq_tstc_fntsy   17.231    2.536    6.794    0.000   17.231    0.612
##    .dsq_displacmnt   14.049    1.406    9.995    0.000   14.049    0.837
##    .dsq_pssv_ggrss    8.942    1.349    6.628    0.000    8.942    0.589
##    .dsq_somatizatn   20.015    2.218    9.025    0.000   20.015    0.880
##    .dsq_acting_out   17.961    1.933    9.293    0.000   17.961    0.750
##    .dsq_projection    9.442    1.352    6.984    0.000    9.442    0.591
##    .dsq_isolation    21.036    2.301    9.143    0.000   21.036    0.874
##    .dsq_dissociatn    8.406    2.015    4.172    0.000    8.406    0.860
##    .dsq_devaluatin    8.221    1.417    5.801    0.000    8.221    0.784
##    .dsq_splitting    15.056    1.782    8.449    0.000   15.056    0.890
##    .dsq_denial        8.918    1.913    4.662    0.000    8.918    0.791
##     Mature            5.013    1.940    2.584    0.010    1.000    1.000
##     Neurotic          2.419    1.787    1.354    0.176    1.000    1.000
##     Immature         10.922    2.578    4.236    0.000    1.000    1.000
##     Image_Distrtng    3.034    2.093    1.450    0.147    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.247
##     dsq_suppressin    0.228
##     dsq_sublimatin    0.148
##     dsq_anticipatn    0.244
##     dsq_rationlztn    0.466
##     dsq_rctn_frmtn    0.149
##     dsq_idealizatn    0.232
##     dsq_undoing       0.150
##     dsq_tstc_fntsy    0.388
##     dsq_displacmnt    0.163
##     dsq_pssv_ggrss    0.411
##     dsq_somatizatn    0.120
##     dsq_acting_out    0.250
##     dsq_projection    0.409
##     dsq_isolation     0.126
##     dsq_dissociatn    0.140
##     dsq_devaluatin    0.216
##     dsq_splitting     0.110
##     dsq_denial        0.209
modindices(fit4_adjds_V, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 82                  Mature =~       dsq_dissociation 28.809  0.715   1.600    0.512    0.512
## 111               Immature =~       dsq_dissociation 27.251 -0.640  -2.114   -0.676   -0.676
## 98                Neurotic =~       dsq_dissociation 21.551  1.175   1.827    0.584    0.584
## 296       dsq_dissociation ~~             dsq_denial 18.388  3.095   3.095    0.357    0.357
## 120       Image_Distorting =~ dsq_reaction_formation 16.168 -1.249  -2.176   -0.540   -0.540
## 107               Immature =~ dsq_reaction_formation 14.332 -0.419  -1.385   -0.344   -0.344
## 232       dsq_idealization ~~          dsq_splitting 10.979  3.566   3.566    0.258    0.258
## 112               Immature =~        dsq_devaluation 10.600  0.429   1.416    0.437    0.437
## 215 dsq_reaction_formation ~~         dsq_acting_out 10.333 -3.893  -3.893   -0.247   -0.247
## 294       dsq_dissociation ~~        dsq_devaluation  9.512 -2.150  -2.150   -0.259   -0.259
## 219 dsq_reaction_formation ~~        dsq_devaluation  8.998 -2.517  -2.517   -0.236   -0.236
## 72                  Mature =~ dsq_reaction_formation  8.691  1.129   2.527    0.628    0.628
## 83                  Mature =~        dsq_devaluation  8.626 -0.417  -0.934   -0.288   -0.288
## 97                Neurotic =~          dsq_isolation  8.055 -1.121  -1.743   -0.355   -0.355
## 109               Immature =~            dsq_undoing  7.938  0.317   1.048    0.256    0.256
## 81                  Mature =~          dsq_isolation  7.249 -0.560  -1.255   -0.256   -0.256
## 74                  Mature =~            dsq_undoing  7.104 -1.038  -2.324   -0.568   -0.568
## 143              dsq_humor ~~       dsq_dissociation  6.992  2.321   2.321    0.205    0.205
## 202    dsq_rationalization ~~         dsq_acting_out  6.319  2.730   2.730    0.216    0.216
## 186       dsq_anticipation ~~ dsq_passive_aggression  5.898  2.214   2.214    0.200    0.200
## 142              dsq_humor ~~          dsq_isolation  5.684 -3.295  -3.295   -0.184   -0.184
## 99                Neurotic =~        dsq_devaluation  5.329 -0.631  -0.981   -0.303   -0.303
## 122       Image_Distorting =~            dsq_undoing  5.265  0.725   1.263    0.309    0.309
## 113               Immature =~          dsq_splitting  5.072  0.359   1.188    0.289    0.289
## 114               Immature =~             dsq_denial  4.676 -0.294  -0.971   -0.289   -0.289
## 156        dsq_suppression ~~       dsq_somatization  4.634 -3.121  -3.121   -0.196   -0.196
## 259       dsq_displacement ~~          dsq_isolation  4.384 -2.708  -2.708   -0.158   -0.158
## 255       dsq_displacement ~~ dsq_passive_aggression  4.312  2.011   2.011    0.179    0.179
## 130              dsq_humor ~~        dsq_sublimation  4.219 -2.352  -2.352   -0.164   -0.164
## 291          dsq_isolation ~~        dsq_devaluation  4.188  2.230   2.230    0.170    0.170
## 194       dsq_anticipation ~~             dsq_denial  4.167 -1.788  -1.788   -0.162   -0.162
## 277       dsq_somatization ~~          dsq_splitting  4.151  3.163   3.163    0.182    0.182
## 283         dsq_acting_out ~~          dsq_splitting  4.084  2.546   2.546    0.155    0.155
## 205    dsq_rationalization ~~       dsq_dissociation  3.860  1.472   1.472    0.170    0.170
## 89                Neurotic =~       dsq_anticipation  3.843  1.035   1.610    0.379    0.379
## 110               Immature =~          dsq_isolation  3.841  0.375   1.239    0.253    0.253

4.2.12 Removing weakest loading defense (splitting) Four Factor Solution VI

model_4f_adj_ds_VI <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_isolation + dsq_dissociation + dsq_devaluation + dsq_denial
'
fit4_adjds_VI <- cfa(model_4f_adj_ds_VI, data = ds_df, estimator = "mlr", missing = "fiml")

summary(fit4_adjds_VI,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 154 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        60
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               213.824     200.844
##   Degrees of freedom                               129         129
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.065
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               630.831     550.238
##   Degrees of freedom                               153         153
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.146
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.822       0.819
##   Tucker-Lewis Index (TLI)                       0.789       0.785
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.849
##   Robust Tucker-Lewis Index (TLI)                            0.821
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -9735.150   -9735.150
##   Scaling correction factor                                  1.159
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -9628.238   -9628.238
##   Scaling correction factor                                  1.095
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               19590.301   19590.301
##   Bayesian (BIC)                             19791.127   19791.127
##   Sample-size adjusted Bayesian (SABIC)      19601.013   19601.013
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.056       0.051
##   90 Percent confidence interval - lower         0.042       0.038
##   90 Percent confidence interval - upper         0.069       0.065
##   P-value H_0: RMSEA <= 0.050                    0.224       0.413
##   P-value H_0: RMSEA >= 0.080                    0.001       0.000
##                                                                   
##   Robust RMSEA                                               0.052
##   90 Percent confidence interval - lower                     0.035
##   90 Percent confidence interval - upper                     0.068
##   P-value H_0: Robust RMSEA <= 0.050                         0.390
##   P-value H_0: Robust RMSEA >= 0.080                         0.001
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.083       0.083
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.291    0.509
##     dsq_suppressin       0.845    0.250    3.379    0.001    1.936    0.478
##     dsq_sublimatin       0.661    0.191    3.459    0.001    1.513    0.380
##     dsq_anticipatn       0.889    0.221    4.014    0.000    2.036    0.479
##     dsq_rationlztn       1.226    0.229    5.344    0.000    2.809    0.688
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.601    0.398
##     dsq_idealizatn       1.207    0.353    3.423    0.001    1.932    0.476
##     dsq_undoing          0.982    0.539    1.822    0.068    1.573    0.384
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.230    0.609
##     dsq_displacmnt       0.540    0.122    4.425    0.000    1.745    0.426
##     dsq_pssv_ggrss       0.790    0.131    6.018    0.000    2.551    0.655
##     dsq_somatizatn       0.510    0.167    3.057    0.002    1.649    0.346
##     dsq_acting_out       0.746    0.147    5.061    0.000    2.411    0.493
##     dsq_projection       0.785    0.122    6.433    0.000    2.535    0.634
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               1.506    0.307
##     dsq_dissociatn       1.079    1.300    0.830    0.407    1.625    0.520
##     dsq_devaluatin       0.794    0.277    2.863    0.004    1.195    0.369
##     dsq_denial           1.328    1.100    1.207    0.228    1.999    0.595
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          3.157    1.228    2.570    0.010    0.861    0.861
##     Immature         -1.254    0.931   -1.346    0.178   -0.169   -0.169
##     Image_Distrtng    1.778    0.584    3.045    0.002    0.516    0.516
##   Neurotic ~~                                                           
##     Immature          1.175    0.933    1.259    0.208    0.227    0.227
##     Image_Distrtng    1.149    0.647    1.775    0.076    0.477    0.477
##   Immature ~~                                                           
##     Image_Distrtng    2.048    3.213    0.637    0.524    0.421    0.421
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.812    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.487    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.646    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.075    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.290   29.127    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.342    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.142    0.000    8.100    1.996
##    .dsq_undoing       9.453    0.290   32.579    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.322    0.376   27.439    0.000   10.322    1.945
##    .dsq_displacmnt   10.041    0.291   34.519    0.000   10.041    2.451
##    .dsq_pssv_ggrss    8.765    0.277   31.681    0.000    8.765    2.250
##    .dsq_somatizatn   11.565    0.388   29.806    0.000   11.565    2.426
##    .dsq_acting_out   10.728    0.347   30.892    0.000   10.728    2.193
##    .dsq_projection    8.164    0.283   28.833    0.000    8.164    2.042
##    .dsq_isolation     9.839    0.349   28.211    0.000    9.839    2.005
##    .dsq_dissociatn    5.264    0.223   23.634    0.000    5.264    1.683
##    .dsq_devaluatin    7.176    0.230   31.225    0.000    7.176    2.216
##    .dsq_denial        5.391    0.239   22.527    0.000    5.391    1.605
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        15.009    1.940    7.738    0.000   15.009    0.741
##    .dsq_suppressin   12.677    2.013    6.297    0.000   12.677    0.772
##    .dsq_sublimatin   13.545    1.524    8.888    0.000   13.545    0.855
##    .dsq_anticipatn   13.926    1.489    9.350    0.000   13.926    0.771
##    .dsq_rationlztn    8.790    1.440    6.104    0.000    8.790    0.527
##    .dsq_rctn_frmtn   13.641    2.032    6.714    0.000   13.641    0.842
##    .dsq_idealizatn   12.738    1.968    6.473    0.000   12.738    0.773
##    .dsq_undoing      14.260    1.872    7.615    0.000   14.260    0.852
##    .dsq_tstc_fntsy   17.716    2.551    6.945    0.000   17.716    0.629
##    .dsq_displacmnt   13.741    1.415    9.708    0.000   13.741    0.819
##    .dsq_pssv_ggrss    8.674    1.309    6.628    0.000    8.674    0.571
##    .dsq_somatizatn   20.013    2.266    8.831    0.000   20.013    0.880
##    .dsq_acting_out   18.120    1.984    9.133    0.000   18.120    0.757
##    .dsq_projection    9.564    1.448    6.604    0.000    9.564    0.598
##    .dsq_isolation    21.802    3.221    6.769    0.000   21.802    0.906
##    .dsq_dissociatn    7.138    2.948    2.422    0.015    7.138    0.730
##    .dsq_devaluatin    9.058    1.987    4.560    0.000    9.058    0.864
##    .dsq_denial        7.283    1.991    3.659    0.000    7.283    0.646
##     Mature            5.248    1.976    2.656    0.008    1.000    1.000
##     Neurotic          2.564    1.815    1.413    0.158    1.000    1.000
##     Immature         10.436    2.552    4.089    0.000    1.000    1.000
##     Image_Distrtng    2.267    3.004    0.755    0.450    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.259
##     dsq_suppressin    0.228
##     dsq_sublimatin    0.145
##     dsq_anticipatn    0.229
##     dsq_rationlztn    0.473
##     dsq_rctn_frmtn    0.158
##     dsq_idealizatn    0.227
##     dsq_undoing       0.148
##     dsq_tstc_fntsy    0.371
##     dsq_displacmnt    0.181
##     dsq_pssv_ggrss    0.429
##     dsq_somatizatn    0.120
##     dsq_acting_out    0.243
##     dsq_projection    0.402
##     dsq_isolation     0.094
##     dsq_dissociatn    0.270
##     dsq_devaluatin    0.136
##     dsq_denial        0.354
modindices(fit4_adjds_VI, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 79                  Mature =~       dsq_dissociation 25.095  0.757   1.735    0.555    0.555
## 107               Immature =~        dsq_devaluation 21.316  0.446   1.441    0.445    0.445
## 106               Immature =~       dsq_dissociation 18.159 -0.417  -1.346   -0.431   -0.431
## 94                Neurotic =~       dsq_dissociation 15.815  1.101   1.763    0.564    0.564
## 273       dsq_dissociation ~~        dsq_devaluation 14.462 -2.742  -2.742   -0.341   -0.341
## 102               Immature =~ dsq_reaction_formation 13.010 -0.414  -1.337   -0.332   -0.332
## 204 dsq_reaction_formation ~~         dsq_acting_out 11.149 -4.055  -4.055   -0.258   -0.258
## 208 dsq_reaction_formation ~~        dsq_devaluation 10.553 -2.759  -2.759   -0.248   -0.248
## 78                  Mature =~          dsq_isolation 10.073 -0.709  -1.625   -0.331   -0.331
## 80                  Mature =~        dsq_devaluation  9.025 -0.446  -1.022   -0.316   -0.316
## 274       dsq_dissociation ~~             dsq_denial  8.992  2.947   2.947    0.409    0.409
## 69                  Mature =~ dsq_reaction_formation  8.732  1.098   2.514    0.625    0.625
## 104               Immature =~            dsq_undoing  8.339  0.334   1.078    0.263    0.263
## 105               Immature =~          dsq_isolation  8.076  0.414   1.337    0.273    0.273
## 71                  Mature =~            dsq_undoing  7.420 -1.018  -2.331   -0.570   -0.570
## 271          dsq_isolation ~~        dsq_devaluation  7.317  2.964   2.964    0.211    0.211
## 192    dsq_rationalization ~~         dsq_acting_out  6.519  2.765   2.765    0.219    0.219
## 136              dsq_humor ~~          dsq_isolation  6.202 -3.457  -3.457   -0.191   -0.191
## 177       dsq_anticipation ~~ dsq_passive_aggression  6.017  2.241   2.241    0.204    0.204
## 137              dsq_humor ~~       dsq_dissociation  5.967  2.082   2.082    0.201    0.201
## 114       Image_Distorting =~ dsq_reaction_formation  5.500 -0.867  -1.305   -0.324   -0.324
## 184       dsq_anticipation ~~             dsq_denial  5.211 -1.966  -1.966   -0.195   -0.195
## 85                Neurotic =~       dsq_anticipation  4.847  1.120   1.793    0.422    0.422
## 93                Neurotic =~          dsq_isolation  4.793 -0.826  -1.322   -0.270   -0.270
## 229            dsq_undoing ~~        dsq_devaluation  4.659  1.868   1.868    0.164    0.164
## 124              dsq_humor ~~        dsq_sublimation  4.418 -2.391  -2.391   -0.168   -0.168
## 266         dsq_projection ~~          dsq_isolation  4.348  2.422   2.422    0.168    0.168
## 149        dsq_suppression ~~       dsq_somatization  4.166 -2.958  -2.958   -0.186   -0.186
## 165        dsq_sublimation ~~         dsq_acting_out  3.985  2.379   2.379    0.152    0.152
## 253 dsq_passive_aggression ~~        dsq_devaluation  3.966  1.460   1.460    0.165    0.165

4.2.13 Removing weakest loading defense (isolation) Four Factor Solution VII

model_4f_adj_ds_VII <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_dissociation + dsq_devaluation + dsq_denial
'
fit4_adjds_VII <- cfa(model_4f_adj_ds_VII, data = ds_df, estimator = "mlr", missing = "fiml")

summary(fit4_adjds_VII,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 156 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        57
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               180.983     166.948
##   Degrees of freedom                               113         113
##   P-value (Chi-square)                           0.000       0.001
##   Scaling correction factor                                  1.084
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               589.461     511.888
##   Degrees of freedom                               136         136
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.152
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.850       0.856
##   Tucker-Lewis Index (TLI)                       0.820       0.827
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.875
##   Robust Tucker-Lewis Index (TLI)                            0.850
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -9143.556   -9143.556
##   Scaling correction factor                                  1.124
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -9053.065   -9053.065
##   Scaling correction factor                                  1.097
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               18401.113   18401.113
##   Bayesian (BIC)                             18591.898   18591.898
##   Sample-size adjusted Bayesian (SABIC)      18411.289   18411.289
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.054       0.048
##   90 Percent confidence interval - lower         0.039       0.032
##   90 Percent confidence interval - upper         0.068       0.062
##   P-value H_0: RMSEA <= 0.050                    0.332       0.589
##   P-value H_0: RMSEA >= 0.080                    0.001       0.000
##                                                                   
##   Robust RMSEA                                               0.050
##   90 Percent confidence interval - lower                     0.030
##   90 Percent confidence interval - upper                     0.067
##   P-value H_0: Robust RMSEA <= 0.050                         0.499
##   P-value H_0: Robust RMSEA >= 0.080                         0.001
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.080       0.080
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.364    0.525
##     dsq_suppressin       0.794    0.230    3.460    0.001    1.877    0.463
##     dsq_sublimatin       0.648    0.181    3.591    0.000    1.533    0.385
##     dsq_anticipatn       0.838    0.188    4.450    0.000    1.980    0.466
##     dsq_rationlztn       1.197    0.209    5.714    0.000    2.829    0.693
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.624    0.404
##     dsq_idealizatn       1.204    0.347    3.466    0.001    1.956    0.482
##     dsq_undoing          0.948    0.547    1.734    0.083    1.541    0.377
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.203    0.604
##     dsq_displacmnt       0.556    0.122    4.559    0.000    1.780    0.434
##     dsq_pssv_ggrss       0.803    0.135    5.935    0.000    2.572    0.660
##     dsq_somatizatn       0.523    0.169    3.099    0.002    1.675    0.352
##     dsq_acting_out       0.756    0.148    5.091    0.000    2.420    0.495
##     dsq_projection       0.780    0.125    6.227    0.000    2.500    0.625
##   Image_Distorting =~                                                      
##     dsq_dissociatn       1.000                               2.077    0.664
##     dsq_devaluatin       0.331    0.441    0.750    0.453    0.687    0.212
##     dsq_denial           0.895    0.448    1.997    0.046    1.859    0.554
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          3.276    1.233    2.657    0.008    0.853    0.853
##     Immature         -1.296    0.945   -1.371    0.170   -0.171   -0.171
##     Image_Distrtng    3.144    1.586    1.982    0.048    0.640    0.640
##   Neurotic ~~                                                           
##     Immature          1.136    0.964    1.178    0.239    0.218    0.218
##     Image_Distrtng    1.807    1.129    1.600    0.110    0.535    0.535
##   Immature ~~                                                           
##     Image_Distrtng    1.453    1.553    0.936    0.349    0.218    0.218
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.811    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.487    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.646    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.074    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.290   29.129    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.343    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.143    0.000    8.100    1.996
##    .dsq_undoing       9.453    0.290   32.582    0.000    9.453    2.311
##    .dsq_tstc_fntsy   10.322    0.376   27.439    0.000   10.322    1.945
##    .dsq_displacmnt   10.041    0.291   34.539    0.000   10.041    2.451
##    .dsq_pssv_ggrss    8.766    0.277   31.683    0.000    8.766    2.250
##    .dsq_somatizatn   11.563    0.388   29.837    0.000   11.563    2.426
##    .dsq_acting_out   10.729    0.347   30.895    0.000   10.729    2.193
##    .dsq_projection    8.164    0.283   28.828    0.000    8.164    2.042
##    .dsq_dissociatn    5.262    0.223   23.631    0.000    5.262    1.683
##    .dsq_devaluatin    7.173    0.230   31.204    0.000    7.173    2.215
##    .dsq_denial        5.388    0.239   22.498    0.000    5.388    1.604
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        14.670    1.810    8.106    0.000   14.670    0.724
##    .dsq_suppressin   12.900    2.034    6.343    0.000   12.900    0.785
##    .dsq_sublimatin   13.486    1.512    8.921    0.000   13.486    0.852
##    .dsq_anticipatn   14.151    1.446    9.786    0.000   14.151    0.783
##    .dsq_rationlztn    8.677    1.355    6.406    0.000    8.677    0.520
##    .dsq_rctn_frmtn   13.567    2.057    6.596    0.000   13.567    0.837
##    .dsq_idealizatn   12.645    1.987    6.363    0.000   12.645    0.768
##    .dsq_undoing      14.359    1.931    7.437    0.000   14.359    0.858
##    .dsq_tstc_fntsy   17.890    2.543    7.034    0.000   17.890    0.635
##    .dsq_displacmnt   13.619    1.380    9.866    0.000   13.619    0.811
##    .dsq_pssv_ggrss    8.564    1.304    6.565    0.000    8.564    0.564
##    .dsq_somatizatn   19.903    2.289    8.695    0.000   19.903    0.876
##    .dsq_acting_out   18.075    1.995    9.058    0.000   18.075    0.755
##    .dsq_projection    9.740    1.475    6.605    0.000    9.740    0.609
##    .dsq_dissociatn    5.463    2.681    2.038    0.042    5.463    0.559
##    .dsq_devaluatin   10.014    1.165    8.599    0.000   10.014    0.955
##    .dsq_denial        7.821    1.589    4.921    0.000    7.821    0.693
##     Mature            5.587    1.871    2.986    0.003    1.000    1.000
##     Neurotic          2.639    1.864    1.416    0.157    1.000    1.000
##     Immature         10.262    2.509    4.090    0.000    1.000    1.000
##     Image_Distrtng    4.314    2.772    1.556    0.120    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.276
##     dsq_suppressin    0.215
##     dsq_sublimatin    0.148
##     dsq_anticipatn    0.217
##     dsq_rationlztn    0.480
##     dsq_rctn_frmtn    0.163
##     dsq_idealizatn    0.232
##     dsq_undoing       0.142
##     dsq_tstc_fntsy    0.365
##     dsq_displacmnt    0.189
##     dsq_pssv_ggrss    0.436
##     dsq_somatizatn    0.124
##     dsq_acting_out    0.245
##     dsq_projection    0.391
##     dsq_dissociatn    0.441
##     dsq_devaluatin    0.045
##     dsq_denial        0.307
modindices(fit4_adjds_VII, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 101               Immature =~        dsq_devaluation 26.658  0.446   1.429    0.441    0.441
## 75                  Mature =~       dsq_dissociation 16.778  1.067   2.522    0.807    0.807
## 100               Immature =~       dsq_dissociation 12.940 -0.367  -1.177   -0.376   -0.376
## 97                Immature =~ dsq_reaction_formation 12.570 -0.412  -1.321   -0.328   -0.328
## 193 dsq_reaction_formation ~~         dsq_acting_out 11.417 -4.100  -4.100   -0.262   -0.262
## 196 dsq_reaction_formation ~~        dsq_devaluation 11.049 -2.881  -2.881   -0.247   -0.247
## 250       dsq_dissociation ~~        dsq_devaluation 10.727 -2.454  -2.454   -0.332   -0.332
## 66                  Mature =~ dsq_reaction_formation  9.332  1.109   2.622    0.651    0.651
## 99                Immature =~            dsq_undoing  8.587  0.340   1.090    0.266    0.266
## 77                  Mature =~             dsq_denial  8.187 -0.672  -1.587   -0.473   -0.473
## 68                  Mature =~            dsq_undoing  7.842 -1.012  -2.392   -0.585   -0.585
## 91                Neurotic =~             dsq_denial  7.322 -1.354  -2.199   -0.655   -0.655
## 76                  Mature =~        dsq_devaluation  6.491 -0.446  -1.054   -0.325   -0.325
## 182    dsq_rationalization ~~         dsq_acting_out  6.361  2.709   2.709    0.216    0.216
## 168       dsq_anticipation ~~ dsq_passive_aggression  5.912  2.229   2.229    0.202    0.202
## 118              dsq_humor ~~        dsq_sublimation  5.347 -2.602  -2.602   -0.185   -0.185
## 81                Neurotic =~       dsq_anticipation  5.333  1.169   1.899    0.447    0.447
## 215            dsq_undoing ~~        dsq_devaluation  5.258  2.033   2.033    0.170    0.170
## 89                Neurotic =~       dsq_dissociation  5.188  1.317   2.139    0.684    0.684
## 223   dsq_autistic_fantasy ~~        dsq_devaluation  5.047  2.346   2.346    0.175    0.175
## 236 dsq_passive_aggression ~~        dsq_devaluation  4.922  1.657   1.657    0.179    0.179
## 146        dsq_suppression ~~        dsq_devaluation  4.353  1.771   1.771    0.156    0.156
## 142        dsq_suppression ~~       dsq_somatization  3.978 -2.897  -2.897   -0.181   -0.181
## 157        dsq_sublimation ~~         dsq_acting_out  3.971  2.370   2.370    0.152    0.152

4.2.14 Removing weakest loading defense (devaluation) Four Factor Solution VIII

model_4f_adj_ds_VIII <- '
  Mature =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation + dsq_rationalization
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_undoing
  Immature =~ dsq_autistic_fantasy + dsq_displacement + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  Image_Distorting =~ dsq_dissociation + dsq_denial
'
fit4_adjds_VIII <- cfa(model_4f_adj_ds_VIII, data = ds_df, estimator = "mlr", missing = "fiml")

summary(fit4_adjds_VIII,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 154 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        54
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               127.559     114.498
##   Degrees of freedom                                98          98
##   P-value (Chi-square)                           0.024       0.122
##   Scaling correction factor                                  1.114
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               532.796     457.883
##   Degrees of freedom                               120         120
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.164
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.928       0.951
##   Tucker-Lewis Index (TLI)                       0.912       0.940
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.956
##   Robust Tucker-Lewis Index (TLI)                            0.946
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -8631.576   -8631.576
##   Scaling correction factor                                  1.084
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -8567.797   -8567.797
##   Scaling correction factor                                  1.103
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               17371.153   17371.153
##   Bayesian (BIC)                             17551.897   17551.897
##   Sample-size adjusted Bayesian (SABIC)      17380.793   17380.793
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.038       0.028
##   90 Percent confidence interval - lower         0.015       0.000
##   90 Percent confidence interval - upper         0.055       0.047
##   P-value H_0: RMSEA <= 0.050                    0.865       0.975
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.030
##   90 Percent confidence interval - lower                     0.000
##   90 Percent confidence interval - upper                     0.053
##   P-value H_0: Robust RMSEA <= 0.050                         0.915
##   P-value H_0: Robust RMSEA >= 0.080                         0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.066       0.066
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               2.394    0.532
##     dsq_suppressin       0.763    0.210    3.628    0.000    1.825    0.450
##     dsq_sublimatin       0.646    0.180    3.579    0.000    1.546    0.389
##     dsq_anticipatn       0.829    0.184    4.496    0.000    1.985    0.467
##     dsq_rationlztn       1.184    0.206    5.738    0.000    2.835    0.694
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.652    0.410
##     dsq_idealizatn       1.191    0.335    3.554    0.000    1.966    0.485
##     dsq_undoing          0.917    0.529    1.734    0.083    1.515    0.370
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               3.196    0.602
##     dsq_displacmnt       0.560    0.125    4.495    0.000    1.790    0.437
##     dsq_pssv_ggrss       0.811    0.138    5.882    0.000    2.591    0.665
##     dsq_somatizatn       0.528    0.172    3.081    0.002    1.689    0.354
##     dsq_acting_out       0.758    0.149    5.103    0.000    2.423    0.495
##     dsq_projection       0.774    0.126    6.121    0.000    2.475    0.619
##   Image_Distorting =~                                                      
##     dsq_dissociatn       1.000                               2.490    0.796
##     dsq_denial           0.653    0.218    2.998    0.003    1.626    0.484
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          3.360    1.200    2.801    0.005    0.850    0.850
##     Immature         -1.300    0.952   -1.365    0.172   -0.170   -0.170
##     Image_Distrtng    3.679    0.928    3.966    0.000    0.617    0.617
##   Neurotic ~~                                                           
##     Immature          1.109    0.987    1.124    0.261    0.210    0.210
##     Image_Distrtng    2.067    1.041    1.986    0.047    0.503    0.503
##   Immature ~~                                                           
##     Image_Distrtng    0.602    1.035    0.582    0.561    0.076    0.076
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         8.244    0.319   25.812    0.000    8.244    1.832
##    .dsq_suppressin    6.760    0.288   23.486    0.000    6.760    1.668
##    .dsq_sublimatin    9.801    0.283   34.647    0.000    9.801    2.463
##    .dsq_anticipatn   11.810    0.302   39.073    0.000   11.810    2.778
##    .dsq_rationlztn    8.435    0.290   29.130    0.000    8.435    2.065
##    .dsq_rctn_frmtn    8.958    0.286   31.346    0.000    8.958    2.225
##    .dsq_idealizatn    8.100    0.288   28.145    0.000    8.100    1.996
##    .dsq_undoing       9.452    0.290   32.586    0.000    9.452    2.311
##    .dsq_tstc_fntsy   10.322    0.376   27.440    0.000   10.322    1.945
##    .dsq_displacmnt   10.042    0.291   34.542    0.000   10.042    2.451
##    .dsq_pssv_ggrss    8.766    0.277   31.684    0.000    8.766    2.250
##    .dsq_somatizatn   11.561    0.388   29.823    0.000   11.561    2.427
##    .dsq_acting_out   10.729    0.347   30.892    0.000   10.729    2.193
##    .dsq_projection    8.164    0.283   28.827    0.000    8.164    2.042
##    .dsq_dissociatn    5.259    0.222   23.666    0.000    5.259    1.682
##    .dsq_denial        5.385    0.239   22.530    0.000    5.385    1.604
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        14.527    1.762    8.246    0.000   14.527    0.717
##    .dsq_suppressin   13.092    2.009    6.517    0.000   13.092    0.797
##    .dsq_sublimatin   13.445    1.508    8.917    0.000   13.445    0.849
##    .dsq_anticipatn   14.131    1.444    9.788    0.000   14.131    0.782
##    .dsq_rationlztn    8.645    1.347    6.420    0.000    8.645    0.518
##    .dsq_rctn_frmtn   13.478    2.039    6.610    0.000   13.478    0.832
##    .dsq_idealizatn   12.604    1.964    6.419    0.000   12.604    0.765
##    .dsq_undoing      14.438    1.922    7.512    0.000   14.438    0.863
##    .dsq_tstc_fntsy   17.939    2.570    6.980    0.000   17.939    0.637
##    .dsq_displacmnt   13.584    1.381    9.836    0.000   13.584    0.809
##    .dsq_pssv_ggrss    8.466    1.304    6.495    0.000    8.466    0.558
##    .dsq_somatizatn   19.845    2.322    8.546    0.000   19.845    0.874
##    .dsq_acting_out   18.062    1.992    9.067    0.000   18.062    0.755
##    .dsq_projection    9.865    1.483    6.653    0.000    9.865    0.617
##    .dsq_dissociatn    3.579    1.959    1.827    0.068    3.579    0.366
##    .dsq_denial        8.634    1.188    7.267    0.000    8.634    0.766
##     Mature            5.730    1.851    3.095    0.002    1.000    1.000
##     Neurotic          2.728    1.879    1.451    0.147    1.000    1.000
##     Immature         10.214    2.523    4.048    0.000    1.000    1.000
##     Image_Distrtng    6.198    2.102    2.949    0.003    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.283
##     dsq_suppressin    0.203
##     dsq_sublimatin    0.151
##     dsq_anticipatn    0.218
##     dsq_rationlztn    0.482
##     dsq_rctn_frmtn    0.168
##     dsq_idealizatn    0.235
##     dsq_undoing       0.137
##     dsq_tstc_fntsy    0.363
##     dsq_displacmnt    0.191
##     dsq_pssv_ggrss    0.442
##     dsq_somatizatn    0.126
##     dsq_acting_out    0.245
##     dsq_projection    0.383
##     dsq_dissociatn    0.634
##     dsq_denial        0.234
modindices(fit4_adjds_VIII, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 92                Immature =~ dsq_reaction_formation 12.464 -0.413  -1.320   -0.328   -0.328
## 182 dsq_reaction_formation ~~         dsq_acting_out 11.519 -4.113  -4.113   -0.264   -0.264
## 63                  Mature =~ dsq_reaction_formation 10.156  1.180   2.826    0.702    0.702
## 94                Immature =~            dsq_undoing  8.958  0.346   1.107    0.271    0.271
## 65                  Mature =~            dsq_undoing  7.862 -1.023  -2.448   -0.598   -0.598
## 172    dsq_rationalization ~~         dsq_acting_out  6.340  2.700   2.700    0.216    0.216
## 95                Immature =~       dsq_dissociation  5.951 -0.311  -0.994   -0.318   -0.318
## 96                Immature =~             dsq_denial  5.951  0.203   0.649    0.193    0.193
## 72                  Mature =~       dsq_dissociation  5.915  1.372   3.285    1.051    1.051
## 73                  Mature =~             dsq_denial  5.915 -0.896  -2.145   -0.639   -0.639
## 112              dsq_humor ~~        dsq_sublimation  5.890 -2.725  -2.725   -0.195   -0.195
## 159       dsq_anticipation ~~ dsq_passive_aggression  5.648  2.174   2.174    0.199    0.199
## 77                Neurotic =~       dsq_anticipation  4.961  1.135   1.874    0.441    0.441
## 149        dsq_sublimation ~~         dsq_acting_out  4.038  2.388   2.388    0.153    0.153
## 135        dsq_suppression ~~       dsq_somatization  3.934 -2.892  -2.892   -0.179   -0.179

4.3 Knekt

4.3.1 One Factor Solution

fit1_kn <- cfa(model_1f_norat, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit1_kn,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 149 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        57
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               480.575     456.078
##   Degrees of freedom                               152         152
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.054
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               774.640     708.842
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.456       0.435
##   Tucker-Lewis Index (TLI)                       0.388       0.364
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.464
##   Robust Tucker-Lewis Index (TLI)                            0.396
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15573.356  -15573.356
##   Scaling correction factor                                  1.055
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -15333.068  -15333.068
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               31260.712   31260.712
##   Bayesian (BIC)                             31472.957   31472.957
##   Sample-size adjusted Bayesian (SABIC)      31292.179   31292.179
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.084       0.081
##   90 Percent confidence interval - lower         0.076       0.073
##   90 Percent confidence interval - upper         0.093       0.089
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.790       0.576
##                                                                   
##   Robust RMSEA                                               0.083
##   90 Percent confidence interval - lower                     0.074
##   90 Percent confidence interval - upper                     0.092
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.700
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.087       0.087
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Factor1 =~                                                            
##     dsq_sublimatin    1.000                               0.309    0.080
##     dsq_humor        -1.114    3.052   -0.365    0.715   -0.345   -0.094
##     dsq_anticipatn    1.758    2.525    0.696    0.486    0.544    0.169
##     dsq_suppressin   -1.851    3.961   -0.467    0.640   -0.573   -0.144
##     dsq_psed_ltrsm    3.143    4.029    0.780    0.435    0.972    0.290
##     dsq_idealizatn    4.425    6.058    0.730    0.465    1.369    0.344
##     dsq_rctn_frmtn    3.938    5.619    0.701    0.483    1.218    0.352
##     dsq_undoing       6.155    9.238    0.666    0.505    1.904    0.484
##     dsq_projection    5.008    8.324    0.602    0.547    1.549    0.430
##     dsq_pssv_ggrss    6.372   10.333    0.617    0.537    1.971    0.560
##     dsq_acting_out    2.419    3.612    0.670    0.503    0.748    0.192
##     dsq_isolation     1.380    2.979    0.463    0.643    0.427    0.096
##     dsq_tstc_fntsy    4.401    7.665    0.574    0.566    1.362    0.261
##     dsq_denial        2.964    4.371    0.678    0.498    0.917    0.316
##     dsq_displacmnt    5.528    8.506    0.650    0.516    1.710    0.452
##     dsq_dissociatn    1.285    1.641    0.783    0.434    0.398    0.157
##     dsq_splitting     4.580    7.327    0.625    0.532    1.417    0.399
##     dsq_devaluatin    2.888    5.129    0.563    0.573    0.893    0.300
##     dsq_somatizatn    5.902    8.986    0.657    0.511    1.826    0.424
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_anticipatn   10.706    0.184   58.190    0.000   10.706    3.326
##    .dsq_suppressin    7.435    0.228   32.558    0.000    7.435    1.868
##    .dsq_psed_ltrsm    9.632    0.192   50.247    0.000    9.632    2.877
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_rctn_frmtn    9.111    0.199   45.870    0.000    9.111    2.634
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_projection    8.023    0.206   38.883    0.000    8.023    2.226
##    .dsq_pssv_ggrss    7.341    0.202   36.318    0.000    7.341    2.085
##    .dsq_acting_out   10.797    0.224   48.222    0.000   10.797    2.766
##    .dsq_isolation     8.098    0.254   31.891    0.000    8.098    1.829
##    .dsq_tstc_fntsy   11.666    0.299   39.043    0.000   11.666    2.239
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_dissociatn    4.413    0.145   30.333    0.000    4.413    1.744
##    .dsq_splitting     7.452    0.203   36.649    0.000    7.452    2.100
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_sublimatin   14.773    0.963   15.346    0.000   14.773    0.994
##    .dsq_humor        13.445    1.003   13.403    0.000   13.445    0.991
##    .dsq_anticipatn   10.062    0.884   11.380    0.000   10.062    0.971
##    .dsq_suppressin   15.522    1.107   14.016    0.000   15.522    0.979
##    .dsq_psed_ltrsm   10.262    1.005   10.209    0.000   10.262    0.916
##    .dsq_idealizatn   13.959    1.540    9.064    0.000   13.959    0.882
##    .dsq_rctn_frmtn   10.480    1.036   10.120    0.000   10.480    0.876
##    .dsq_undoing      11.883    1.260    9.432    0.000   11.883    0.766
##    .dsq_projection   10.594    1.193    8.882    0.000   10.594    0.815
##    .dsq_pssv_ggrss    8.518    1.118    7.621    0.000    8.518    0.687
##    .dsq_acting_out   14.678    0.973   15.090    0.000   14.678    0.963
##    .dsq_isolation    19.413    1.151   16.866    0.000   19.413    0.991
##    .dsq_tstc_fntsy   25.302    1.976   12.802    0.000   25.302    0.932
##    .dsq_denial        7.579    0.601   12.604    0.000    7.579    0.900
##    .dsq_displacmnt   11.406    0.912   12.507    0.000   11.406    0.796
##    .dsq_dissociatn    6.249    0.541   11.548    0.000    6.249    0.975
##    .dsq_splitting    10.583    0.974   10.866    0.000   10.583    0.841
##    .dsq_devaluatin    8.079    0.784   10.302    0.000    8.079    0.910
##    .dsq_somatizatn   15.221    1.365   11.154    0.000   15.221    0.820
##     Factor1           0.096    0.294    0.325    0.745    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_sublimatin    0.006
##     dsq_humor         0.009
##     dsq_anticipatn    0.029
##     dsq_suppressin    0.021
##     dsq_psed_ltrsm    0.084
##     dsq_idealizatn    0.118
##     dsq_rctn_frmtn    0.124
##     dsq_undoing       0.234
##     dsq_projection    0.185
##     dsq_pssv_ggrss    0.313
##     dsq_acting_out    0.037
##     dsq_isolation     0.009
##     dsq_tstc_fntsy    0.068
##     dsq_denial        0.100
##     dsq_displacmnt    0.204
##     dsq_dissociatn    0.025
##     dsq_splitting     0.159
##     dsq_devaluatin    0.090
##     dsq_somatizatn    0.180

4.3.2 Three Factor Solution

fit3_kn <- cfa(model_3f_norat, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_kn,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 150 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        60
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               392.122     374.564
##   Degrees of freedom                               149         149
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.047
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               774.640     708.842
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.597       0.581
##   Tucker-Lewis Index (TLI)                       0.538       0.519
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.609
##   Robust Tucker-Lewis Index (TLI)                            0.551
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15529.129  -15529.129
##   Scaling correction factor                                  1.072
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -15333.068  -15333.068
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               31178.259   31178.259
##   Bayesian (BIC)                             31401.674   31401.674
##   Sample-size adjusted Bayesian (SABIC)      31211.382   31211.382
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.073       0.070
##   90 Percent confidence interval - lower         0.064       0.062
##   90 Percent confidence interval - upper         0.082       0.079
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.099       0.034
##                                                                   
##   Robust RMSEA                                               0.071
##   90 Percent confidence interval - lower                     0.062
##   90 Percent confidence interval - upper                     0.081
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.066
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.079       0.079
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.807    0.491
##     dsq_suppressin    1.010    0.684    1.477    0.140    1.825    0.458
##     dsq_sublimatin    1.034    0.814    1.270    0.204    1.868    0.484
##     dsq_anticipatn    0.082    0.316    0.259    0.795    0.148    0.046
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.932    0.558
##     dsq_idealizatn    0.804    0.251    3.207    0.001    1.553    0.390
##     dsq_psed_ltrsm    0.714    0.184    3.886    0.000    1.379    0.412
##     dsq_undoing       1.208    0.206    5.873    0.000    2.333    0.592
##   Immature =~                                                           
##     dsq_isolation     1.000                               0.569    0.128
##     dsq_dissociatn    0.481    0.586    0.820    0.412    0.273    0.108
##     dsq_devaluatin    1.944    1.211    1.606    0.108    1.106    0.371
##     dsq_splitting     2.556    2.074    1.233    0.218    1.453    0.410
##     dsq_denial        1.494    1.118    1.337    0.181    0.849    0.293
##     dsq_tstc_fntsy    2.799    1.832    1.527    0.127    1.591    0.305
##     dsq_displacmnt    2.900    2.300    1.260    0.208    1.649    0.436
##     dsq_pssv_ggrss    3.743    2.662    1.406    0.160    2.128    0.605
##     dsq_somatizatn    2.987    2.362    1.265    0.206    1.699    0.394
##     dsq_acting_out    1.206    1.212    0.995    0.320    0.686    0.176
##     dsq_projection    3.176    2.311    1.375    0.169    1.806    0.501
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.047    0.814    1.287    0.198    0.300    0.300
##     Immature         -0.290    0.464   -0.626    0.532   -0.282   -0.282
##   Neurotic ~~                                                           
##     Immature          0.600    0.459    1.309    0.191    0.546    0.546
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.542    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_anticipatn   10.706    0.184   58.190    0.000   10.706    3.326
##    .dsq_rctn_frmtn    9.107    0.199   45.846    0.000    9.107    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.275    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_isolation     8.098    0.254   31.894    0.000    8.098    1.829
##    .dsq_dissociatn    4.413    0.145   30.343    0.000    4.413    1.743
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.453    0.203   36.640    0.000    7.453    2.101
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.665    0.299   39.036    0.000   11.665    2.239
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.341    0.202   36.339    0.000    7.341    2.085
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.797    0.224   48.221    0.000   10.797    2.766
##    .dsq_projection    8.023    0.206   38.895    0.000    8.023    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.299    2.572    4.004    0.000   10.299    0.759
##    .dsq_suppressin   12.523    2.223    5.634    0.000   12.523    0.790
##    .dsq_sublimatin   11.379    2.763    4.119    0.000   11.379    0.765
##    .dsq_anticipatn   10.336    0.893   11.570    0.000   10.336    0.998
##    .dsq_rctn_frmtn    8.244    0.967    8.525    0.000    8.244    0.688
##    .dsq_idealizatn   13.420    1.422    9.435    0.000   13.420    0.848
##    .dsq_psed_ltrsm    9.304    0.939    9.904    0.000    9.304    0.830
##    .dsq_undoing      10.066    1.396    7.210    0.000   10.066    0.649
##    .dsq_isolation    19.271    1.172   16.438    0.000   19.271    0.983
##    .dsq_dissociatn    6.332    0.546   11.597    0.000    6.332    0.988
##    .dsq_devaluatin    7.655    0.739   10.352    0.000    7.655    0.862
##    .dsq_splitting    10.473    0.895   11.701    0.000   10.473    0.832
##    .dsq_denial        7.698    0.615   12.523    0.000    7.698    0.914
##    .dsq_tstc_fntsy   24.620    1.995   12.344    0.000   24.620    0.907
##    .dsq_displacmnt   11.612    0.991   11.720    0.000   11.612    0.810
##    .dsq_pssv_ggrss    7.864    0.928    8.472    0.000    7.864    0.635
##    .dsq_somatizatn   15.669    1.400   11.195    0.000   15.669    0.844
##    .dsq_acting_out   14.768    0.953   15.489    0.000   14.768    0.969
##    .dsq_projection    9.730    1.072    9.077    0.000    9.730    0.749
##     Mature            3.264    2.662    1.226    0.220    1.000    1.000
##     Neurotic          3.732    1.056    3.535    0.000    1.000    1.000
##     Immature          0.323    0.459    0.705    0.481    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.241
##     dsq_suppressin    0.210
##     dsq_sublimatin    0.235
##     dsq_anticipatn    0.002
##     dsq_rctn_frmtn    0.312
##     dsq_idealizatn    0.152
##     dsq_psed_ltrsm    0.170
##     dsq_undoing       0.351
##     dsq_isolation     0.017
##     dsq_dissociatn    0.012
##     dsq_devaluatin    0.138
##     dsq_splitting     0.168
##     dsq_denial        0.086
##     dsq_tstc_fntsy    0.093
##     dsq_displacmnt    0.190
##     dsq_pssv_ggrss    0.365
##     dsq_somatizatn    0.156
##     dsq_acting_out    0.031
##     dsq_projection    0.251

4.3.3 Four Factor Solution

fit4_kn <- cfa(model_4f_norat, data = kn_df, estimator = "mlr", missing = "fiml")
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite ; use lavInspect(fit, "cov.lv") to investigate.
summary(fit4_kn,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 156 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        63
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               387.267     373.735
##   Degrees of freedom                               146         146
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.036
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               774.640     708.842
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.600       0.577
##   Tucker-Lewis Index (TLI)                       0.532       0.504
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.611
##   Robust Tucker-Lewis Index (TLI)                            0.545
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15526.702  -15526.702
##   Scaling correction factor                                  1.095
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -15333.068  -15333.068
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               31179.404   31179.404
##   Bayesian (BIC)                             31413.990   31413.990
##   Sample-size adjusted Bayesian (SABIC)      31214.183   31214.183
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.073       0.071
##   90 Percent confidence interval - lower         0.065       0.063
##   90 Percent confidence interval - upper         0.082       0.080
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.117       0.055
##                                                                   
##   Robust RMSEA                                               0.072
##   90 Percent confidence interval - lower                     0.062
##   90 Percent confidence interval - upper                     0.081
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.079
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.079       0.079
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                                
##     dsq_humor            1.000                               1.659    0.450
##     dsq_suppressin       1.208    0.596    2.027    0.043    2.004    0.503
##     dsq_sublimatin       1.154    0.584    1.976    0.048    1.914    0.496
##     dsq_anticipatn       0.074    0.264    0.279    0.780    0.123    0.038
##   Neurotic =~                                                              
##     dsq_rctn_frmtn       1.000                               1.937    0.560
##     dsq_idealizatn       0.786    0.234    3.363    0.001    1.522    0.382
##     dsq_psed_ltrsm       0.724    0.186    3.895    0.000    1.403    0.419
##     dsq_undoing          1.202    0.212    5.679    0.000    2.329    0.591
##   Immature =~                                                              
##     dsq_tstc_fntsy       1.000                               1.695    0.325
##     dsq_displacmnt       0.955    0.339    2.815    0.005    1.619    0.428
##     dsq_pssv_ggrss       1.213    0.376    3.229    0.001    2.057    0.584
##     dsq_somatizatn       1.012    0.357    2.832    0.005    1.715    0.398
##     dsq_acting_out       0.396    0.235    1.687    0.092    0.672    0.172
##     dsq_projection       1.020    0.368    2.772    0.006    1.728    0.479
##   Image_Distorting =~                                                      
##     dsq_isolation        1.000                               0.629    0.142
##     dsq_dissociatn       0.751    0.788    0.953    0.341    0.472    0.186
##     dsq_devaluatin       1.823    1.223    1.490    0.136    1.146    0.385
##     dsq_splitting        2.387    2.299    1.039    0.299    1.501    0.423
##     dsq_denial           1.533    1.265    1.212    0.226    0.964    0.332
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          0.887    0.756    1.174    0.240    0.276    0.276
##     Immature         -0.956    0.857   -1.116    0.265   -0.340   -0.340
##     Image_Distrtng   -0.045    0.331   -0.136    0.892   -0.043   -0.043
##   Neurotic ~~                                                           
##     Immature          1.903    0.668    2.850    0.004    0.580    0.580
##     Image_Distrtng    0.580    0.500    1.159    0.246    0.476    0.476
##   Immature ~~                                                           
##     Image_Distrtng    1.010    0.866    1.167    0.243    0.948    0.948
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.547    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_anticipatn   10.706    0.184   58.190    0.000   10.706    3.326
##    .dsq_rctn_frmtn    9.107    0.199   45.853    0.000    9.107    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.277    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_tstc_fntsy   11.665    0.299   39.043    0.000   11.665    2.239
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.340    0.202   36.337    0.000    7.340    2.085
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.797    0.224   48.224    0.000   10.797    2.766
##    .dsq_projection    8.023    0.206   38.900    0.000    8.023    2.226
##    .dsq_isolation     8.098    0.254   31.896    0.000    8.098    1.829
##    .dsq_dissociatn    4.412    0.145   30.330    0.000    4.412    1.743
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.452    0.203   36.637    0.000    7.452    2.101
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.812    1.638    6.600    0.000   10.812    0.797
##    .dsq_suppressin   11.835    2.159    5.481    0.000   11.835    0.747
##    .dsq_sublimatin   11.207    1.874    5.979    0.000   11.207    0.754
##    .dsq_anticipatn   10.343    0.894   11.565    0.000   10.343    0.999
##    .dsq_rctn_frmtn    8.223    0.938    8.763    0.000    8.223    0.687
##    .dsq_idealizatn   13.517    1.391    9.718    0.000   13.517    0.854
##    .dsq_psed_ltrsm    9.237    0.974    9.487    0.000    9.237    0.824
##    .dsq_undoing      10.083    1.462    6.896    0.000   10.083    0.650
##    .dsq_tstc_fntsy   24.279    2.095   11.587    0.000   24.279    0.894
##    .dsq_displacmnt   11.710    0.989   11.836    0.000   11.710    0.817
##    .dsq_pssv_ggrss    8.165    1.015    8.043    0.000    8.165    0.659
##    .dsq_somatizatn   15.615    1.400   11.150    0.000   15.615    0.842
##    .dsq_acting_out   14.787    0.960   15.408    0.000   14.787    0.970
##    .dsq_projection   10.008    1.113    8.991    0.000   10.008    0.770
##    .dsq_isolation    19.199    1.246   15.403    0.000   19.199    0.980
##    .dsq_dissociatn    6.183    0.623    9.925    0.000    6.183    0.965
##    .dsq_devaluatin    7.565    0.949    7.975    0.000    7.565    0.852
##    .dsq_splitting    10.333    0.952   10.858    0.000   10.333    0.821
##    .dsq_denial        7.490    0.703   10.654    0.000    7.490    0.890
##     Mature            2.751    1.673    1.645    0.100    1.000    1.000
##     Neurotic          3.753    1.018    3.685    0.000    1.000    1.000
##     Immature          2.872    1.518    1.892    0.059    1.000    1.000
##     Image_Distrtng    0.395    0.666    0.593    0.553    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.203
##     dsq_suppressin    0.253
##     dsq_sublimatin    0.246
##     dsq_anticipatn    0.001
##     dsq_rctn_frmtn    0.313
##     dsq_idealizatn    0.146
##     dsq_psed_ltrsm    0.176
##     dsq_undoing       0.350
##     dsq_tstc_fntsy    0.106
##     dsq_displacmnt    0.183
##     dsq_pssv_ggrss    0.341
##     dsq_somatizatn    0.158
##     dsq_acting_out    0.030
##     dsq_projection    0.230
##     dsq_isolation     0.020
##     dsq_dissociatn    0.035
##     dsq_devaluatin    0.148
##     dsq_splitting     0.179
##     dsq_denial        0.110

4.3.4 Model Comparison

# Likelihood Ratio Tests (Nested)
anova(fit1_kn, fit3_kn)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit3_kn 149 31178 31402 392.12                                  
## fit1_kn 152 31261 31473 480.58     63.488       3  1.056e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(fit1_kn, fit4_kn)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit4_kn 146 31179 31414 387.27                                  
## fit1_kn 152 31261 31473 480.58     63.062       6  1.072e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# BIC (Non-Nested)
fitMeasures(fit3_kn, "bic")
##      bic 
## 31401.67
fitMeasures(fit4_kn, "bic")
##      bic 
## 31413.99

4.3.5 Model comparison winner: Three Factor Solution

modindices(fit3_kn, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 72                  Mature =~       dsq_dissociation 24.169  0.581   1.050    0.415    0.415
## 190       dsq_idealization ~~          dsq_splitting 21.908  3.424   3.424    0.289    0.289
## 222          dsq_isolation ~~        dsq_devaluation 21.634  3.377   3.377    0.278    0.278
## 199    dsq_pseudo_altruism ~~          dsq_isolation 17.973 -3.406  -3.406   -0.254   -0.254
## 177 dsq_reaction_formation ~~          dsq_splitting 15.562 -2.427  -2.427   -0.261   -0.261
## 70                  Mature =~            dsq_undoing 14.018 -0.711  -1.284   -0.326   -0.326
## 233       dsq_dissociation ~~             dsq_denial 13.591  1.515   1.515    0.217    0.217
## 201    dsq_pseudo_altruism ~~        dsq_devaluation 11.151 -1.732  -1.732   -0.205   -0.205
## 253          dsq_splitting ~~         dsq_acting_out 10.908  2.500   2.500    0.201    0.201
## 76                  Mature =~   dsq_autistic_fantasy 10.204 -0.761  -1.375   -0.264   -0.264
## 87                Neurotic =~       dsq_dissociation  9.897  0.398   0.769    0.304    0.304
## 207    dsq_pseudo_altruism ~~       dsq_somatization  9.796  2.333   2.333    0.193    0.193
## 142        dsq_sublimation ~~       dsq_idealization  9.317  2.467   2.467    0.200    0.200
## 123        dsq_suppression ~~        dsq_sublimation  8.700  3.803   3.803    0.319    0.319
## 131        dsq_suppression ~~        dsq_devaluation  8.607  1.825   1.825    0.186    0.186
## 83                Neurotic =~        dsq_suppression  8.342 -0.483  -0.934   -0.234   -0.234
## 99                Immature =~        dsq_sublimation  7.985  1.526   0.868    0.225    0.225
## 146        dsq_sublimation ~~       dsq_dissociation  7.960  1.496   1.496    0.176    0.176
## 229          dsq_isolation ~~         dsq_acting_out  7.922 -2.763  -2.763   -0.164   -0.164
## 113              dsq_humor ~~       dsq_dissociation  7.642  1.399   1.399    0.173    0.173
## 173 dsq_reaction_formation ~~            dsq_undoing  7.550  2.756   2.756    0.303    0.303
## 245        dsq_devaluation ~~       dsq_somatization  7.469 -1.874  -1.874   -0.171   -0.171
## 128        dsq_suppression ~~            dsq_undoing  7.288 -2.197  -2.197   -0.196   -0.196
## 272 dsq_passive_aggression ~~         dsq_projection  7.273  1.878   1.878    0.215    0.215
## 112              dsq_humor ~~          dsq_isolation  7.238 -2.374  -2.374   -0.169   -0.169
## 75                  Mature =~             dsq_denial  7.220  0.356   0.643    0.222    0.222
## 171 dsq_reaction_formation ~~       dsq_idealization  7.112 -2.148  -2.148   -0.204   -0.204
## 242        dsq_devaluation ~~   dsq_autistic_fantasy  6.972  2.221   2.221    0.162    0.162
## 106              dsq_humor ~~        dsq_sublimation  6.721 -3.343  -3.343   -0.309   -0.309
## 114              dsq_humor ~~        dsq_devaluation  6.700 -1.479  -1.479   -0.167   -0.167
## 84                Neurotic =~        dsq_sublimation  6.581  0.423   0.817    0.212    0.212
## 104               Immature =~            dsq_undoing  6.491  1.802   1.025    0.260    0.260
## 237       dsq_dissociation ~~       dsq_somatization  6.315 -1.506  -1.506   -0.151   -0.151
## 187       dsq_idealization ~~          dsq_isolation  6.246 -2.395  -2.395   -0.149   -0.149
## 100               Immature =~       dsq_anticipation  6.084  1.017   0.578    0.180    0.180
## 90                Neurotic =~             dsq_denial  6.067  0.350   0.677    0.233    0.233
## 92                Neurotic =~       dsq_displacement  5.985  0.447   0.864    0.228    0.228
## 183 dsq_reaction_formation ~~         dsq_acting_out  5.907 -1.707  -1.707   -0.155   -0.155
## 273       dsq_somatization ~~         dsq_acting_out  5.643  2.183   2.183    0.143    0.143
## 129        dsq_suppression ~~          dsq_isolation  5.620  2.280   2.280    0.147    0.147
## 225          dsq_isolation ~~   dsq_autistic_fantasy  5.503  3.022   3.022    0.139    0.139
## 140        dsq_sublimation ~~       dsq_anticipation  5.453  1.716   1.716    0.158    0.158
## 174 dsq_reaction_formation ~~          dsq_isolation  5.399  1.861   1.861    0.148    0.148
## 210            dsq_undoing ~~          dsq_isolation  5.373  2.084   2.084    0.150    0.150
## 96                Neurotic =~         dsq_projection  5.284 -0.398  -0.770   -0.214   -0.214
## 192       dsq_idealization ~~   dsq_autistic_fantasy  5.106 -2.487  -2.487   -0.137   -0.137
## 215            dsq_undoing ~~   dsq_autistic_fantasy  4.923  2.300   2.300    0.146    0.146
## 69                  Mature =~    dsq_pseudo_altruism  4.808  0.338   0.611    0.183    0.183
## 220            dsq_undoing ~~         dsq_projection  4.793 -1.508  -1.508   -0.152   -0.152
## 208    dsq_pseudo_altruism ~~         dsq_acting_out  4.758  1.538   1.538    0.131    0.131
## 85                Neurotic =~       dsq_anticipation  4.711  0.275   0.531    0.165    0.165
## 255             dsq_denial ~~   dsq_autistic_fantasy  4.677  1.791   1.791    0.130    0.130
## 252          dsq_splitting ~~       dsq_somatization  4.552  1.740   1.740    0.136    0.136
## 94                Neurotic =~       dsq_somatization  4.366  0.436   0.843    0.196    0.196
## 107              dsq_humor ~~       dsq_anticipation  4.336 -1.466  -1.466   -0.142   -0.142
## 121              dsq_humor ~~         dsq_acting_out  4.334  1.613   1.613    0.131    0.131
## 110              dsq_humor ~~    dsq_pseudo_altruism  4.263  1.339   1.339    0.137    0.137
## 108              dsq_humor ~~ dsq_reaction_formation  4.137  1.352   1.352    0.147    0.147
## 152        dsq_sublimation ~~ dsq_passive_aggression  4.132  1.365   1.365    0.144    0.144
## 88                Neurotic =~        dsq_devaluation  4.076 -0.292  -0.565   -0.190   -0.190
## 261   dsq_autistic_fantasy ~~       dsq_displacement  4.034 -2.126  -2.126   -0.126   -0.126
## 274       dsq_somatization ~~         dsq_projection  3.889 -1.620  -1.620   -0.131   -0.131
## 226          dsq_isolation ~~       dsq_displacement  3.887 -1.796  -1.796   -0.120   -0.120

4.3.6 Adding correlated errors in Three Factor Solution I

model_3f_adj_kn_I <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_isolation + dsq_dissociation + dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
             
  # Add residual correlation within Immature factor
   dsq_isolation ~~ dsq_devaluation
  
'
fit3_adjkn_I <- cfa(model_3f_adj_kn_I, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_I,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 194 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        61
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               369.836     351.746
##   Degrees of freedom                               148         148
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.051
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               774.640     708.842
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.633       0.621
##   Tucker-Lewis Index (TLI)                       0.575       0.562
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.644
##   Robust Tucker-Lewis Index (TLI)                            0.589
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15517.986  -15517.986
##   Scaling correction factor                                  1.060
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -15333.068  -15333.068
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               31157.973   31157.973
##   Bayesian (BIC)                             31385.111   31385.111
##   Sample-size adjusted Bayesian (SABIC)      31191.647   31191.647
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.070       0.067
##   90 Percent confidence interval - lower         0.061       0.058
##   90 Percent confidence interval - upper         0.079       0.076
##   P-value H_0: RMSEA <= 0.050                    0.000       0.001
##   P-value H_0: RMSEA >= 0.080                    0.033       0.007
##                                                                   
##   Robust RMSEA                                               0.068
##   90 Percent confidence interval - lower                     0.059
##   90 Percent confidence interval - upper                     0.078
##   P-value H_0: Robust RMSEA <= 0.050                         0.001
##   P-value H_0: Robust RMSEA >= 0.080                         0.021
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.077       0.077
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.741    0.473
##     dsq_suppressin    1.073    0.597    1.799    0.072    1.868    0.469
##     dsq_sublimatin    1.104    0.742    1.488    0.137    1.922    0.498
##     dsq_anticipatn    0.100    0.307    0.326    0.745    0.174    0.054
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.895    0.547
##     dsq_idealizatn    0.844    0.261    3.228    0.001    1.599    0.402
##     dsq_psed_ltrsm    0.749    0.192    3.891    0.000    1.418    0.424
##     dsq_undoing       1.211    0.200    6.054    0.000    2.294    0.582
##   Immature =~                                                           
##     dsq_isolation     1.000                               0.315    0.071
##     dsq_dissociatn    0.904    1.421    0.637    0.524    0.285    0.112
##     dsq_devaluatin    3.304    3.821    0.865    0.387    1.040    0.349
##     dsq_splitting     4.756    6.092    0.781    0.435    1.497    0.422
##     dsq_denial        2.626    3.129    0.839    0.401    0.826    0.285
##     dsq_tstc_fntsy    4.801    5.447    0.881    0.378    1.511    0.290
##     dsq_displacmnt    5.377    6.744    0.797    0.425    1.692    0.447
##     dsq_pssv_ggrss    6.740    8.015    0.841    0.400    2.121    0.603
##     dsq_somatizatn    5.546    6.871    0.807    0.420    1.745    0.405
##     dsq_acting_out    2.393    3.371    0.710    0.478    0.753    0.193
##     dsq_projection    5.710    6.921    0.825    0.409    1.797    0.499
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_isolation ~~                                                      
##    .dsq_devaluatin    3.391    0.762    4.452    0.000    3.391    0.275
##   Mature ~~                                                             
##     Neurotic          1.005    0.723    1.390    0.165    0.305    0.305
##     Immature         -0.146    0.275   -0.532    0.595   -0.267   -0.267
##   Neurotic ~~                                                           
##     Immature          0.329    0.416    0.791    0.429    0.552    0.552
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.425    0.228   32.544    0.000    7.425    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_anticipatn   10.706    0.184   58.190    0.000   10.706    3.326
##    .dsq_rctn_frmtn    9.107    0.199   45.843    0.000    9.107    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.635    0.192   50.274    0.000    9.635    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_isolation     8.097    0.254   31.906    0.000    8.097    1.830
##    .dsq_dissociatn    4.413    0.145   30.344    0.000    4.413    1.743
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.452    0.203   36.642    0.000    7.452    2.101
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.665    0.299   39.031    0.000   11.665    2.238
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.343    0.202   36.354    0.000    7.343    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.797    0.224   48.220    0.000   10.797    2.766
##    .dsq_projection    8.022    0.206   38.893    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.534    2.106    5.002    0.000   10.534    0.777
##    .dsq_suppressin   12.366    1.986    6.228    0.000   12.366    0.780
##    .dsq_sublimatin   11.174    2.478    4.508    0.000   11.174    0.752
##    .dsq_anticipatn   10.328    0.894   11.550    0.000   10.328    0.997
##    .dsq_rctn_frmtn    8.387    0.971    8.636    0.000    8.387    0.700
##    .dsq_idealizatn   13.277    1.425    9.319    0.000   13.277    0.839
##    .dsq_psed_ltrsm    9.195    0.937    9.808    0.000    9.195    0.820
##    .dsq_undoing      10.249    1.429    7.171    0.000   10.249    0.661
##    .dsq_isolation    19.487    1.126   17.312    0.000   19.487    0.995
##    .dsq_dissociatn    6.326    0.546   11.590    0.000    6.326    0.987
##    .dsq_devaluatin    7.796    0.712   10.954    0.000    7.796    0.878
##    .dsq_splitting    10.346    0.894   11.579    0.000   10.346    0.822
##    .dsq_denial        7.736    0.611   12.663    0.000    7.736    0.919
##    .dsq_tstc_fntsy   24.871    1.957   12.711    0.000   24.871    0.916
##    .dsq_displacmnt   11.467    0.971   11.813    0.000   11.467    0.800
##    .dsq_pssv_ggrss    7.896    0.961    8.213    0.000    7.896    0.637
##    .dsq_somatizatn   15.508    1.412   10.986    0.000   15.508    0.836
##    .dsq_acting_out   14.671    0.957   15.336    0.000   14.671    0.963
##    .dsq_projection    9.763    1.079    9.049    0.000    9.763    0.751
##     Mature            3.030    2.174    1.394    0.163    1.000    1.000
##     Neurotic          3.590    1.051    3.416    0.001    1.000    1.000
##     Immature          0.099    0.238    0.416    0.677    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.223
##     dsq_suppressin    0.220
##     dsq_sublimatin    0.248
##     dsq_anticipatn    0.003
##     dsq_rctn_frmtn    0.300
##     dsq_idealizatn    0.161
##     dsq_psed_ltrsm    0.180
##     dsq_undoing       0.339
##     dsq_isolation     0.005
##     dsq_dissociatn    0.013
##     dsq_devaluatin    0.122
##     dsq_splitting     0.178
##     dsq_denial        0.081
##     dsq_tstc_fntsy    0.084
##     dsq_displacmnt    0.200
##     dsq_pssv_ggrss    0.363
##     dsq_somatizatn    0.164
##     dsq_acting_out    0.037
##     dsq_projection    0.249
modindices(fit3_adjkn_I, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 73                  Mature =~       dsq_dissociation 24.066  0.597   1.039    0.411    0.411
## 191       dsq_idealization ~~          dsq_splitting 21.018  3.337   3.337    0.285    0.285
## 178 dsq_reaction_formation ~~          dsq_splitting 15.608 -2.433  -2.433   -0.261   -0.261
## 233       dsq_dissociation ~~             dsq_denial 13.456  1.509   1.509    0.216    0.216
## 71                  Mature =~            dsq_undoing 13.328 -0.720  -1.253   -0.318   -0.318
## 200    dsq_pseudo_altruism ~~          dsq_isolation 11.180 -2.584  -2.584   -0.193   -0.193
## 77                  Mature =~   dsq_autistic_fantasy 10.557 -0.799  -1.391   -0.267   -0.267
## 88                Neurotic =~       dsq_dissociation 10.037  0.413   0.782    0.309    0.309
## 253          dsq_splitting ~~         dsq_acting_out 10.026  2.390   2.390    0.194    0.194
## 174 dsq_reaction_formation ~~            dsq_undoing  9.674  3.008   3.008    0.324    0.324
## 84                Neurotic =~        dsq_suppression  9.495 -0.531  -1.006   -0.253   -0.253
## 143        dsq_sublimation ~~       dsq_idealization  9.169  2.443   2.443    0.201    0.201
## 208    dsq_pseudo_altruism ~~       dsq_somatization  8.890  2.213   2.213    0.185    0.185
## 100               Immature =~        dsq_sublimation  8.104  2.780   0.875    0.227    0.227
## 147        dsq_sublimation ~~       dsq_dissociation  7.832  1.480   1.480    0.176    0.176
## 272 dsq_passive_aggression ~~         dsq_projection  7.704  1.937   1.937    0.221    0.221
## 114              dsq_humor ~~       dsq_dissociation  7.603  1.399   1.399    0.171    0.171
## 172 dsq_reaction_formation ~~       dsq_idealization  7.374 -2.189  -2.189   -0.207   -0.207
## 124        dsq_suppression ~~        dsq_sublimation  7.232  3.689   3.689    0.314    0.314
## 129        dsq_suppression ~~            dsq_undoing  7.203 -2.188  -2.188   -0.194   -0.194
## 85                Neurotic =~        dsq_sublimation  6.817  0.445   0.843    0.219    0.219
## 76                  Mature =~             dsq_denial  6.759  0.355   0.618    0.213    0.213
## 237       dsq_dissociation ~~       dsq_somatization  6.746 -1.553  -1.553   -0.157   -0.157
## 175 dsq_reaction_formation ~~          dsq_isolation  6.478  1.973   1.973    0.154    0.154
## 101               Immature =~       dsq_anticipation  6.380  1.870   0.589    0.183    0.183
## 211            dsq_undoing ~~          dsq_isolation  6.229  2.172   2.172    0.154    0.154
## 91                Neurotic =~             dsq_denial  6.174  0.364   0.691    0.238    0.238
## 107              dsq_humor ~~        dsq_sublimation  6.081 -3.158  -3.158   -0.291   -0.291
## 184 dsq_reaction_formation ~~         dsq_acting_out  6.032 -1.728  -1.728   -0.156   -0.156
## 132        dsq_suppression ~~        dsq_devaluation  5.588  1.417   1.417    0.144    0.144
## 93                Neurotic =~       dsq_displacement  5.579  0.444   0.842    0.222    0.222
## 245        dsq_devaluation ~~       dsq_somatization  5.559 -1.556  -1.556   -0.142   -0.142
## 216            dsq_undoing ~~   dsq_autistic_fantasy  5.497  2.444   2.444    0.153    0.153
## 105               Immature =~            dsq_undoing  5.441  2.995   0.943    0.239    0.239
## 97                Neurotic =~         dsq_projection  5.417 -0.416  -0.788   -0.219   -0.219
## 202    dsq_pseudo_altruism ~~        dsq_devaluation  5.359 -1.157  -1.157   -0.137   -0.137
## 229          dsq_isolation ~~         dsq_acting_out  5.222 -2.158  -2.158   -0.128   -0.128
## 141        dsq_sublimation ~~       dsq_anticipation  5.220  1.691   1.691    0.157    0.157
## 255             dsq_denial ~~   dsq_autistic_fantasy  5.172  1.891   1.891    0.136    0.136
## 193       dsq_idealization ~~   dsq_autistic_fantasy  5.128 -2.494  -2.494   -0.137   -0.137
## 224          dsq_isolation ~~             dsq_denial  5.060  1.556   1.556    0.127    0.127
## 113              dsq_humor ~~          dsq_isolation  4.949 -1.897  -1.897   -0.132   -0.132
## 273       dsq_somatization ~~         dsq_acting_out  4.945  2.037   2.037    0.135    0.135
## 86                Neurotic =~       dsq_anticipation  4.918  0.288   0.545    0.169    0.169
## 242        dsq_devaluation ~~   dsq_autistic_fantasy  4.653  1.753   1.753    0.126    0.126
## 111              dsq_humor ~~    dsq_pseudo_altruism  4.445  1.366   1.366    0.139    0.139
## 274       dsq_somatization ~~         dsq_projection  4.436 -1.733  -1.733   -0.141   -0.141
## 209    dsq_pseudo_altruism ~~         dsq_acting_out  4.411  1.474   1.474    0.127    0.127
## 108              dsq_humor ~~       dsq_anticipation  4.367 -1.460  -1.460   -0.140   -0.140
## 122              dsq_humor ~~         dsq_acting_out  4.321  1.611   1.611    0.130    0.130
## 89                Neurotic =~        dsq_devaluation  4.301 -0.298  -0.565   -0.189   -0.189
## 188       dsq_idealization ~~          dsq_isolation  4.250 -1.901  -1.901   -0.118   -0.118
## 95                Neurotic =~       dsq_somatization  4.191  0.440   0.834    0.194    0.194
## 221            dsq_undoing ~~         dsq_projection  4.175 -1.413  -1.413   -0.141   -0.141
## 70                  Mature =~    dsq_pseudo_altruism  4.113  0.326   0.568    0.170    0.170
## 153        dsq_sublimation ~~ dsq_passive_aggression  4.109  1.360   1.360    0.145    0.145
## 109              dsq_humor ~~ dsq_reaction_formation  4.093  1.343   1.343    0.143    0.143
## 181 dsq_reaction_formation ~~       dsq_displacement  4.055  1.312   1.312    0.134    0.134
## 115              dsq_humor ~~        dsq_devaluation  4.012 -1.107  -1.107   -0.122   -0.122
## 225          dsq_isolation ~~   dsq_autistic_fantasy  3.942  2.473   2.473    0.112    0.112
## 99                Immature =~        dsq_suppression  3.915 -1.952  -0.614   -0.154   -0.154
## 252          dsq_splitting ~~       dsq_somatization  3.841  1.597   1.597    0.126    0.126

4.3.7 Adding correlated errors in Three Factor Solution II

model_3f_adj_kn_II <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_isolation + dsq_dissociation + dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
             
  # Add residual correlation within Immature factor
   dsq_isolation ~~ dsq_devaluation
   dsq_dissociation ~~ dsq_denial
  
'
fit3_adjkn_II <- cfa(model_3f_adj_kn_II, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_II,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 205 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        62
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               355.923     338.249
##   Degrees of freedom                               147         147
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.052
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               774.640     708.842
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.654       0.644
##   Tucker-Lewis Index (TLI)                       0.597       0.586
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.667
##   Robust Tucker-Lewis Index (TLI)                            0.612
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15511.030  -15511.030
##   Scaling correction factor                                  1.058
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -15333.068  -15333.068
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               31146.060   31146.060
##   Bayesian (BIC)                             31376.922   31376.922
##   Sample-size adjusted Bayesian (SABIC)      31180.287   31180.287
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.068       0.065
##   90 Percent confidence interval - lower         0.059       0.056
##   90 Percent confidence interval - upper         0.077       0.074
##   P-value H_0: RMSEA <= 0.050                    0.001       0.003
##   P-value H_0: RMSEA >= 0.080                    0.015       0.003
##                                                                   
##   Robust RMSEA                                               0.066
##   90 Percent confidence interval - lower                     0.057
##   90 Percent confidence interval - upper                     0.076
##   P-value H_0: Robust RMSEA <= 0.050                         0.003
##   P-value H_0: Robust RMSEA >= 0.080                         0.009
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.076       0.076
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.786    0.485
##     dsq_suppressin    1.034    0.596    1.734    0.083    1.846    0.464
##     dsq_sublimatin    1.053    0.707    1.490    0.136    1.881    0.488
##     dsq_anticipatn    0.083    0.292    0.284    0.777    0.148    0.046
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.900    0.549
##     dsq_idealizatn    0.837    0.259    3.232    0.001    1.591    0.400
##     dsq_psed_ltrsm    0.746    0.192    3.892    0.000    1.418    0.424
##     dsq_undoing       1.207    0.200    6.025    0.000    2.295    0.583
##   Immature =~                                                           
##     dsq_isolation     1.000                               0.325    0.073
##     dsq_dissociatn    0.616    1.112    0.554    0.579    0.200    0.079
##     dsq_devaluatin    3.180    3.621    0.878    0.380    1.033    0.347
##     dsq_splitting     4.587    5.799    0.791    0.429    1.490    0.420
##     dsq_denial        2.438    2.843    0.858    0.391    0.792    0.273
##     dsq_tstc_fntsy    4.692    5.227    0.898    0.369    1.525    0.293
##     dsq_displacmnt    5.216    6.462    0.807    0.420    1.695    0.448
##     dsq_pssv_ggrss    6.517    7.656    0.851    0.395    2.118    0.601
##     dsq_somatizatn    5.464    6.664    0.820    0.412    1.775    0.412
##     dsq_acting_out    2.300    3.214    0.716    0.474    0.747    0.191
##     dsq_projection    5.527    6.621    0.835    0.404    1.796    0.498
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_isolation ~~                                                         
##    .dsq_devaluatin       3.382    0.764    4.427    0.000    3.382    0.274
##  .dsq_dissociation ~~                                                      
##    .dsq_denial           1.533    0.431    3.558    0.000    1.533    0.218
##   Mature ~~                                                                
##     Neurotic             1.036    0.746    1.389    0.165    0.305    0.305
##     Immature            -0.172    0.310   -0.556    0.578   -0.297   -0.297
##   Neurotic ~~                                                              
##     Immature             0.337    0.421    0.801    0.423    0.546    0.546
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.543    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_anticipatn   10.706    0.184   58.190    0.000   10.706    3.326
##    .dsq_rctn_frmtn    9.108    0.199   45.844    0.000    9.108    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.273    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_isolation     8.097    0.254   31.906    0.000    8.097    1.830
##    .dsq_dissociatn    4.412    0.145   30.344    0.000    4.412    1.743
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.453    0.203   36.640    0.000    7.453    2.101
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.664    0.299   39.028    0.000   11.664    2.238
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.343    0.202   36.356    0.000    7.343    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.797    0.224   48.222    0.000   10.797    2.766
##    .dsq_projection    8.022    0.206   38.895    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.375    2.159    4.804    0.000   10.375    0.765
##    .dsq_suppressin   12.448    2.046    6.083    0.000   12.448    0.785
##    .dsq_sublimatin   11.331    2.426    4.672    0.000   11.331    0.762
##    .dsq_anticipatn   10.336    0.894   11.567    0.000   10.336    0.998
##    .dsq_rctn_frmtn    8.365    0.972    8.608    0.000    8.365    0.698
##    .dsq_idealizatn   13.303    1.415    9.404    0.000   13.303    0.840
##    .dsq_psed_ltrsm    9.195    0.937    9.810    0.000    9.195    0.821
##    .dsq_undoing      10.244    1.417    7.228    0.000   10.244    0.660
##    .dsq_isolation    19.481    1.128   17.278    0.000   19.481    0.995
##    .dsq_dissociatn    6.370    0.541   11.779    0.000    6.370    0.994
##    .dsq_devaluatin    7.810    0.718   10.877    0.000    7.810    0.880
##    .dsq_splitting    10.366    0.900   11.524    0.000   10.366    0.824
##    .dsq_denial        7.792    0.615   12.660    0.000    7.792    0.925
##    .dsq_tstc_fntsy   24.830    1.973   12.588    0.000   24.830    0.914
##    .dsq_displacmnt   11.459    0.975   11.755    0.000   11.459    0.800
##    .dsq_pssv_ggrss    7.912    0.966    8.192    0.000    7.912    0.638
##    .dsq_somatizatn   15.404    1.431   10.761    0.000   15.404    0.830
##    .dsq_acting_out   14.680    0.955   15.372    0.000   14.680    0.963
##    .dsq_projection    9.768    1.093    8.937    0.000    9.768    0.752
##     Mature            3.189    2.238    1.425    0.154    1.000    1.000
##     Neurotic          3.612    1.055    3.423    0.001    1.000    1.000
##     Immature          0.106    0.250    0.423    0.673    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.235
##     dsq_suppressin    0.215
##     dsq_sublimatin    0.238
##     dsq_anticipatn    0.002
##     dsq_rctn_frmtn    0.302
##     dsq_idealizatn    0.160
##     dsq_psed_ltrsm    0.179
##     dsq_undoing       0.340
##     dsq_isolation     0.005
##     dsq_dissociatn    0.006
##     dsq_devaluatin    0.120
##     dsq_splitting     0.176
##     dsq_denial        0.075
##     dsq_tstc_fntsy    0.086
##     dsq_displacmnt    0.200
##     dsq_pssv_ggrss    0.362
##     dsq_somatizatn    0.170
##     dsq_acting_out    0.037
##     dsq_projection    0.248
modindices(fit3_adjkn_II, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 192       dsq_idealization ~~          dsq_splitting 21.239  3.359   3.359    0.286    0.286
## 74                  Mature =~       dsq_dissociation 19.819  0.521   0.930    0.367    0.367
## 179 dsq_reaction_formation ~~          dsq_splitting 15.503 -2.426  -2.426   -0.261   -0.261
## 72                  Mature =~            dsq_undoing 13.222 -0.695  -1.241   -0.315   -0.315
## 201    dsq_pseudo_altruism ~~          dsq_isolation 11.240 -2.591  -2.591   -0.194   -0.194
## 253          dsq_splitting ~~         dsq_acting_out 10.117  2.402   2.402    0.195    0.195
## 78                  Mature =~   dsq_autistic_fantasy  9.822 -0.759  -1.356   -0.260   -0.260
## 175 dsq_reaction_formation ~~            dsq_undoing  9.480  2.989   2.989    0.323    0.323
## 144        dsq_sublimation ~~       dsq_idealization  9.287  2.461   2.461    0.200    0.200
## 209    dsq_pseudo_altruism ~~       dsq_somatization  9.023  2.226   2.226    0.187    0.187
## 85                Neurotic =~        dsq_suppression  8.916 -0.510  -0.969   -0.243   -0.243
## 89                Neurotic =~       dsq_dissociation  8.726  0.370   0.704    0.278    0.278
## 101               Immature =~        dsq_sublimation  7.944  2.691   0.874    0.227    0.227
## 272 dsq_passive_aggression ~~         dsq_projection  7.818  1.953   1.953    0.222    0.222
## 125        dsq_suppression ~~        dsq_sublimation  7.805  3.584   3.584    0.302    0.302
## 173 dsq_reaction_formation ~~       dsq_idealization  7.314 -2.180  -2.180   -0.207   -0.207
## 130        dsq_suppression ~~            dsq_undoing  7.234 -2.194  -2.194   -0.194   -0.194
## 86                Neurotic =~        dsq_sublimation  6.722  0.436   0.828    0.215    0.215
## 148        dsq_sublimation ~~       dsq_dissociation  6.645  1.334   1.334    0.157    0.157
## 237       dsq_dissociation ~~       dsq_somatization  6.566 -1.496  -1.496   -0.151   -0.151
## 225          dsq_isolation ~~             dsq_denial  6.541  1.728   1.728    0.140    0.140
## 176 dsq_reaction_formation ~~          dsq_isolation  6.466  1.970   1.970    0.154    0.154
## 102               Immature =~       dsq_anticipation  6.442  1.846   0.600    0.186    0.186
## 212            dsq_undoing ~~          dsq_isolation  6.173  2.162   2.162    0.153    0.153
## 185 dsq_reaction_formation ~~         dsq_acting_out  6.056 -1.731  -1.731   -0.156   -0.156
## 108              dsq_humor ~~        dsq_sublimation  5.998 -3.059  -3.059   -0.282   -0.282
## 94                Neurotic =~       dsq_displacement  5.992  0.454   0.862    0.228    0.228
## 255             dsq_denial ~~   dsq_autistic_fantasy  5.897  1.970   1.970    0.142    0.142
## 106               Immature =~            dsq_undoing  5.883  2.966   0.964    0.245    0.245
## 245        dsq_devaluation ~~       dsq_somatization  5.733 -1.580  -1.580   -0.144   -0.144
## 115              dsq_humor ~~       dsq_dissociation  5.697  1.181   1.181    0.145    0.145
## 133        dsq_suppression ~~        dsq_devaluation  5.659  1.429   1.429    0.145    0.145
## 142        dsq_sublimation ~~       dsq_anticipation  5.463  1.715   1.715    0.158    0.158
## 217            dsq_undoing ~~   dsq_autistic_fantasy  5.424  2.428   2.428    0.152    0.152
## 230          dsq_isolation ~~         dsq_acting_out  5.278 -2.170  -2.170   -0.128   -0.128
## 203    dsq_pseudo_altruism ~~        dsq_devaluation  5.218 -1.143  -1.143   -0.135   -0.135
## 194       dsq_idealization ~~   dsq_autistic_fantasy  5.053 -2.476  -2.476   -0.136   -0.136
## 114              dsq_humor ~~          dsq_isolation  5.029 -1.909  -1.909   -0.134   -0.134
## 87                Neurotic =~       dsq_anticipation  5.011  0.289   0.549    0.171    0.171
## 273       dsq_somatization ~~         dsq_acting_out  4.931  2.033   2.033    0.135    0.135
## 274       dsq_somatization ~~         dsq_projection  4.872 -1.817  -1.817   -0.148   -0.148
## 98                Neurotic =~         dsq_projection  4.851 -0.388  -0.737   -0.205   -0.205
## 242        dsq_devaluation ~~   dsq_autistic_fantasy  4.653  1.754   1.754    0.126    0.126
## 154        dsq_sublimation ~~ dsq_passive_aggression  4.594  1.443   1.443    0.152    0.152
## 123              dsq_humor ~~         dsq_acting_out  4.542  1.649   1.649    0.134    0.134
## 210    dsq_pseudo_altruism ~~         dsq_acting_out  4.437  1.479   1.479    0.127    0.127
## 112              dsq_humor ~~    dsq_pseudo_altruism  4.338  1.350   1.350    0.138    0.138
## 222            dsq_undoing ~~         dsq_projection  4.317 -1.438  -1.438   -0.144   -0.144
## 189       dsq_idealization ~~          dsq_isolation  4.275 -1.907  -1.907   -0.118   -0.118
## 96                Neurotic =~       dsq_somatization  4.209  0.434   0.825    0.192    0.192
## 109              dsq_humor ~~       dsq_anticipation  4.197 -1.434  -1.434   -0.138   -0.138
## 71                  Mature =~    dsq_pseudo_altruism  4.105  0.316   0.564    0.168    0.168
## 182 dsq_reaction_formation ~~       dsq_displacement  4.008  1.304   1.304    0.133    0.133
## 90                Neurotic =~        dsq_devaluation  3.931 -0.281  -0.533   -0.179   -0.179
## 226          dsq_isolation ~~   dsq_autistic_fantasy  3.902  2.460   2.460    0.112    0.112
## 120              dsq_humor ~~       dsq_displacement  3.895  1.409   1.409    0.129    0.129
## 110              dsq_humor ~~ dsq_reaction_formation  3.890  1.312   1.312    0.141    0.141
## 261   dsq_autistic_fantasy ~~       dsq_displacement  3.885 -2.087  -2.087   -0.124   -0.124

4.3.8 Adding correlated errors in Three Factor Solution III

model_3f_adj_kn_III <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_isolation + dsq_dissociation + dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
             
  # Add residual correlation within Immature factor
   dsq_isolation ~~ dsq_devaluation
   dsq_dissociation ~~ dsq_denial
   dsq_splitting ~~ dsq_acting_out
  
'
fit3_adjkn_III <- cfa(model_3f_adj_kn_III, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_III,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 195 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        63
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               345.704     329.167
##   Degrees of freedom                               146         146
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.050
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               774.640     708.842
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.669       0.659
##   Tucker-Lewis Index (TLI)                       0.613       0.601
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.682
##   Robust Tucker-Lewis Index (TLI)                            0.628
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15505.920  -15505.920
##   Scaling correction factor                                  1.063
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -15333.068  -15333.068
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               31137.841   31137.841
##   Bayesian (BIC)                             31372.427   31372.427
##   Sample-size adjusted Bayesian (SABIC)      31172.620   31172.620
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.067       0.064
##   90 Percent confidence interval - lower         0.058       0.055
##   90 Percent confidence interval - upper         0.076       0.073
##   P-value H_0: RMSEA <= 0.050                    0.001       0.006
##   P-value H_0: RMSEA >= 0.080                    0.008       0.001
##                                                                   
##   Robust RMSEA                                               0.065
##   90 Percent confidence interval - lower                     0.055
##   90 Percent confidence interval - upper                     0.075
##   P-value H_0: Robust RMSEA <= 0.050                         0.006
##   P-value H_0: Robust RMSEA >= 0.080                         0.005
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.075       0.075
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.831    0.497
##     dsq_suppressin    0.990    0.624    1.587    0.112    1.813    0.455
##     dsq_sublimatin    1.007    0.724    1.391    0.164    1.844    0.478
##     dsq_anticipatn    0.073    0.290    0.250    0.802    0.133    0.041
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.930    0.558
##     dsq_idealizatn    0.809    0.246    3.289    0.001    1.562    0.393
##     dsq_psed_ltrsm    0.726    0.183    3.962    0.000    1.401    0.418
##     dsq_undoing       1.194    0.198    6.042    0.000    2.305    0.585
##   Immature =~                                                           
##     dsq_isolation     1.000                               0.389    0.088
##     dsq_dissociatn    0.492    0.832    0.592    0.554    0.191    0.076
##     dsq_devaluatin    2.725    2.551    1.068    0.285    1.059    0.355
##     dsq_splitting     3.660    3.850    0.951    0.342    1.422    0.401
##     dsq_denial        2.073    2.020    1.026    0.305    0.806    0.278
##     dsq_tstc_fntsy    3.987    3.655    1.091    0.275    1.549    0.297
##     dsq_displacmnt    4.344    4.527    0.959    0.337    1.688    0.446
##     dsq_pssv_ggrss    5.508    5.378    1.024    0.306    2.140    0.608
##     dsq_somatizatn    4.441    4.516    0.983    0.325    1.726    0.401
##     dsq_acting_out    1.484    1.869    0.794    0.427    0.577    0.148
##     dsq_projection    4.676    4.671    1.001    0.317    1.817    0.504
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_isolation ~~                                                         
##    .dsq_devaluatin       3.307    0.762    4.340    0.000    3.307    0.269
##  .dsq_dissociation ~~                                                      
##    .dsq_denial           1.538    0.432    3.559    0.000    1.538    0.219
##  .dsq_splitting ~~                                                         
##    .dsq_acting_out       2.414    0.867    2.783    0.005    2.414    0.192
##   Mature ~~                                                                
##     Neurotic             1.080    0.788    1.370    0.171    0.305    0.305
##     Immature            -0.221    0.361   -0.610    0.542   -0.310   -0.310
##   Neurotic ~~                                                              
##     Immature             0.409    0.424    0.965    0.335    0.546    0.546
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.543    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_anticipatn   10.706    0.184   58.190    0.000   10.706    3.326
##    .dsq_rctn_frmtn    9.107    0.199   45.843    0.000    9.107    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.273    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_isolation     8.097    0.254   31.905    0.000    8.097    1.829
##    .dsq_dissociatn    4.412    0.145   30.344    0.000    4.412    1.743
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.453    0.203   36.629    0.000    7.453    2.100
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.665    0.299   39.030    0.000   11.665    2.238
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.343    0.202   36.363    0.000    7.343    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.796    0.224   48.217    0.000   10.796    2.766
##    .dsq_projection    8.022    0.206   38.896    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.209    2.367    4.312    0.000   10.209    0.753
##    .dsq_suppressin   12.567    2.151    5.844    0.000   12.567    0.793
##    .dsq_sublimatin   11.469    2.530    4.533    0.000   11.469    0.771
##    .dsq_anticipatn   10.340    0.893   11.583    0.000   10.340    0.998
##    .dsq_rctn_frmtn    8.251    0.958    8.611    0.000    8.251    0.689
##    .dsq_idealizatn   13.392    1.400    9.563    0.000   13.392    0.846
##    .dsq_psed_ltrsm    9.244    0.930    9.938    0.000    9.244    0.825
##    .dsq_undoing      10.197    1.372    7.432    0.000   10.197    0.657
##    .dsq_isolation    19.435    1.135   17.122    0.000   19.435    0.992
##    .dsq_dissociatn    6.374    0.541   11.782    0.000    6.374    0.994
##    .dsq_devaluatin    7.757    0.723   10.731    0.000    7.757    0.874
##    .dsq_splitting    10.572    0.885   11.952    0.000   10.572    0.839
##    .dsq_denial        7.770    0.619   12.554    0.000    7.770    0.923
##    .dsq_tstc_fntsy   24.754    1.984   12.477    0.000   24.754    0.912
##    .dsq_displacmnt   11.482    0.998   11.505    0.000   11.482    0.801
##    .dsq_pssv_ggrss    7.814    0.947    8.252    0.000    7.814    0.630
##    .dsq_somatizatn   15.577    1.402   11.113    0.000   15.577    0.840
##    .dsq_acting_out   14.906    0.945   15.780    0.000   14.906    0.978
##    .dsq_projection    9.691    1.091    8.883    0.000    9.691    0.746
##     Mature            3.354    2.454    1.367    0.172    1.000    1.000
##     Neurotic          3.726    1.044    3.569    0.000    1.000    1.000
##     Immature          0.151    0.295    0.512    0.608    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.247
##     dsq_suppressin    0.207
##     dsq_sublimatin    0.229
##     dsq_anticipatn    0.002
##     dsq_rctn_frmtn    0.311
##     dsq_idealizatn    0.154
##     dsq_psed_ltrsm    0.175
##     dsq_undoing       0.343
##     dsq_isolation     0.008
##     dsq_dissociatn    0.006
##     dsq_devaluatin    0.126
##     dsq_splitting     0.161
##     dsq_denial        0.077
##     dsq_tstc_fntsy    0.088
##     dsq_displacmnt    0.199
##     dsq_pssv_ggrss    0.370
##     dsq_somatizatn    0.160
##     dsq_acting_out    0.022
##     dsq_projection    0.254
modindices(fit3_adjkn_III, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 193       dsq_idealization ~~          dsq_splitting 20.820  3.275   3.275    0.275    0.275
## 75                  Mature =~       dsq_dissociation 19.689  0.509   0.932    0.368    0.368
## 73                  Mature =~            dsq_undoing 13.271 -0.677  -1.240   -0.315   -0.315
## 180 dsq_reaction_formation ~~          dsq_splitting 12.315 -2.119  -2.119   -0.227   -0.227
## 202    dsq_pseudo_altruism ~~          dsq_isolation 11.484 -2.622  -2.622   -0.196   -0.196
## 210    dsq_pseudo_altruism ~~       dsq_somatization  9.484  2.291   2.291    0.191    0.191
## 79                  Mature =~   dsq_autistic_fantasy  9.482 -0.731  -1.338   -0.257   -0.257
## 145        dsq_sublimation ~~       dsq_idealization  9.345  2.472   2.472    0.199    0.199
## 90                Neurotic =~       dsq_dissociation  8.833  0.366   0.706    0.279    0.279
## 126        dsq_suppression ~~        dsq_sublimation  8.671  3.610   3.610    0.301    0.301
## 176 dsq_reaction_formation ~~            dsq_undoing  8.280  2.841   2.841    0.310    0.310
## 86                Neurotic =~        dsq_suppression  8.173 -0.478  -0.922   -0.232   -0.232
## 102               Immature =~        dsq_sublimation  7.808  2.235   0.868    0.225    0.225
## 174 dsq_reaction_formation ~~       dsq_idealization  7.323 -2.181  -2.181   -0.207   -0.207
## 131        dsq_suppression ~~            dsq_undoing  7.300 -2.203  -2.203   -0.195   -0.195
## 272 dsq_passive_aggression ~~         dsq_projection  6.991  1.870   1.870    0.215    0.215
## 149        dsq_sublimation ~~       dsq_dissociation  6.721  1.344   1.344    0.157    0.157
## 87                Neurotic =~        dsq_sublimation  6.557  0.420   0.811    0.210    0.210
## 109              dsq_humor ~~        dsq_sublimation  6.352 -3.149  -3.149   -0.291   -0.291
## 177 dsq_reaction_formation ~~          dsq_isolation  6.305  1.941   1.941    0.153    0.153
## 226          dsq_isolation ~~             dsq_denial  6.264  1.690   1.690    0.138    0.138
## 107               Immature =~            dsq_undoing  6.261  2.551   0.991    0.252    0.252
## 238       dsq_dissociation ~~       dsq_somatization  6.245 -1.463  -1.463   -0.147   -0.147
## 95                Neurotic =~       dsq_displacement  6.133  0.451   0.870    0.230    0.230
## 103               Immature =~       dsq_anticipation  6.088  1.511   0.587    0.182    0.182
## 213            dsq_undoing ~~          dsq_isolation  5.775  2.090   2.090    0.148    0.148
## 134        dsq_suppression ~~        dsq_devaluation  5.713  1.437   1.437    0.146    0.146
## 255             dsq_denial ~~   dsq_autistic_fantasy  5.683  1.933   1.933    0.139    0.139
## 116              dsq_humor ~~       dsq_dissociation  5.616  1.170   1.170    0.145    0.145
## 143        dsq_sublimation ~~       dsq_anticipation  5.569  1.723   1.723    0.158    0.158
## 246        dsq_devaluation ~~       dsq_somatization  5.511 -1.552  -1.552   -0.141   -0.141
## 211    dsq_pseudo_altruism ~~         dsq_acting_out  5.419  1.609   1.609    0.137    0.137
## 218            dsq_undoing ~~   dsq_autistic_fantasy  5.220  2.378   2.378    0.150    0.150
## 204    dsq_pseudo_altruism ~~        dsq_devaluation  5.147 -1.135  -1.135   -0.134   -0.134
## 99                Neurotic =~         dsq_projection  5.048 -0.389  -0.751   -0.208   -0.208
## 115              dsq_humor ~~          dsq_isolation  4.994 -1.899  -1.899   -0.135   -0.135
## 273       dsq_somatization ~~         dsq_acting_out  4.963  2.011   2.011    0.132    0.132
## 195       dsq_idealization ~~   dsq_autistic_fantasy  4.936 -2.449  -2.449   -0.135   -0.135
## 124              dsq_humor ~~         dsq_acting_out  4.932  1.686   1.686    0.137    0.137
## 155        dsq_sublimation ~~ dsq_passive_aggression  4.881  1.491   1.491    0.158    0.158
## 88                Neurotic =~       dsq_anticipation  4.821  0.278   0.537    0.167    0.167
## 223            dsq_undoing ~~         dsq_projection  4.813 -1.517  -1.517   -0.153   -0.153
## 243        dsq_devaluation ~~   dsq_autistic_fantasy  4.501  1.724   1.724    0.124    0.124
## 274       dsq_somatization ~~         dsq_projection  4.485 -1.747  -1.747   -0.142   -0.142
## 190       dsq_idealization ~~          dsq_isolation  4.440 -1.947  -1.947   -0.121   -0.121
## 72                  Mature =~    dsq_pseudo_altruism  4.400  0.318   0.582    0.174    0.174
## 97                Neurotic =~       dsq_somatization  4.314  0.432   0.834    0.194    0.194
## 231          dsq_isolation ~~         dsq_acting_out  4.246 -1.910  -1.910   -0.112   -0.112
## 121              dsq_humor ~~       dsq_displacement  4.214  1.467   1.467    0.136    0.136
## 113              dsq_humor ~~    dsq_pseudo_altruism  4.195  1.327   1.327    0.137    0.137
## 110              dsq_humor ~~       dsq_anticipation  4.194 -1.440  -1.440   -0.140   -0.140
## 80                  Mature =~       dsq_displacement  4.193  0.345   0.632    0.167    0.167
## 91                Neurotic =~        dsq_devaluation  4.055 -0.280  -0.540   -0.181   -0.181
## 261   dsq_autistic_fantasy ~~       dsq_displacement  4.042 -2.131  -2.131   -0.126   -0.126
## 111              dsq_humor ~~ dsq_reaction_formation  3.876  1.312   1.312    0.143    0.143

4.3.9 Adding correlated errors in Three Factor Solution IV

model_3f_adj_kn_IV <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation + dsq_anticipation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_isolation + dsq_dissociation + dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
             
  # Add residual correlation within Immature factor
   dsq_isolation ~~ dsq_devaluation
   dsq_dissociation ~~ dsq_denial
   dsq_splitting ~~ dsq_acting_out
   
 # Add residual correlation within Immature factor
   dsq_suppression ~~        dsq_sublimation
  
'
fit3_adjkn_IV <- cfa(model_3f_adj_kn_IV, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_IV,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 217 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        64
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               336.084     313.491
##   Degrees of freedom                               145         145
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.072
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               774.640     708.842
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.683       0.687
##   Tucker-Lewis Index (TLI)                       0.627       0.631
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.697
##   Robust Tucker-Lewis Index (TLI)                            0.643
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15501.111  -15501.111
##   Scaling correction factor                                  1.013
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -15333.068  -15333.068
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               31130.221   31130.221
##   Bayesian (BIC)                             31368.531   31368.531
##   Sample-size adjusted Bayesian (SABIC)      31165.552   31165.552
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.066       0.062
##   90 Percent confidence interval - lower         0.056       0.053
##   90 Percent confidence interval - upper         0.075       0.071
##   P-value H_0: RMSEA <= 0.050                    0.003       0.018
##   P-value H_0: RMSEA >= 0.080                    0.005       0.000
##                                                                   
##   Robust RMSEA                                               0.064
##   90 Percent confidence interval - lower                     0.054
##   90 Percent confidence interval - upper                     0.073
##   P-value H_0: Robust RMSEA <= 0.050                         0.012
##   P-value H_0: Robust RMSEA >= 0.080                         0.003
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.075       0.075
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               2.448    0.665
##     dsq_suppressin    0.497    0.219    2.272    0.023    1.216    0.305
##     dsq_sublimatin    0.462    0.282    1.640    0.101    1.130    0.293
##     dsq_anticipatn   -0.055    0.136   -0.408    0.683   -0.136   -0.042
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.975    0.571
##     dsq_idealizatn    0.751    0.216    3.481    0.001    1.484    0.373
##     dsq_psed_ltrsm    0.703    0.177    3.977    0.000    1.388    0.415
##     dsq_undoing       1.182    0.188    6.288    0.000    2.334    0.593
##   Immature =~                                                           
##     dsq_isolation     1.000                               0.481    0.109
##     dsq_dissociatn    0.376    0.560    0.671    0.502    0.181    0.071
##     dsq_devaluatin    2.290    1.696    1.350    0.177    1.102    0.370
##     dsq_splitting     2.961    2.517    1.177    0.239    1.425    0.402
##     dsq_denial        1.627    1.242    1.310    0.190    0.783    0.270
##     dsq_tstc_fntsy    3.217    2.359    1.364    0.173    1.548    0.297
##     dsq_displacmnt    3.377    2.838    1.190    0.234    1.625    0.429
##     dsq_pssv_ggrss    4.507    3.512    1.283    0.199    2.169    0.616
##     dsq_somatizatn    3.512    2.876    1.221    0.222    1.690    0.392
##     dsq_acting_out    1.075    1.174    0.916    0.360    0.517    0.133
##     dsq_projection    3.832    3.089    1.240    0.215    1.844    0.512
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .dsq_isolation ~~                                                         
##    .dsq_devaluatin       3.188    0.762    4.185    0.000    3.188    0.262
##  .dsq_dissociation ~~                                                      
##    .dsq_denial           1.550    0.427    3.629    0.000    1.550    0.220
##  .dsq_splitting ~~                                                         
##    .dsq_acting_out       2.497    0.857    2.914    0.004    2.497    0.199
##  .dsq_suppression ~~                                                       
##    .dsq_sublimatin       3.103    0.996    3.115    0.002    3.103    0.222
##   Mature ~~                                                                
##     Neurotic             1.418    0.733    1.934    0.053    0.293    0.293
##     Immature            -0.439    0.419   -1.048    0.294   -0.373   -0.373
##   Neurotic ~~                                                              
##     Immature             0.509    0.426    1.193    0.233    0.535    0.535
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.425    0.228   32.546    0.000    7.425    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_anticipatn   10.706    0.184   58.190    0.000   10.706    3.326
##    .dsq_rctn_frmtn    9.107    0.199   45.841    0.000    9.107    2.631
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.272    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_isolation     8.097    0.254   31.905    0.000    8.097    1.829
##    .dsq_dissociatn    4.412    0.145   30.344    0.000    4.412    1.743
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.452    0.203   36.626    0.000    7.452    2.100
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.664    0.299   39.031    0.000   11.664    2.238
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.341    0.202   36.351    0.000    7.341    2.085
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.796    0.224   48.217    0.000   10.796    2.766
##    .dsq_projection    8.022    0.206   38.896    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         7.570    3.027    2.501    0.012    7.570    0.558
##    .dsq_suppressin   14.376    1.217   11.817    0.000   14.376    0.907
##    .dsq_sublimatin   13.591    1.279   10.626    0.000   13.591    0.914
##    .dsq_anticipatn   10.339    0.903   11.447    0.000   10.339    0.998
##    .dsq_rctn_frmtn    8.077    0.899    8.989    0.000    8.077    0.674
##    .dsq_idealizatn   13.631    1.347   10.121    0.000   13.631    0.861
##    .dsq_psed_ltrsm    9.280    0.939    9.884    0.000    9.280    0.828
##    .dsq_undoing      10.063    1.331    7.558    0.000   10.063    0.649
##    .dsq_isolation    19.355    1.144   16.919    0.000   19.355    0.988
##    .dsq_dissociatn    6.378    0.539   11.823    0.000    6.378    0.995
##    .dsq_devaluatin    7.663    0.707   10.843    0.000    7.663    0.863
##    .dsq_splitting    10.564    0.897   11.774    0.000   10.564    0.839
##    .dsq_denial        7.806    0.615   12.700    0.000    7.806    0.927
##    .dsq_tstc_fntsy   24.757    1.968   12.581    0.000   24.757    0.912
##    .dsq_displacmnt   11.690    0.965   12.113    0.000   11.690    0.816
##    .dsq_pssv_ggrss    7.691    0.895    8.593    0.000    7.691    0.621
##    .dsq_somatizatn   15.699    1.362   11.524    0.000   15.699    0.846
##    .dsq_acting_out   14.971    0.945   15.834    0.000   14.971    0.982
##    .dsq_projection    9.593    1.064    9.020    0.000    9.593    0.738
##     Mature            5.993    3.095    1.936    0.053    1.000    1.000
##     Neurotic          3.901    1.000    3.900    0.000    1.000    1.000
##     Immature          0.232    0.357    0.649    0.516    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.442
##     dsq_suppressin    0.093
##     dsq_sublimatin    0.086
##     dsq_anticipatn    0.002
##     dsq_rctn_frmtn    0.326
##     dsq_idealizatn    0.139
##     dsq_psed_ltrsm    0.172
##     dsq_undoing       0.351
##     dsq_isolation     0.012
##     dsq_dissociatn    0.005
##     dsq_devaluatin    0.137
##     dsq_splitting     0.161
##     dsq_denial        0.073
##     dsq_tstc_fntsy    0.088
##     dsq_displacmnt    0.184
##     dsq_pssv_ggrss    0.379
##     dsq_somatizatn    0.154
##     dsq_acting_out    0.018
##     dsq_projection    0.262
modindices(fit3_adjkn_IV, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                  rhs     mi    epc sepc.lv sepc.all sepc.nox
## 193       dsq_idealization ~~        dsq_splitting 20.912  3.290   3.290    0.274    0.274
## 76                  Mature =~     dsq_dissociation 16.714  0.355   0.869    0.343    0.343
## 180 dsq_reaction_formation ~~        dsq_splitting 11.612 -2.047  -2.047   -0.222   -0.222
## 202    dsq_pseudo_altruism ~~        dsq_isolation 11.248 -2.597  -2.597   -0.194   -0.194
## 145        dsq_sublimation ~~     dsq_idealization 11.180  2.675   2.675    0.197    0.197
## 74                  Mature =~          dsq_undoing 11.097 -0.448  -1.096   -0.278   -0.278
## 210    dsq_pseudo_altruism ~~     dsq_somatization  9.812  2.335   2.335    0.193    0.193
## 81                  Mature =~     dsq_displacement  8.282  0.368   0.900    0.238    0.238
## 96                Neurotic =~     dsq_displacement  8.254  0.498   0.983    0.260    0.260
## 91                Neurotic =~     dsq_dissociation  8.126  0.334   0.659    0.260    0.260
## 88                Neurotic =~      dsq_sublimation  8.107  0.402   0.794    0.206    0.206
## 117              dsq_humor ~~     dsq_dissociation  6.925  1.292   1.292    0.186    0.186
## 149        dsq_sublimation ~~     dsq_dissociation  6.923  1.358   1.358    0.146    0.146
## 177 dsq_reaction_formation ~~        dsq_isolation  6.806  2.008   2.008    0.161    0.161
## 174 dsq_reaction_formation ~~     dsq_idealization  6.268 -2.006  -2.006   -0.191   -0.191
## 108               Immature =~          dsq_undoing  6.250  1.990   0.958    0.243    0.243
## 87                Neurotic =~      dsq_suppression  6.218 -0.365  -0.721   -0.181   -0.181
## 176 dsq_reaction_formation ~~          dsq_undoing  6.098  2.519   2.519    0.279    0.279
## 238       dsq_dissociation ~~     dsq_somatization  6.050 -1.440  -1.440   -0.144   -0.144
## 213            dsq_undoing ~~        dsq_isolation  6.028  2.129   2.129    0.153    0.153
## 122              dsq_humor ~~     dsq_displacement  5.954  1.773   1.773    0.188    0.188
## 255             dsq_denial ~~ dsq_autistic_fantasy  5.841  1.959   1.959    0.141    0.141
## 226          dsq_isolation ~~           dsq_denial  5.790  1.626   1.626    0.132    0.132
## 272 dsq_passive_aggression ~~       dsq_projection  5.698  1.683   1.683    0.196    0.196
## 246        dsq_devaluation ~~     dsq_somatization  5.644 -1.567  -1.567   -0.143   -0.143
## 143        dsq_sublimation ~~     dsq_anticipation  5.511  1.592   1.592    0.134    0.134
## 103               Immature =~      dsq_sublimation  5.477  1.405   0.676    0.175    0.175
## 80                  Mature =~ dsq_autistic_fantasy  5.458 -0.420  -1.027   -0.197   -0.197
## 125              dsq_humor ~~       dsq_acting_out  5.445  1.764   1.764    0.166    0.166
## 273       dsq_somatization ~~       dsq_acting_out  5.419  2.102   2.102    0.137    0.137
## 116              dsq_humor ~~        dsq_isolation  5.355 -1.957  -1.957   -0.162   -0.162
## 100               Neurotic =~       dsq_projection  5.297 -0.378  -0.746   -0.207   -0.207
## 211    dsq_pseudo_altruism ~~       dsq_acting_out  5.215  1.580   1.580    0.134    0.134
## 134        dsq_suppression ~~      dsq_devaluation  5.133  1.344   1.344    0.128    0.128
## 195       dsq_idealization ~~ dsq_autistic_fantasy  5.132 -2.507  -2.507   -0.136   -0.136
## 89                Neurotic =~     dsq_anticipation  5.053  0.275   0.543    0.169    0.169
## 223            dsq_undoing ~~       dsq_projection  5.025 -1.543  -1.543   -0.157   -0.157
## 204    dsq_pseudo_altruism ~~      dsq_devaluation  4.950 -1.111  -1.111   -0.132   -0.132
## 104               Immature =~     dsq_anticipation  4.921  1.133   0.545    0.169    0.169
## 218            dsq_undoing ~~ dsq_autistic_fantasy  4.795  2.272   2.272    0.144    0.144
## 98                Neurotic =~     dsq_somatization  4.771  0.432   0.854    0.198    0.198
## 92                Neurotic =~      dsq_devaluation  4.581 -0.283  -0.558   -0.187   -0.187
## 131        dsq_suppression ~~          dsq_undoing  4.513 -1.684  -1.684   -0.140   -0.140
## 102               Immature =~      dsq_suppression  4.477 -1.320  -0.635   -0.160   -0.160
## 73                  Mature =~  dsq_pseudo_altruism  4.459  0.231   0.566    0.169    0.169
## 243        dsq_devaluation ~~ dsq_autistic_fantasy  4.395  1.699   1.699    0.123    0.123
## 115              dsq_humor ~~          dsq_undoing  4.346 -1.726  -1.726   -0.198   -0.198
## 79                  Mature =~           dsq_denial  4.335  0.203   0.497    0.171    0.171
## 274       dsq_somatization ~~       dsq_projection  4.330 -1.708  -1.708   -0.139   -0.139
## 231          dsq_isolation ~~       dsq_acting_out  4.303 -1.923  -1.923   -0.113   -0.113
## 94                Neurotic =~           dsq_denial  4.275  0.272   0.538    0.185    0.185
## 190       dsq_idealization ~~        dsq_isolation  4.245 -1.912  -1.912   -0.118   -0.118

4.3.10 Removing weakest loading defense (anticipation) Three Factor Solution V

model_3f_adj_kn_V <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_isolation + dsq_dissociation + dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  
'
fit3_adjkn_V <- cfa(model_3f_adj_kn_V, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_V,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 145 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        57
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               368.430     351.270
##   Degrees of freedom                               132         132
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.049
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               750.691     691.208
##   Degrees of freedom                               153         153
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.086
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.604       0.593
##   Tucker-Lewis Index (TLI)                       0.541       0.528
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.613
##   Robust Tucker-Lewis Index (TLI)                            0.552
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -14737.387  -14737.387
##   Scaling correction factor                                  1.035
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -14553.171  -14553.171
##   Scaling correction factor                                  1.045
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               29588.773   29588.773
##   Bayesian (BIC)                             29801.017   29801.017
##   Sample-size adjusted Bayesian (SABIC)      29620.240   29620.240
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.077       0.074
##   90 Percent confidence interval - lower         0.067       0.065
##   90 Percent confidence interval - upper         0.086       0.083
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.275       0.131
##                                                                   
##   Robust RMSEA                                               0.075
##   90 Percent confidence interval - lower                     0.065
##   90 Percent confidence interval - upper                     0.085
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.215
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.080       0.080
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.884    0.512
##     dsq_suppressin    0.948    0.541    1.752    0.080    1.787    0.449
##     dsq_sublimatin    0.946    0.536    1.764    0.078    1.783    0.462
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.941    0.561
##     dsq_idealizatn    0.795    0.236    3.373    0.001    1.543    0.388
##     dsq_psed_ltrsm    0.710    0.178    3.997    0.000    1.377    0.411
##     dsq_undoing       1.203    0.203    5.918    0.000    2.334    0.593
##   Immature =~                                                           
##     dsq_isolation     1.000                               0.576    0.130
##     dsq_dissociatn    0.463    0.547    0.846    0.397    0.267    0.105
##     dsq_devaluatin    1.926    1.178    1.635    0.102    1.110    0.372
##     dsq_splitting     2.520    2.006    1.256    0.209    1.452    0.409
##     dsq_denial        1.465    1.063    1.378    0.168    0.844    0.291
##     dsq_tstc_fntsy    2.777    1.796    1.547    0.122    1.600    0.307
##     dsq_displacmnt    2.851    2.217    1.286    0.198    1.643    0.434
##     dsq_pssv_ggrss    3.698    2.583    1.432    0.152    2.130    0.605
##     dsq_somatizatn    2.950    2.294    1.286    0.198    1.700    0.395
##     dsq_acting_out    1.182    1.168    1.012    0.311    0.681    0.174
##     dsq_projection    3.138    2.245    1.398    0.162    1.808    0.502
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.080    0.809    1.336    0.182    0.295    0.295
##     Immature         -0.330    0.409   -0.806    0.420   -0.304   -0.304
##   Neurotic ~~                                                           
##     Immature          0.609    0.456    1.336    0.182    0.545    0.545
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.549    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_rctn_frmtn    9.107    0.199   45.844    0.000    9.107    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.272    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_isolation     8.098    0.254   31.895    0.000    8.098    1.829
##    .dsq_dissociatn    4.413    0.145   30.343    0.000    4.413    1.743
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.453    0.203   36.640    0.000    7.453    2.101
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.665    0.299   39.038    0.000   11.665    2.239
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.341    0.202   36.336    0.000    7.341    2.085
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.797    0.224   48.221    0.000   10.797    2.766
##    .dsq_projection    8.023    0.206   38.896    0.000    8.023    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.013    2.008    4.986    0.000   10.013    0.738
##    .dsq_suppressin   12.661    2.134    5.933    0.000   12.661    0.799
##    .dsq_sublimatin   11.689    1.939    6.029    0.000   11.689    0.786
##    .dsq_rctn_frmtn    8.210    0.935    8.783    0.000    8.210    0.686
##    .dsq_idealizatn   13.453    1.385    9.713    0.000   13.453    0.850
##    .dsq_psed_ltrsm    9.310    0.936    9.948    0.000    9.310    0.831
##    .dsq_undoing      10.060    1.373    7.326    0.000   10.060    0.649
##    .dsq_isolation    19.262    1.172   16.430    0.000   19.262    0.983
##    .dsq_dissociatn    6.336    0.543   11.665    0.000    6.336    0.989
##    .dsq_devaluatin    7.647    0.734   10.417    0.000    7.647    0.861
##    .dsq_splitting    10.477    0.896   11.691    0.000   10.477    0.833
##    .dsq_denial        7.707    0.611   12.616    0.000    7.707    0.915
##    .dsq_tstc_fntsy   24.592    1.990   12.357    0.000   24.592    0.906
##    .dsq_displacmnt   11.633    0.984   11.816    0.000   11.633    0.812
##    .dsq_pssv_ggrss    7.856    0.919    8.549    0.000    7.856    0.634
##    .dsq_somatizatn   15.666    1.397   11.218    0.000   15.666    0.844
##    .dsq_acting_out   14.775    0.953   15.501    0.000   14.775    0.970
##    .dsq_projection    9.723    1.065    9.126    0.000    9.723    0.748
##     Mature            3.550    2.086    1.702    0.089    1.000    1.000
##     Neurotic          3.767    1.025    3.674    0.000    1.000    1.000
##     Immature          0.332    0.461    0.720    0.472    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.262
##     dsq_suppressin    0.201
##     dsq_sublimatin    0.214
##     dsq_rctn_frmtn    0.314
##     dsq_idealizatn    0.150
##     dsq_psed_ltrsm    0.169
##     dsq_undoing       0.351
##     dsq_isolation     0.017
##     dsq_dissociatn    0.011
##     dsq_devaluatin    0.139
##     dsq_splitting     0.167
##     dsq_denial        0.085
##     dsq_tstc_fntsy    0.094
##     dsq_displacmnt    0.188
##     dsq_pssv_ggrss    0.366
##     dsq_somatizatn    0.156
##     dsq_acting_out    0.030
##     dsq_projection    0.252
modindices(fit3_adjkn_V, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 69                  Mature =~       dsq_dissociation 24.187  0.563   1.061    0.419    0.419
## 167       dsq_idealization ~~          dsq_splitting 21.929  3.427   3.427    0.289    0.289
## 199          dsq_isolation ~~        dsq_devaluation 21.531  3.367   3.367    0.277    0.277
## 176    dsq_pseudo_altruism ~~          dsq_isolation 17.931 -3.402  -3.402   -0.254   -0.254
## 154 dsq_reaction_formation ~~          dsq_splitting 15.499 -2.421  -2.421   -0.261   -0.261
## 67                  Mature =~            dsq_undoing 13.853 -0.674  -1.271   -0.323   -0.323
## 210       dsq_dissociation ~~             dsq_denial 13.683  1.520   1.520    0.218    0.218
## 178    dsq_pseudo_altruism ~~        dsq_devaluation 11.096 -1.727  -1.727   -0.205   -0.205
## 230          dsq_splitting ~~         dsq_acting_out 10.963  2.506   2.506    0.201    0.201
## 117        dsq_suppression ~~        dsq_sublimation 10.254  3.851   3.851    0.317    0.317
## 83                Neurotic =~       dsq_dissociation 10.061  0.398   0.772    0.305    0.305
## 73                  Mature =~   dsq_autistic_fantasy  9.968 -0.729  -1.373   -0.263   -0.263
## 184    dsq_pseudo_altruism ~~       dsq_somatization  9.875  2.342   2.342    0.194    0.194
## 134        dsq_sublimation ~~       dsq_idealization  9.584  2.508   2.508    0.200    0.200
## 124        dsq_suppression ~~        dsq_devaluation  8.607  1.828   1.828    0.186    0.186
## 138        dsq_sublimation ~~       dsq_dissociation  8.186  1.523   1.523    0.177    0.177
## 95                Immature =~        dsq_sublimation  7.997  1.505   0.867    0.225    0.225
## 206          dsq_isolation ~~         dsq_acting_out  7.936 -2.765  -2.765   -0.164   -0.164
## 72                  Mature =~             dsq_denial  7.758  0.358   0.674    0.232    0.232
## 107              dsq_humor ~~       dsq_dissociation  7.691  1.400   1.400    0.176    0.176
## 222        dsq_devaluation ~~       dsq_somatization  7.549 -1.883  -1.883   -0.172   -0.172
## 80                Neurotic =~        dsq_suppression  7.372 -0.449  -0.871   -0.219   -0.219
## 106              dsq_humor ~~          dsq_isolation  7.278 -2.374  -2.374   -0.171   -0.171
## 150 dsq_reaction_formation ~~            dsq_undoing  7.233  2.712   2.712    0.298    0.298
## 121        dsq_suppression ~~            dsq_undoing  7.197 -2.185  -2.185   -0.194   -0.194
## 249 dsq_passive_aggression ~~         dsq_projection  7.158  1.860   1.860    0.213    0.213
## 148 dsq_reaction_formation ~~       dsq_idealization  7.044 -2.137  -2.137   -0.203   -0.203
## 219        dsq_devaluation ~~   dsq_autistic_fantasy  6.878  2.205   2.205    0.161    0.161
## 81                Neurotic =~        dsq_sublimation  6.784  0.419   0.814    0.211    0.211
## 99                Immature =~            dsq_undoing  6.662  1.789   1.031    0.262    0.262
## 108              dsq_humor ~~        dsq_devaluation  6.458 -1.450  -1.450   -0.166   -0.166
## 101              dsq_humor ~~        dsq_sublimation  6.416 -3.254  -3.254   -0.301   -0.301
## 86                Neurotic =~             dsq_denial  6.305  0.354   0.687    0.237    0.237
## 164       dsq_idealization ~~          dsq_isolation  6.224 -2.392  -2.392   -0.149   -0.149
## 214       dsq_dissociation ~~       dsq_somatization  6.206 -1.492  -1.492   -0.150   -0.150
## 88                Neurotic =~       dsq_displacement  6.187  0.450   0.874    0.231    0.231
## 160 dsq_reaction_formation ~~         dsq_acting_out  5.927 -1.708  -1.708   -0.155   -0.155
## 122        dsq_suppression ~~          dsq_isolation  5.701  2.300   2.300    0.147    0.147
## 250       dsq_somatization ~~         dsq_acting_out  5.682  2.190   2.190    0.144    0.144
## 202          dsq_isolation ~~   dsq_autistic_fantasy  5.449  3.006   3.006    0.138    0.138
## 151 dsq_reaction_formation ~~          dsq_isolation  5.441  1.866   1.866    0.148    0.148
## 187            dsq_undoing ~~          dsq_isolation  5.352  2.080   2.080    0.149    0.149
## 92                Neurotic =~         dsq_projection  5.247 -0.393  -0.763   -0.212   -0.212
## 169       dsq_idealization ~~   dsq_autistic_fantasy  5.109 -2.488  -2.488   -0.137   -0.137
## 192            dsq_undoing ~~   dsq_autistic_fantasy  4.870  2.286   2.286    0.145    0.145
## 197            dsq_undoing ~~         dsq_projection  4.849 -1.517  -1.517   -0.153   -0.153
## 185    dsq_pseudo_altruism ~~         dsq_acting_out  4.769  1.540   1.540    0.131    0.131
## 66                  Mature =~    dsq_pseudo_altruism  4.708  0.319   0.602    0.180    0.180
## 232             dsq_denial ~~   dsq_autistic_fantasy  4.683  1.792   1.792    0.130    0.130
## 115              dsq_humor ~~         dsq_acting_out  4.596  1.657   1.657    0.136    0.136
## 229          dsq_splitting ~~       dsq_somatization  4.555  1.740   1.740    0.136    0.136
## 90                Neurotic =~       dsq_somatization  4.303  0.429   0.833    0.193    0.193
## 104              dsq_humor ~~    dsq_pseudo_altruism  4.122  1.317   1.317    0.136    0.136
## 84                Neurotic =~        dsq_devaluation  4.096 -0.290  -0.563   -0.189   -0.189
## 238   dsq_autistic_fantasy ~~       dsq_displacement  4.046 -2.128  -2.128   -0.126   -0.126
## 144        dsq_sublimation ~~ dsq_passive_aggression  4.043  1.353   1.353    0.141    0.141
## 112              dsq_humor ~~       dsq_displacement  4.005  1.431   1.431    0.133    0.133
## 203          dsq_isolation ~~       dsq_displacement  3.920 -1.804  -1.804   -0.120   -0.120
## 251       dsq_somatization ~~         dsq_projection  3.919 -1.625  -1.625   -0.132   -0.132
## 142        dsq_sublimation ~~   dsq_autistic_fantasy  3.880 -2.102  -2.102   -0.124   -0.124

4.3.11 Removing weakest loading defense (dissociation) Three Factor Solution VI

model_3f_adj_kn_VI <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_isolation + dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  
'
fit3_adjkn_VI <- cfa(model_3f_adj_kn_VI, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_VI,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 145 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        54
## 
##   Number of observations                           306
##   Number of missing patterns                        10
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               310.965     292.089
##   Degrees of freedom                               116         116
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.065
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               690.998     628.448
##   Degrees of freedom                               136         136
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.100
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.649       0.642
##   Tucker-Lewis Index (TLI)                       0.588       0.581
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.660
##   Robust Tucker-Lewis Index (TLI)                            0.602
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -14027.158  -14027.158
##   Scaling correction factor                                  1.023
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -13871.676  -13871.676
##   Scaling correction factor                                  1.051
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               28162.316   28162.316
##   Bayesian (BIC)                             28363.390   28363.390
##   Sample-size adjusted Bayesian (SABIC)      28192.127   28192.127
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.074       0.070
##   90 Percent confidence interval - lower         0.064       0.061
##   90 Percent confidence interval - upper         0.084       0.080
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.171       0.054
##                                                                   
##   Robust RMSEA                                               0.072
##   90 Percent confidence interval - lower                     0.062
##   90 Percent confidence interval - upper                     0.083
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.120
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.076       0.076
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.924    0.522
##     dsq_suppressin    0.914    0.503    1.817    0.069    1.757    0.441
##     dsq_sublimatin    0.910    0.492    1.849    0.064    1.750    0.454
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.947    0.562
##     dsq_idealizatn    0.788    0.233    3.379    0.001    1.535    0.386
##     dsq_psed_ltrsm    0.707    0.177    3.997    0.000    1.377    0.411
##     dsq_undoing       1.199    0.202    5.936    0.000    2.335    0.593
##   Immature =~                                                           
##     dsq_isolation     1.000                               0.589    0.133
##     dsq_devaluatin    1.873    1.118    1.676    0.094    1.103    0.370
##     dsq_splitting     2.450    1.920    1.276    0.202    1.442    0.407
##     dsq_denial        1.379    0.972    1.418    0.156    0.812    0.280
##     dsq_tstc_fntsy    2.744    1.749    1.569    0.117    1.616    0.310
##     dsq_displacmnt    2.792    2.148    1.300    0.194    1.644    0.434
##     dsq_pssv_ggrss    3.605    2.482    1.453    0.146    2.123    0.603
##     dsq_somatizatn    2.939    2.262    1.299    0.194    1.730    0.402
##     dsq_acting_out    1.142    1.121    1.019    0.308    0.672    0.172
##     dsq_projection    3.065    2.159    1.420    0.156    1.804    0.501
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.114    0.799    1.395    0.163    0.298    0.298
##     Immature         -0.377    0.426   -0.887    0.375   -0.333   -0.333
##   Neurotic ~~                                                           
##     Immature          0.618    0.456    1.355    0.175    0.539    0.539
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.550    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_rctn_frmtn    9.107    0.199   45.845    0.000    9.107    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.271    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_isolation     8.098    0.254   31.894    0.000    8.098    1.829
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.453    0.203   36.637    0.000    7.453    2.101
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.665    0.299   39.036    0.000   11.665    2.239
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.341    0.202   36.336    0.000    7.341    2.085
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.798    0.224   48.220    0.000   10.798    2.766
##    .dsq_projection    8.023    0.206   38.897    0.000    8.023    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.863    1.948    5.063    0.000    9.863    0.727
##    .dsq_suppressin   12.766    2.064    6.186    0.000   12.766    0.805
##    .dsq_sublimatin   11.806    1.852    6.375    0.000   11.806    0.794
##    .dsq_rctn_frmtn    8.187    0.933    8.772    0.000    8.187    0.684
##    .dsq_idealizatn   13.477    1.377    9.788    0.000   13.477    0.851
##    .dsq_psed_ltrsm    9.310    0.935    9.956    0.000    9.310    0.831
##    .dsq_undoing      10.058    1.361    7.392    0.000   10.058    0.649
##    .dsq_isolation    19.248    1.179   16.331    0.000   19.248    0.982
##    .dsq_devaluatin    7.661    0.740   10.358    0.000    7.661    0.863
##    .dsq_splitting    10.505    0.902   11.652    0.000   10.505    0.835
##    .dsq_denial        7.760    0.615   12.615    0.000    7.760    0.922
##    .dsq_tstc_fntsy   24.541    1.997   12.288    0.000   24.541    0.904
##    .dsq_displacmnt   11.628    0.987   11.777    0.000   11.628    0.811
##    .dsq_pssv_ggrss    7.888    0.919    8.585    0.000    7.888    0.636
##    .dsq_somatizatn   15.561    1.397   11.140    0.000   15.561    0.839
##    .dsq_acting_out   14.786    0.952   15.539    0.000   14.786    0.970
##    .dsq_projection    9.737    1.069    9.108    0.000    9.737    0.749
##     Mature            3.700    2.021    1.830    0.067    1.000    1.000
##     Neurotic          3.789    1.025    3.698    0.000    1.000    1.000
##     Immature          0.347    0.474    0.732    0.464    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.273
##     dsq_suppressin    0.195
##     dsq_sublimatin    0.206
##     dsq_rctn_frmtn    0.316
##     dsq_idealizatn    0.149
##     dsq_psed_ltrsm    0.169
##     dsq_undoing       0.351
##     dsq_isolation     0.018
##     dsq_devaluatin    0.137
##     dsq_splitting     0.165
##     dsq_denial        0.078
##     dsq_tstc_fntsy    0.096
##     dsq_displacmnt    0.189
##     dsq_pssv_ggrss    0.364
##     dsq_somatizatn    0.161
##     dsq_acting_out    0.030
##     dsq_projection    0.251
modindices(fit3_adjkn_VI, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 157       dsq_idealization ~~          dsq_splitting 22.167  3.450   3.450    0.290    0.290
## 186          dsq_isolation ~~        dsq_devaluation 21.357  3.355   3.355    0.276    0.276
## 166    dsq_pseudo_altruism ~~          dsq_isolation 17.900 -3.398  -3.398   -0.254   -0.254
## 145 dsq_reaction_formation ~~          dsq_splitting 15.385 -2.413  -2.413   -0.260   -0.260
## 64                  Mature =~            dsq_undoing 13.742 -0.653  -1.257   -0.319   -0.319
## 208          dsq_splitting ~~         dsq_acting_out 11.084  2.522   2.522    0.202    0.202
## 167    dsq_pseudo_altruism ~~        dsq_devaluation 10.856 -1.709  -1.709   -0.202   -0.202
## 111        dsq_suppression ~~        dsq_sublimation 10.434  3.676   3.676    0.299    0.299
## 173    dsq_pseudo_altruism ~~       dsq_somatization 10.039  2.358   2.358    0.196    0.196
## 127        dsq_sublimation ~~       dsq_idealization  9.655  2.520   2.520    0.200    0.200
## 69                  Mature =~   dsq_autistic_fantasy  9.094 -0.688  -1.324   -0.254   -0.254
## 117        dsq_suppression ~~        dsq_devaluation  8.695  1.841   1.841    0.186    0.186
## 68                  Mature =~             dsq_denial  8.324  0.367   0.706    0.243    0.243
## 193          dsq_isolation ~~         dsq_acting_out  7.958 -2.769  -2.769   -0.164   -0.164
## 200        dsq_devaluation ~~       dsq_somatization  7.844 -1.919  -1.919   -0.176   -0.176
## 90                Immature =~        dsq_sublimation  7.696  1.463   0.861    0.223    0.223
## 227 dsq_passive_aggression ~~         dsq_projection  7.400  1.891   1.891    0.216    0.216
## 115        dsq_suppression ~~            dsq_undoing  7.188 -2.184  -2.184   -0.193   -0.193
## 94                Immature =~            dsq_undoing  7.147  1.782   1.049    0.266    0.266
## 101              dsq_humor ~~          dsq_isolation  7.128 -2.344  -2.344   -0.170   -0.170
## 142 dsq_reaction_formation ~~            dsq_undoing  7.039  2.684   2.684    0.296    0.296
## 140 dsq_reaction_formation ~~       dsq_idealization  6.978 -2.127  -2.127   -0.202   -0.202
## 76                Neurotic =~        dsq_suppression  6.934 -0.431  -0.839   -0.211   -0.211
## 81                Neurotic =~             dsq_denial  6.905  0.365   0.711    0.245    0.245
## 197        dsq_devaluation ~~   dsq_autistic_fantasy  6.832  2.198   2.198    0.160    0.160
## 83                Neurotic =~       dsq_displacement  6.636  0.459   0.894    0.236    0.236
## 77                Neurotic =~        dsq_sublimation  6.592  0.409   0.796    0.206    0.206
## 96               dsq_humor ~~        dsq_sublimation  6.292 -3.147  -3.147   -0.292   -0.292
## 155       dsq_idealization ~~          dsq_isolation  6.194 -2.387  -2.387   -0.148   -0.148
## 102              dsq_humor ~~        dsq_devaluation  6.039 -1.402  -1.402   -0.161   -0.161
## 151 dsq_reaction_formation ~~         dsq_acting_out  5.959 -1.713  -1.713   -0.156   -0.156
## 116        dsq_suppression ~~          dsq_isolation  5.816  2.325   2.325    0.148    0.148
## 228       dsq_somatization ~~         dsq_acting_out  5.700  2.191   2.191    0.144    0.144
## 143 dsq_reaction_formation ~~          dsq_isolation  5.450  1.867   1.867    0.149    0.149
## 189          dsq_isolation ~~   dsq_autistic_fantasy  5.357  2.979   2.979    0.137    0.137
## 176            dsq_undoing ~~          dsq_isolation  5.266  2.062   2.062    0.148    0.148
## 159       dsq_idealization ~~   dsq_autistic_fantasy  5.028 -2.468  -2.468   -0.136   -0.136
## 185            dsq_undoing ~~         dsq_projection  4.991 -1.540  -1.540   -0.156   -0.156
## 210             dsq_denial ~~   dsq_autistic_fantasy  4.872  1.830   1.830    0.133    0.133
## 109              dsq_humor ~~         dsq_acting_out  4.792  1.689   1.689    0.140    0.140
## 174    dsq_pseudo_altruism ~~         dsq_acting_out  4.792  1.545   1.545    0.132    0.132
## 180            dsq_undoing ~~   dsq_autistic_fantasy  4.772  2.262   2.262    0.144    0.144
## 63                  Mature =~    dsq_pseudo_altruism  4.731  0.312   0.599    0.179    0.179
## 70                  Mature =~       dsq_displacement  4.688  0.352   0.676    0.179    0.179
## 87                Neurotic =~         dsq_projection  4.618 -0.363  -0.708   -0.196   -0.196
## 136        dsq_sublimation ~~ dsq_passive_aggression  4.546  1.440   1.440    0.149    0.149
## 106              dsq_humor ~~       dsq_displacement  4.433  1.506   1.506    0.141    0.141
## 207          dsq_splitting ~~       dsq_somatization  4.407  1.711   1.711    0.134    0.134
## 85                Neurotic =~       dsq_somatization  4.329  0.424   0.825    0.191    0.191
## 229       dsq_somatization ~~         dsq_projection  4.298 -1.702  -1.702   -0.138   -0.138
## 216   dsq_autistic_fantasy ~~       dsq_displacement  4.196 -2.167  -2.167   -0.128   -0.128
## 190          dsq_isolation ~~       dsq_displacement  4.035 -1.830  -1.830   -0.122   -0.122
## 99               dsq_humor ~~    dsq_pseudo_altruism  3.986  1.294   1.294    0.135    0.135

4.3.12 Removing weakest loading defense (isolation) Three Factor Solution VII

model_3f_adj_kn_VII <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_acting_out + dsq_projection
  
'
fit3_adjkn_VII <- cfa(model_3f_adj_kn_VII, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_VII,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 118 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        51
## 
##   Number of observations                           306
##   Number of missing patterns                         9
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               246.221     231.112
##   Degrees of freedom                               101         101
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.065
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               622.809     566.624
##   Degrees of freedom                               120         120
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.099
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.711       0.709
##   Tucker-Lewis Index (TLI)                       0.657       0.654
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.724
##   Robust Tucker-Lewis Index (TLI)                            0.672
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -13145.278  -13145.278
##   Scaling correction factor                                  1.020
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -13022.168  -13022.168
##   Scaling correction factor                                  1.050
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               26392.556   26392.556
##   Bayesian (BIC)                             26582.459   26582.459
##   Sample-size adjusted Bayesian (SABIC)      26420.711   26420.711
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.069       0.065
##   90 Percent confidence interval - lower         0.058       0.054
##   90 Percent confidence interval - upper         0.079       0.076
##   P-value H_0: RMSEA <= 0.050                    0.003       0.012
##   P-value H_0: RMSEA >= 0.080                    0.042       0.009
##                                                                   
##   Robust RMSEA                                               0.066
##   90 Percent confidence interval - lower                     0.055
##   90 Percent confidence interval - upper                     0.078
##   P-value H_0: Robust RMSEA <= 0.050                         0.011
##   P-value H_0: Robust RMSEA >= 0.080                         0.027
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.070       0.070
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.864    0.506
##     dsq_suppressin    0.970    0.487    1.990    0.047    1.808    0.454
##     dsq_sublimatin    0.963    0.474    2.030    0.042    1.795    0.466
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.915    0.553
##     dsq_idealizatn    0.821    0.237    3.464    0.001    1.573    0.395
##     dsq_psed_ltrsm    0.737    0.179    4.125    0.000    1.411    0.421
##     dsq_undoing       1.203    0.199    6.036    0.000    2.303    0.585
##   Immature =~                                                           
##     dsq_devaluatin    1.000                               1.037    0.348
##     dsq_splitting     1.427    0.417    3.421    0.001    1.479    0.417
##     dsq_denial        0.765    0.278    2.757    0.006    0.793    0.273
##     dsq_tstc_fntsy    1.492    0.425    3.507    0.000    1.547    0.297
##     dsq_displacmnt    1.626    0.466    3.492    0.000    1.685    0.445
##     dsq_pssv_ggrss    2.043    0.436    4.689    0.000    2.118    0.602
##     dsq_somatizatn    1.715    0.609    2.817    0.005    1.778    0.413
##     dsq_acting_out    0.707    0.372    1.900    0.057    0.732    0.188
##     dsq_projection    1.732    0.355    4.877    0.000    1.796    0.498
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.069    0.761    1.404    0.160    0.299    0.299
##     Immature         -0.621    0.471   -1.320    0.187   -0.322   -0.322
##   Neurotic ~~                                                           
##     Immature          1.081    0.281    3.841    0.000    0.544    0.544
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.550    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_rctn_frmtn    9.107    0.199   45.843    0.000    9.107    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.271    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.453    0.203   36.638    0.000    7.453    2.101
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.664    0.299   39.033    0.000   11.664    2.238
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.343    0.202   36.356    0.000    7.343    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_acting_out   10.797    0.224   48.217    0.000   10.797    2.766
##    .dsq_projection    8.022    0.206   38.892    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.090    1.743    5.788    0.000   10.090    0.744
##    .dsq_suppressin   12.587    1.999    6.296    0.000   12.587    0.794
##    .dsq_sublimatin   11.647    1.750    6.654    0.000   11.647    0.783
##    .dsq_rctn_frmtn    8.310    0.930    8.932    0.000    8.310    0.694
##    .dsq_idealizatn   13.359    1.364    9.794    0.000   13.359    0.844
##    .dsq_psed_ltrsm    9.217    0.925    9.968    0.000    9.217    0.822
##    .dsq_undoing      10.206    1.365    7.477    0.000   10.206    0.658
##    .dsq_devaluatin    7.803    0.713   10.939    0.000    7.803    0.879
##    .dsq_splitting    10.398    0.892   11.660    0.000   10.398    0.826
##    .dsq_denial        7.790    0.612   12.738    0.000    7.790    0.925
##    .dsq_tstc_fntsy   24.760    1.954   12.673    0.000   24.760    0.912
##    .dsq_displacmnt   11.491    0.968   11.869    0.000   11.491    0.802
##    .dsq_pssv_ggrss    7.907    0.946    8.360    0.000    7.907    0.638
##    .dsq_somatizatn   15.394    1.401   10.987    0.000   15.394    0.830
##    .dsq_acting_out   14.702    0.949   15.486    0.000   14.702    0.965
##    .dsq_projection    9.768    1.080    9.040    0.000    9.768    0.752
##     Mature            3.474    1.803    1.927    0.054    1.000    1.000
##     Neurotic          3.667    1.009    3.633    0.000    1.000    1.000
##     Immature          1.075    0.456    2.358    0.018    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.256
##     dsq_suppressin    0.206
##     dsq_sublimatin    0.217
##     dsq_rctn_frmtn    0.306
##     dsq_idealizatn    0.156
##     dsq_psed_ltrsm    0.178
##     dsq_undoing       0.342
##     dsq_devaluatin    0.121
##     dsq_splitting     0.174
##     dsq_denial        0.075
##     dsq_tstc_fntsy    0.088
##     dsq_displacmnt    0.198
##     dsq_pssv_ggrss    0.362
##     dsq_somatizatn    0.170
##     dsq_acting_out    0.035
##     dsq_projection    0.248
modindices(fit3_adjkn_VII, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 147       dsq_idealization ~~          dsq_splitting 21.396  3.376   3.376    0.286    0.286
## 136 dsq_reaction_formation ~~          dsq_splitting 15.462 -2.422  -2.422   -0.261   -0.261
## 61                  Mature =~            dsq_undoing 13.142 -0.660  -1.231   -0.312   -0.312
## 156    dsq_pseudo_altruism ~~        dsq_devaluation 11.094 -1.734  -1.734   -0.204   -0.204
## 187          dsq_splitting ~~         dsq_acting_out 10.312  2.426   2.426    0.196    0.196
## 120        dsq_sublimation ~~       dsq_idealization  9.572  2.504   2.504    0.201    0.201
## 65                  Mature =~   dsq_autistic_fantasy  9.533 -0.725  -1.351   -0.259   -0.259
## 105        dsq_suppression ~~        dsq_sublimation  9.375  3.653   3.653    0.302    0.302
## 162    dsq_pseudo_altruism ~~       dsq_somatization  9.216  2.250   2.250    0.189    0.189
## 134 dsq_reaction_formation ~~            dsq_undoing  8.822  2.912   2.912    0.316    0.316
## 110        dsq_suppression ~~        dsq_devaluation  8.408  1.815   1.815    0.183    0.183
## 85                Immature =~        dsq_sublimation  7.958  0.845   0.876    0.227    0.227
## 64                  Mature =~             dsq_denial  7.918  0.368   0.686    0.236    0.236
## 72                Neurotic =~        dsq_suppression  7.828 -0.470  -0.900   -0.226   -0.226
## 176        dsq_devaluation ~~   dsq_autistic_fantasy  7.818  2.364   2.364    0.170    0.170
## 206 dsq_passive_aggression ~~         dsq_projection  7.767  1.943   1.943    0.221    0.221
## 132 dsq_reaction_formation ~~       dsq_idealization  7.201 -2.162  -2.162   -0.205   -0.205
## 109        dsq_suppression ~~            dsq_undoing  7.154 -2.183  -2.183   -0.193   -0.193
## 179        dsq_devaluation ~~       dsq_somatization  7.131 -1.833  -1.833   -0.167   -0.167
## 76                Neurotic =~             dsq_denial  6.966  0.377   0.722    0.249    0.249
## 73                Neurotic =~        dsq_sublimation  6.896  0.429   0.822    0.213    0.213
## 96               dsq_humor ~~        dsq_devaluation  6.854 -1.502  -1.502   -0.169   -0.169
## 89                Immature =~            dsq_undoing  6.229  0.951   0.986    0.250    0.250
## 78                Neurotic =~       dsq_displacement  6.223  0.457   0.874    0.231    0.231
## 142 dsq_reaction_formation ~~         dsq_acting_out  6.072 -1.732  -1.732   -0.157   -0.157
## 91               dsq_humor ~~        dsq_sublimation  5.723 -2.968  -2.968   -0.274   -0.274
## 189             dsq_denial ~~   dsq_autistic_fantasy  5.280  1.911   1.911    0.138    0.138
## 168            dsq_undoing ~~   dsq_autistic_fantasy  5.267  2.389   2.389    0.150    0.150
## 207       dsq_somatization ~~         dsq_acting_out  5.055  2.058   2.058    0.137    0.137
## 149       dsq_idealization ~~   dsq_autistic_fantasy  5.054 -2.477  -2.477   -0.136   -0.136
## 208       dsq_somatization ~~         dsq_projection  4.904 -1.821  -1.821   -0.149   -0.149
## 103              dsq_humor ~~         dsq_acting_out  4.820  1.695   1.695    0.139    0.139
## 82                Neurotic =~         dsq_projection  4.765 -0.380  -0.727   -0.202   -0.202
## 128        dsq_sublimation ~~ dsq_passive_aggression  4.569  1.444   1.444    0.150    0.150
## 163    dsq_pseudo_altruism ~~         dsq_acting_out  4.495  1.490   1.490    0.128    0.128
## 173            dsq_undoing ~~         dsq_projection  4.475 -1.463  -1.463   -0.147   -0.147
## 66                  Mature =~       dsq_displacement  4.330  0.347   0.646    0.171    0.171
## 100              dsq_humor ~~       dsq_displacement  4.219  1.467   1.467    0.136    0.136
## 94               dsq_humor ~~    dsq_pseudo_altruism  4.200  1.328   1.328    0.138    0.138
## 80                Neurotic =~       dsq_somatization  4.124  0.424   0.812    0.189    0.189
## 60                  Mature =~    dsq_pseudo_altruism  4.089  0.300   0.559    0.167    0.167
## 195   dsq_autistic_fantasy ~~       dsq_displacement  3.989 -2.114  -2.114   -0.125   -0.125
## 139 dsq_reaction_formation ~~       dsq_displacement  3.910  1.288   1.288    0.132    0.132

4.3.13 Removing weakest loading defense (acting out) Three Factor Solution VIII

model_3f_adj_kn_VIII <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_devaluation
             + dsq_splitting + dsq_denial + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_projection
  
'
fit3_adjkn_VIII <- cfa(model_3f_adj_kn_VIII, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_VIII,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 113 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        48
## 
##   Number of observations                           306
##   Number of missing patterns                         8
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               217.212     206.089
##   Degrees of freedom                                87          87
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.054
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               586.594     536.796
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.730       0.724
##   Tucker-Lewis Index (TLI)                       0.674       0.667
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.741
##   Robust Tucker-Lewis Index (TLI)                            0.688
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12303.494  -12303.494
##   Scaling correction factor                                  1.024
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -12194.888  -12194.888
##   Scaling correction factor                                  1.043
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               24702.987   24702.987
##   Bayesian (BIC)                             24881.719   24881.719
##   Sample-size adjusted Bayesian (SABIC)      24729.485   24729.485
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.070       0.067
##   90 Percent confidence interval - lower         0.058       0.055
##   90 Percent confidence interval - upper         0.082       0.078
##   P-value H_0: RMSEA <= 0.050                    0.003       0.009
##   P-value H_0: RMSEA >= 0.080                    0.080       0.030
##                                                                   
##   Robust RMSEA                                               0.068
##   90 Percent confidence interval - lower                     0.056
##   90 Percent confidence interval - upper                     0.080
##   P-value H_0: Robust RMSEA <= 0.050                         0.010
##   P-value H_0: Robust RMSEA >= 0.080                         0.056
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.070       0.070
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.923    0.522
##     dsq_suppressin    0.914    0.477    1.915    0.055    1.757    0.441
##     dsq_sublimatin    0.911    0.470    1.940    0.052    1.751    0.454
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.950    0.564
##     dsq_idealizatn    0.792    0.225    3.525    0.000    1.544    0.388
##     dsq_psed_ltrsm    0.712    0.168    4.236    0.000    1.389    0.415
##     dsq_undoing       1.184    0.194    6.097    0.000    2.310    0.587
##   Immature =~                                                           
##     dsq_devaluatin    1.000                               1.074    0.361
##     dsq_splitting     1.313    0.361    3.633    0.000    1.411    0.398
##     dsq_denial        0.748    0.263    2.841    0.005    0.804    0.277
##     dsq_tstc_fntsy    1.460    0.404    3.616    0.000    1.569    0.301
##     dsq_displacmnt    1.556    0.431    3.615    0.000    1.672    0.442
##     dsq_pssv_ggrss    1.994    0.404    4.941    0.000    2.142    0.608
##     dsq_somatizatn    1.589    0.538    2.950    0.003    1.707    0.396
##     dsq_projection    1.699    0.337    5.042    0.000    1.825    0.506
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.132    0.783    1.447    0.148    0.302    0.302
##     Immature         -0.694    0.504   -1.376    0.169   -0.336   -0.336
##   Neurotic ~~                                                           
##     Immature          1.135    0.277    4.092    0.000    0.542    0.542
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.550    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_rctn_frmtn    9.107    0.199   45.841    0.000    9.107    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.271    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.453    0.203   36.636    0.000    7.453    2.101
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_tstc_fntsy   11.665    0.299   39.037    0.000   11.665    2.239
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.343    0.202   36.358    0.000    7.343    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_projection    8.022    0.206   38.892    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.866    1.842    5.357    0.000    9.866    0.727
##    .dsq_suppressin   12.767    1.993    6.404    0.000   12.767    0.805
##    .dsq_sublimatin   11.801    1.790    6.593    0.000   11.801    0.794
##    .dsq_rctn_frmtn    8.173    0.915    8.933    0.000    8.173    0.682
##    .dsq_idealizatn   13.449    1.352    9.945    0.000   13.449    0.849
##    .dsq_psed_ltrsm    9.277    0.917   10.119    0.000    9.277    0.828
##    .dsq_undoing      10.173    1.316    7.729    0.000   10.173    0.656
##    .dsq_devaluatin    7.724    0.710   10.881    0.000    7.724    0.870
##    .dsq_splitting    10.596    0.882   12.015    0.000   10.596    0.842
##    .dsq_denial        7.774    0.617   12.604    0.000    7.774    0.923
##    .dsq_tstc_fntsy   24.693    1.960   12.599    0.000   24.693    0.909
##    .dsq_displacmnt   11.535    0.989   11.663    0.000   11.535    0.805
##    .dsq_pssv_ggrss    7.807    0.917    8.511    0.000    7.807    0.630
##    .dsq_somatizatn   15.642    1.348   11.603    0.000   15.642    0.843
##    .dsq_projection    9.662    1.062    9.100    0.000    9.662    0.744
##     Mature            3.697    1.909    1.937    0.053    1.000    1.000
##     Neurotic          3.804    0.999    3.808    0.000    1.000    1.000
##     Immature          1.154    0.449    2.572    0.010    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.273
##     dsq_suppressin    0.195
##     dsq_sublimatin    0.206
##     dsq_rctn_frmtn    0.318
##     dsq_idealizatn    0.151
##     dsq_psed_ltrsm    0.172
##     dsq_undoing       0.344
##     dsq_devaluatin    0.130
##     dsq_splitting     0.158
##     dsq_denial        0.077
##     dsq_tstc_fntsy    0.091
##     dsq_displacmnt    0.195
##     dsq_pssv_ggrss    0.370
##     dsq_somatizatn    0.157
##     dsq_projection    0.256
modindices(fit3_adjkn_VIII, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 138       dsq_idealization ~~          dsq_splitting 21.978  3.445   3.445    0.289    0.289
## 128 dsq_reaction_formation ~~          dsq_splitting 15.303 -2.415  -2.415   -0.259   -0.259
## 58                  Mature =~            dsq_undoing 13.108 -0.637  -1.224   -0.311   -0.311
## 146    dsq_pseudo_altruism ~~        dsq_devaluation 10.847 -1.712  -1.712   -0.202   -0.202
## 99         dsq_suppression ~~        dsq_sublimation 10.319  3.639   3.639    0.296    0.296
## 152    dsq_pseudo_altruism ~~       dsq_somatization  9.844  2.338   2.338    0.194    0.194
## 113        dsq_sublimation ~~       dsq_idealization  9.630  2.516   2.516    0.200    0.200
## 62                  Mature =~   dsq_autistic_fantasy  9.008 -0.686  -1.320   -0.253   -0.253
## 104        dsq_suppression ~~        dsq_devaluation  8.502  1.825   1.825    0.184    0.184
## 61                  Mature =~             dsq_denial  8.357  0.368   0.708    0.244    0.244
## 80                Immature =~        dsq_sublimation  7.702  0.804   0.864    0.224    0.224
## 126 dsq_reaction_formation ~~            dsq_undoing  7.530  2.745   2.745    0.301    0.301
## 164        dsq_devaluation ~~   dsq_autistic_fantasy  7.390  2.294   2.294    0.166    0.166
## 124 dsq_reaction_formation ~~       dsq_idealization  7.349 -2.187  -2.187   -0.209   -0.209
## 103        dsq_suppression ~~            dsq_undoing  7.231 -2.193  -2.193   -0.192   -0.192
## 72                Neurotic =~             dsq_denial  7.056  0.370   0.721    0.249    0.249
## 167        dsq_devaluation ~~       dsq_somatization  6.989 -1.818  -1.818   -0.165   -0.165
## 68                Neurotic =~        dsq_suppression  6.971 -0.432  -0.843   -0.212   -0.212
## 188 dsq_passive_aggression ~~         dsq_projection  6.748  1.837   1.837    0.212    0.212
## 69                Neurotic =~        dsq_sublimation  6.632  0.410   0.800    0.208    0.208
## 84                Immature =~            dsq_undoing  6.558  0.933   1.003    0.255    0.255
## 74                Neurotic =~       dsq_displacement  6.547  0.457   0.891    0.235    0.235
## 86               dsq_humor ~~        dsq_sublimation  6.246 -3.117  -3.117   -0.289   -0.289
## 91               dsq_humor ~~        dsq_devaluation  6.172 -1.421  -1.421   -0.163   -0.163
## 175             dsq_denial ~~   dsq_autistic_fantasy  5.126  1.882   1.882    0.136    0.136
## 157            dsq_undoing ~~   dsq_autistic_fantasy  5.099  2.348   2.348    0.148    0.148
## 161            dsq_undoing ~~         dsq_projection  5.003 -1.546  -1.546   -0.156   -0.156
## 140       dsq_idealization ~~   dsq_autistic_fantasy  4.927 -2.448  -2.448   -0.134   -0.134
## 77                Neurotic =~         dsq_projection  4.915 -0.376  -0.734   -0.204   -0.204
## 173          dsq_splitting ~~       dsq_somatization  4.894  1.810   1.810    0.141    0.141
## 63                  Mature =~       dsq_displacement  4.893  0.359   0.691    0.183    0.183
## 121        dsq_sublimation ~~ dsq_passive_aggression  4.839  1.490   1.490    0.155    0.155
## 95               dsq_humor ~~       dsq_displacement  4.636  1.540   1.540    0.144    0.144
## 57                  Mature =~    dsq_pseudo_altruism  4.502  0.304   0.585    0.175    0.175
## 76                Neurotic =~       dsq_somatization  4.373  0.427   0.832    0.193    0.193
## 189       dsq_somatization ~~         dsq_projection  4.324 -1.715  -1.715   -0.139   -0.139
## 180   dsq_autistic_fantasy ~~       dsq_displacement  4.059 -2.135  -2.135   -0.127   -0.127
## 89               dsq_humor ~~    dsq_pseudo_altruism  3.974  1.293   1.293    0.135    0.135

4.3.14 Removing weakest loading defense (denial) Three Factor Solution VIV

model_3f_adj_kn_VIV <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_devaluation
             + dsq_splitting + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_projection
  
'
fit3_adjkn_VIV <- cfa(model_3f_adj_kn_VIV, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_VIV,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 114 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        45
## 
##   Number of observations                           306
##   Number of missing patterns                         8
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               195.143     183.570
##   Degrees of freedom                                74          74
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.063
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               548.554     497.001
##   Degrees of freedom                                91          91
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.104
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.735       0.730
##   Tucker-Lewis Index (TLI)                       0.674       0.668
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.747
##   Robust Tucker-Lewis Index (TLI)                            0.689
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -11551.314  -11551.314
##   Scaling correction factor                                  1.022
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -11453.743  -11453.743
##   Scaling correction factor                                  1.047
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               23192.628   23192.628
##   Bayesian (BIC)                             23360.189   23360.189
##   Sample-size adjusted Bayesian (SABIC)      23217.470   23217.470
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.073       0.070
##   90 Percent confidence interval - lower         0.061       0.057
##   90 Percent confidence interval - upper         0.086       0.082
##   P-value H_0: RMSEA <= 0.050                    0.001       0.005
##   P-value H_0: RMSEA >= 0.080                    0.191       0.083
##                                                                   
##   Robust RMSEA                                               0.071
##   90 Percent confidence interval - lower                     0.058
##   90 Percent confidence interval - upper                     0.084
##   P-value H_0: Robust RMSEA <= 0.050                         0.006
##   P-value H_0: Robust RMSEA >= 0.080                         0.140
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.070       0.070
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.985    0.539
##     dsq_suppressin    0.858    0.441    1.942    0.052    1.702    0.428
##     dsq_sublimatin    0.858    0.438    1.960    0.050    1.703    0.442
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.947    0.563
##     dsq_idealizatn    0.792    0.228    3.473    0.001    1.542    0.388
##     dsq_psed_ltrsm    0.712    0.170    4.189    0.000    1.387    0.414
##     dsq_undoing       1.190    0.200    5.956    0.000    2.317    0.588
##   Immature =~                                                           
##     dsq_devaluatin    1.000                               1.089    0.366
##     dsq_splitting     1.336    0.359    3.726    0.000    1.455    0.410
##     dsq_tstc_fntsy    1.361    0.386    3.529    0.000    1.482    0.284
##     dsq_displacmnt    1.489    0.408    3.646    0.000    1.622    0.428
##     dsq_pssv_ggrss    1.999    0.398    5.017    0.000    2.177    0.618
##     dsq_somatizatn    1.526    0.516    2.956    0.003    1.663    0.386
##     dsq_projection    1.719    0.335    5.136    0.000    1.873    0.520
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.178    0.776    1.519    0.129    0.305    0.305
##     Immature         -0.803    0.520   -1.545    0.122   -0.371   -0.371
##   Neurotic ~~                                                           
##     Immature          1.083    0.269    4.020    0.000    0.510    0.510
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.427    0.228   32.551    0.000    7.427    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_rctn_frmtn    9.108    0.199   45.846    0.000    9.108    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.269    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.452    0.203   36.643    0.000    7.452    2.100
##    .dsq_tstc_fntsy   11.665    0.299   39.035    0.000   11.665    2.238
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.344    0.202   36.360    0.000    7.344    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_projection    8.022    0.206   38.894    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.622    1.845    5.214    0.000    9.622    0.709
##    .dsq_suppressin   12.954    1.923    6.736    0.000   12.954    0.817
##    .dsq_sublimatin   11.970    1.751    6.837    0.000   11.970    0.805
##    .dsq_rctn_frmtn    8.185    0.930    8.803    0.000    8.185    0.683
##    .dsq_idealizatn   13.453    1.348    9.982    0.000   13.453    0.850
##    .dsq_psed_ltrsm    9.282    0.923   10.060    0.000    9.282    0.828
##    .dsq_undoing      10.141    1.340    7.569    0.000   10.141    0.654
##    .dsq_devaluatin    7.691    0.699   11.004    0.000    7.691    0.866
##    .dsq_splitting    10.468    0.870   12.039    0.000   10.468    0.832
##    .dsq_tstc_fntsy   24.958    1.932   12.915    0.000   24.958    0.919
##    .dsq_displacmnt   11.702    0.984   11.890    0.000   11.702    0.817
##    .dsq_pssv_ggrss    7.656    0.908    8.431    0.000    7.656    0.618
##    .dsq_somatizatn   15.790    1.338   11.806    0.000   15.790    0.851
##    .dsq_projection    9.484    1.078    8.798    0.000    9.484    0.730
##     Mature            3.941    1.928    2.044    0.041    1.000    1.000
##     Neurotic          3.792    1.012    3.746    0.000    1.000    1.000
##     Immature          1.187    0.445    2.668    0.008    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.291
##     dsq_suppressin    0.183
##     dsq_sublimatin    0.195
##     dsq_rctn_frmtn    0.317
##     dsq_idealizatn    0.150
##     dsq_psed_ltrsm    0.172
##     dsq_undoing       0.346
##     dsq_devaluatin    0.134
##     dsq_splitting     0.168
##     dsq_tstc_fntsy    0.081
##     dsq_displacmnt    0.183
##     dsq_pssv_ggrss    0.382
##     dsq_somatizatn    0.149
##     dsq_projection    0.270
modindices(fit3_adjkn_VIV, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 129       dsq_idealization ~~          dsq_splitting 22.388  3.469   3.469    0.292    0.292
## 120 dsq_reaction_formation ~~          dsq_splitting 14.848 -2.377  -2.377   -0.257   -0.257
## 55                  Mature =~            dsq_undoing 13.292 -0.619  -1.228   -0.312   -0.312
## 93         dsq_suppression ~~        dsq_sublimation 11.008  3.545   3.545    0.285    0.285
## 136    dsq_pseudo_altruism ~~        dsq_devaluation 10.375 -1.674  -1.674   -0.198   -0.198
## 141    dsq_pseudo_altruism ~~       dsq_somatization 10.267  2.396   2.396    0.198    0.198
## 106        dsq_sublimation ~~       dsq_idealization  9.813  2.543   2.543    0.200    0.200
## 98         dsq_suppression ~~        dsq_devaluation  8.344  1.811   1.811    0.181    0.181
## 69                Neurotic =~       dsq_displacement  8.217  0.496   0.966    0.255    0.255
## 151        dsq_devaluation ~~   dsq_autistic_fantasy  7.867  2.375   2.375    0.171    0.171
## 58                  Mature =~   dsq_autistic_fantasy  7.772 -0.630  -1.250   -0.240   -0.240
## 118 dsq_reaction_formation ~~            dsq_undoing  7.765  2.852   2.852    0.313    0.313
## 75                Immature =~        dsq_sublimation  7.434  0.797   0.868    0.225    0.225
## 116 dsq_reaction_formation ~~       dsq_idealization  7.363 -2.209  -2.209   -0.211   -0.211
## 97         dsq_suppression ~~            dsq_undoing  7.216 -2.192  -2.192   -0.191   -0.191
## 79                Immature =~            dsq_undoing  7.053  0.915   0.997    0.253    0.253
## 154        dsq_devaluation ~~       dsq_somatization  6.764 -1.795  -1.795   -0.163   -0.163
## 81               dsq_humor ~~        dsq_sublimation  6.515 -3.164  -3.164   -0.295   -0.295
## 65                Neurotic =~        dsq_sublimation  6.416  0.403   0.785    0.204    0.204
## 64                Neurotic =~        dsq_suppression  6.317 -0.411  -0.800   -0.201   -0.201
## 59                  Mature =~       dsq_displacement  6.297  0.403   0.800    0.211    0.211
## 145            dsq_undoing ~~   dsq_autistic_fantasy  5.674  2.486   2.486    0.156    0.156
## 113        dsq_sublimation ~~ dsq_passive_aggression  5.588  1.610   1.610    0.168    0.168
## 71                Neurotic =~       dsq_somatization  5.559  0.466   0.907    0.211    0.211
## 86               dsq_humor ~~        dsq_devaluation  5.476 -1.337  -1.337   -0.155   -0.155
## 149            dsq_undoing ~~         dsq_projection  5.364 -1.600  -1.600   -0.163   -0.163
## 169 dsq_passive_aggression ~~         dsq_projection  5.177  1.668   1.668    0.196    0.196
## 89               dsq_humor ~~       dsq_displacement  4.973  1.601   1.601    0.151    0.151
## 159          dsq_splitting ~~       dsq_somatization  4.880  1.814   1.814    0.141    0.141
## 54                  Mature =~    dsq_pseudo_altruism  4.664  0.299   0.593    0.177    0.177
## 130       dsq_idealization ~~   dsq_autistic_fantasy  4.568 -2.366  -2.366   -0.129   -0.129
## 170       dsq_somatization ~~         dsq_projection  4.462 -1.754  -1.754   -0.143   -0.143
## 100        dsq_suppression ~~   dsq_autistic_fantasy  4.105 -2.263  -2.263   -0.126   -0.126
## 122 dsq_reaction_formation ~~       dsq_displacement  4.015  1.310   1.310    0.134    0.134
## 72                Neurotic =~         dsq_projection  4.005 -0.329  -0.640   -0.178   -0.178

4.3.15 Removing weakest loading defense (denial) Three Factor Solution IX

model_3f_adj_kn_IX <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_devaluation
             + dsq_splitting + dsq_autistic_fantasy + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_projection
  
'
fit3_adjkn_IX <- cfa(model_3f_adj_kn_IX, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_IX,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 114 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        45
## 
##   Number of observations                           306
##   Number of missing patterns                         8
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               195.143     183.570
##   Degrees of freedom                                74          74
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.063
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               548.554     497.001
##   Degrees of freedom                                91          91
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.104
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.735       0.730
##   Tucker-Lewis Index (TLI)                       0.674       0.668
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.747
##   Robust Tucker-Lewis Index (TLI)                            0.689
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -11551.314  -11551.314
##   Scaling correction factor                                  1.022
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -11453.743  -11453.743
##   Scaling correction factor                                  1.047
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               23192.628   23192.628
##   Bayesian (BIC)                             23360.189   23360.189
##   Sample-size adjusted Bayesian (SABIC)      23217.470   23217.470
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.073       0.070
##   90 Percent confidence interval - lower         0.061       0.057
##   90 Percent confidence interval - upper         0.086       0.082
##   P-value H_0: RMSEA <= 0.050                    0.001       0.005
##   P-value H_0: RMSEA >= 0.080                    0.191       0.083
##                                                                   
##   Robust RMSEA                                               0.071
##   90 Percent confidence interval - lower                     0.058
##   90 Percent confidence interval - upper                     0.084
##   P-value H_0: Robust RMSEA <= 0.050                         0.006
##   P-value H_0: Robust RMSEA >= 0.080                         0.140
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.070       0.070
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.985    0.539
##     dsq_suppressin    0.858    0.441    1.942    0.052    1.702    0.428
##     dsq_sublimatin    0.858    0.438    1.960    0.050    1.703    0.442
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.947    0.563
##     dsq_idealizatn    0.792    0.228    3.473    0.001    1.542    0.388
##     dsq_psed_ltrsm    0.712    0.170    4.189    0.000    1.387    0.414
##     dsq_undoing       1.190    0.200    5.956    0.000    2.317    0.588
##   Immature =~                                                           
##     dsq_devaluatin    1.000                               1.089    0.366
##     dsq_splitting     1.336    0.359    3.726    0.000    1.455    0.410
##     dsq_tstc_fntsy    1.361    0.386    3.529    0.000    1.482    0.284
##     dsq_displacmnt    1.489    0.408    3.646    0.000    1.622    0.428
##     dsq_pssv_ggrss    1.999    0.398    5.017    0.000    2.177    0.618
##     dsq_somatizatn    1.526    0.516    2.956    0.003    1.663    0.386
##     dsq_projection    1.719    0.335    5.136    0.000    1.873    0.520
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.178    0.776    1.519    0.129    0.305    0.305
##     Immature         -0.803    0.520   -1.545    0.122   -0.371   -0.371
##   Neurotic ~~                                                           
##     Immature          1.083    0.269    4.020    0.000    0.510    0.510
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.427    0.228   32.551    0.000    7.427    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_rctn_frmtn    9.108    0.199   45.846    0.000    9.108    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.269    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.452    0.203   36.643    0.000    7.452    2.100
##    .dsq_tstc_fntsy   11.665    0.299   39.035    0.000   11.665    2.238
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.344    0.202   36.360    0.000    7.344    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_projection    8.022    0.206   38.894    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.622    1.845    5.214    0.000    9.622    0.709
##    .dsq_suppressin   12.954    1.923    6.736    0.000   12.954    0.817
##    .dsq_sublimatin   11.970    1.751    6.837    0.000   11.970    0.805
##    .dsq_rctn_frmtn    8.185    0.930    8.803    0.000    8.185    0.683
##    .dsq_idealizatn   13.453    1.348    9.982    0.000   13.453    0.850
##    .dsq_psed_ltrsm    9.282    0.923   10.060    0.000    9.282    0.828
##    .dsq_undoing      10.141    1.340    7.569    0.000   10.141    0.654
##    .dsq_devaluatin    7.691    0.699   11.004    0.000    7.691    0.866
##    .dsq_splitting    10.468    0.870   12.039    0.000   10.468    0.832
##    .dsq_tstc_fntsy   24.958    1.932   12.915    0.000   24.958    0.919
##    .dsq_displacmnt   11.702    0.984   11.890    0.000   11.702    0.817
##    .dsq_pssv_ggrss    7.656    0.908    8.431    0.000    7.656    0.618
##    .dsq_somatizatn   15.790    1.338   11.806    0.000   15.790    0.851
##    .dsq_projection    9.484    1.078    8.798    0.000    9.484    0.730
##     Mature            3.941    1.928    2.044    0.041    1.000    1.000
##     Neurotic          3.792    1.012    3.746    0.000    1.000    1.000
##     Immature          1.187    0.445    2.668    0.008    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.291
##     dsq_suppressin    0.183
##     dsq_sublimatin    0.195
##     dsq_rctn_frmtn    0.317
##     dsq_idealizatn    0.150
##     dsq_psed_ltrsm    0.172
##     dsq_undoing       0.346
##     dsq_devaluatin    0.134
##     dsq_splitting     0.168
##     dsq_tstc_fntsy    0.081
##     dsq_displacmnt    0.183
##     dsq_pssv_ggrss    0.382
##     dsq_somatizatn    0.149
##     dsq_projection    0.270
modindices(fit3_adjkn_IX, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 129       dsq_idealization ~~          dsq_splitting 22.388  3.469   3.469    0.292    0.292
## 120 dsq_reaction_formation ~~          dsq_splitting 14.848 -2.377  -2.377   -0.257   -0.257
## 55                  Mature =~            dsq_undoing 13.292 -0.619  -1.228   -0.312   -0.312
## 93         dsq_suppression ~~        dsq_sublimation 11.008  3.545   3.545    0.285    0.285
## 136    dsq_pseudo_altruism ~~        dsq_devaluation 10.375 -1.674  -1.674   -0.198   -0.198
## 141    dsq_pseudo_altruism ~~       dsq_somatization 10.267  2.396   2.396    0.198    0.198
## 106        dsq_sublimation ~~       dsq_idealization  9.813  2.543   2.543    0.200    0.200
## 98         dsq_suppression ~~        dsq_devaluation  8.344  1.811   1.811    0.181    0.181
## 69                Neurotic =~       dsq_displacement  8.217  0.496   0.966    0.255    0.255
## 151        dsq_devaluation ~~   dsq_autistic_fantasy  7.867  2.375   2.375    0.171    0.171
## 58                  Mature =~   dsq_autistic_fantasy  7.772 -0.630  -1.250   -0.240   -0.240
## 118 dsq_reaction_formation ~~            dsq_undoing  7.765  2.852   2.852    0.313    0.313
## 75                Immature =~        dsq_sublimation  7.434  0.797   0.868    0.225    0.225
## 116 dsq_reaction_formation ~~       dsq_idealization  7.363 -2.209  -2.209   -0.211   -0.211
## 97         dsq_suppression ~~            dsq_undoing  7.216 -2.192  -2.192   -0.191   -0.191
## 79                Immature =~            dsq_undoing  7.053  0.915   0.997    0.253    0.253
## 154        dsq_devaluation ~~       dsq_somatization  6.764 -1.795  -1.795   -0.163   -0.163
## 81               dsq_humor ~~        dsq_sublimation  6.515 -3.164  -3.164   -0.295   -0.295
## 65                Neurotic =~        dsq_sublimation  6.416  0.403   0.785    0.204    0.204
## 64                Neurotic =~        dsq_suppression  6.317 -0.411  -0.800   -0.201   -0.201
## 59                  Mature =~       dsq_displacement  6.297  0.403   0.800    0.211    0.211
## 145            dsq_undoing ~~   dsq_autistic_fantasy  5.674  2.486   2.486    0.156    0.156
## 113        dsq_sublimation ~~ dsq_passive_aggression  5.588  1.610   1.610    0.168    0.168
## 71                Neurotic =~       dsq_somatization  5.559  0.466   0.907    0.211    0.211
## 86               dsq_humor ~~        dsq_devaluation  5.476 -1.337  -1.337   -0.155   -0.155
## 149            dsq_undoing ~~         dsq_projection  5.364 -1.600  -1.600   -0.163   -0.163
## 169 dsq_passive_aggression ~~         dsq_projection  5.177  1.668   1.668    0.196    0.196
## 89               dsq_humor ~~       dsq_displacement  4.973  1.601   1.601    0.151    0.151
## 159          dsq_splitting ~~       dsq_somatization  4.880  1.814   1.814    0.141    0.141
## 54                  Mature =~    dsq_pseudo_altruism  4.664  0.299   0.593    0.177    0.177
## 130       dsq_idealization ~~   dsq_autistic_fantasy  4.568 -2.366  -2.366   -0.129   -0.129
## 170       dsq_somatization ~~         dsq_projection  4.462 -1.754  -1.754   -0.143   -0.143
## 100        dsq_suppression ~~   dsq_autistic_fantasy  4.105 -2.263  -2.263   -0.126   -0.126
## 122 dsq_reaction_formation ~~       dsq_displacement  4.015  1.310   1.310    0.134    0.134
## 72                Neurotic =~         dsq_projection  4.005 -0.329  -0.640   -0.178   -0.178

4.3.16 Removing weakest loading defense (autistic fantasy) Three Factor Solution X

model_3f_adj_kn_X <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_devaluation
             + dsq_splitting + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_projection
  
'
fit3_adjkn_X <- cfa(model_3f_adj_kn_X, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_X,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 103 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        42
## 
##   Number of observations                           306
##   Number of missing patterns                         7
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               166.202     159.161
##   Degrees of freedom                                62          62
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.044
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               503.165     459.774
##   Degrees of freedom                                78          78
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.094
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.755       0.746
##   Tucker-Lewis Index (TLI)                       0.692       0.680
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.766
##   Robust Tucker-Lewis Index (TLI)                            0.705
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10626.295  -10626.295
##   Scaling correction factor                                  1.030
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10543.194  -10543.194
##   Scaling correction factor                                  1.039
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21336.589   21336.589
##   Bayesian (BIC)                             21492.980   21492.980
##   Sample-size adjusted Bayesian (SABIC)      21359.775   21359.775
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.074       0.072
##   90 Percent confidence interval - lower         0.061       0.058
##   90 Percent confidence interval - upper         0.088       0.085
##   P-value H_0: RMSEA <= 0.050                    0.002       0.005
##   P-value H_0: RMSEA >= 0.080                    0.249       0.157
##                                                                   
##   Robust RMSEA                                               0.072
##   90 Percent confidence interval - lower                     0.058
##   90 Percent confidence interval - upper                     0.087
##   P-value H_0: Robust RMSEA <= 0.050                         0.007
##   P-value H_0: Robust RMSEA >= 0.080                         0.194
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.068       0.068
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.929    0.524
##     dsq_suppressin    0.900    0.521    1.727    0.084    1.736    0.436
##     dsq_sublimatin    0.911    0.539    1.691    0.091    1.757    0.456
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.938    0.560
##     dsq_idealizatn    0.813    0.240    3.390    0.001    1.576    0.396
##     dsq_psed_ltrsm    0.725    0.176    4.107    0.000    1.404    0.420
##     dsq_undoing       1.176    0.195    6.028    0.000    2.278    0.579
##   Immature =~                                                           
##     dsq_devaluatin    1.000                               1.014    0.340
##     dsq_splitting     1.455    0.394    3.691    0.000    1.475    0.416
##     dsq_displacmnt    1.667    0.461    3.613    0.000    1.690    0.447
##     dsq_pssv_ggrss    2.189    0.438    5.002    0.000    2.219    0.630
##     dsq_somatizatn    1.609    0.565    2.850    0.004    1.631    0.379
##     dsq_projection    1.889    0.357    5.294    0.000    1.915    0.531
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.159    0.806    1.439    0.150    0.310    0.310
##     Immature         -0.613    0.499   -1.229    0.219   -0.313   -0.313
##   Neurotic ~~                                                           
##     Immature          1.005    0.257    3.903    0.000    0.511    0.511
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.427    0.228   32.549    0.000    7.427    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_rctn_frmtn    9.108    0.199   45.842    0.000    9.108    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.268    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.450    0.203   36.638    0.000    7.450    2.100
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.347    0.202   36.355    0.000    7.347    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_projection    8.022    0.206   38.893    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor         9.841    2.093    4.701    0.000    9.841    0.726
##    .dsq_suppressin   12.838    2.071    6.199    0.000   12.838    0.810
##    .dsq_sublimatin   11.781    2.016    5.843    0.000   11.781    0.792
##    .dsq_rctn_frmtn    8.220    0.952    8.634    0.000    8.220    0.686
##    .dsq_idealizatn   13.348    1.350    9.890    0.000   13.348    0.843
##    .dsq_psed_ltrsm    9.234    0.928    9.955    0.000    9.234    0.824
##    .dsq_undoing      10.319    1.363    7.569    0.000   10.319    0.665
##    .dsq_devaluatin    7.850    0.690   11.383    0.000    7.850    0.884
##    .dsq_splitting    10.412    0.867   12.015    0.000   10.412    0.827
##    .dsq_displacmnt   11.474    0.982   11.690    0.000   11.474    0.801
##    .dsq_pssv_ggrss    7.476    0.938    7.973    0.000    7.476    0.603
##    .dsq_somatizatn   15.894    1.325   11.997    0.000   15.894    0.857
##    .dsq_projection    9.324    1.104    8.448    0.000    9.324    0.718
##     Mature            3.722    2.169    1.716    0.086    1.000    1.000
##     Neurotic          3.756    1.034    3.634    0.000    1.000    1.000
##     Immature          1.028    0.409    2.514    0.012    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.274
##     dsq_suppressin    0.190
##     dsq_sublimatin    0.208
##     dsq_rctn_frmtn    0.314
##     dsq_idealizatn    0.157
##     dsq_psed_ltrsm    0.176
##     dsq_undoing       0.335
##     dsq_devaluatin    0.116
##     dsq_splitting     0.173
##     dsq_displacmnt    0.199
##     dsq_pssv_ggrss    0.397
##     dsq_somatizatn    0.143
##     dsq_projection    0.282
modindices(fit3_adjkn_X, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 120       dsq_idealization ~~          dsq_splitting 21.690  3.408   3.408    0.289    0.289
## 112 dsq_reaction_formation ~~          dsq_splitting 15.018 -2.393  -2.393   -0.259   -0.259
## 52                  Mature =~            dsq_undoing 12.710 -0.633  -1.221   -0.310   -0.310
## 87         dsq_suppression ~~        dsq_sublimation 11.133  3.871   3.871    0.315    0.315
## 126    dsq_pseudo_altruism ~~        dsq_devaluation 10.120 -1.662  -1.662   -0.195   -0.195
## 130    dsq_pseudo_altruism ~~       dsq_somatization  9.881  2.355   2.355    0.194    0.194
## 99         dsq_sublimation ~~       dsq_idealization  9.660  2.520   2.520    0.201    0.201
## 110 dsq_reaction_formation ~~            dsq_undoing  9.201  3.066   3.066    0.333    0.333
## 108 dsq_reaction_formation ~~       dsq_idealization  8.240 -2.359  -2.359   -0.225   -0.225
## 70                Immature =~        dsq_sublimation  8.080  0.872   0.885    0.229    0.229
## 64                Neurotic =~       dsq_displacement  7.446  0.481   0.932    0.246    0.246
## 91         dsq_suppression ~~            dsq_undoing  7.396 -2.222  -2.222   -0.193   -0.193
## 76               dsq_humor ~~        dsq_sublimation  7.338 -3.542  -3.542   -0.329   -0.329
## 92         dsq_suppression ~~        dsq_devaluation  6.987  1.665   1.665    0.166    0.166
## 60                Neurotic =~        dsq_suppression  6.871 -0.439  -0.850   -0.214   -0.214
## 61                Neurotic =~        dsq_sublimation  6.803  0.427   0.827    0.215    0.215
## 81               dsq_humor ~~        dsq_devaluation  6.577 -1.475  -1.475   -0.168   -0.168
## 66                Neurotic =~       dsq_somatization  5.673  0.480   0.930    0.216    0.216
## 67                Neurotic =~         dsq_projection  5.313 -0.388  -0.751   -0.208   -0.208
## 141        dsq_devaluation ~~       dsq_somatization  5.197 -1.584  -1.584   -0.142   -0.142
## 74                Immature =~            dsq_undoing  5.078  0.846   0.858    0.218    0.218
## 145          dsq_splitting ~~       dsq_somatization  5.022  1.849   1.849    0.144    0.144
## 55                  Mature =~       dsq_displacement  4.751  0.352   0.680    0.180    0.180
## 83               dsq_humor ~~       dsq_displacement  4.741  1.560   1.560    0.147    0.147
## 152       dsq_somatization ~~         dsq_projection  4.725 -1.822  -1.822   -0.150   -0.150
## 137            dsq_undoing ~~         dsq_projection  4.572 -1.481  -1.481   -0.151   -0.151
## 105        dsq_sublimation ~~ dsq_passive_aggression  4.503  1.442   1.442    0.154    0.154
## 51                  Mature =~    dsq_pseudo_altruism  4.421  0.305   0.589    0.176    0.176
## 113 dsq_reaction_formation ~~       dsq_displacement  4.046  1.313   1.313    0.135    0.135
## 79               dsq_humor ~~    dsq_pseudo_altruism  3.944  1.289   1.289    0.135    0.135

4.3.17 Removing weakest loading defense (devaluation) Three Factor Solution XI

model_3f_adj_kn_XI <- '
  Mature   =~ dsq_humor + dsq_suppression + dsq_sublimation
  Neurotic =~ dsq_reaction_formation + dsq_idealization + dsq_pseudo_altruism + dsq_undoing
  Immature =~ dsq_splitting + dsq_displacement
             + dsq_passive_aggression + dsq_somatization + dsq_projection
  
'
fit3_adjkn_XI <- cfa(model_3f_adj_kn_XI, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit3_adjkn_XI,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 102 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        39
## 
##   Number of observations                           306
##   Number of missing patterns                         7
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               136.275     130.527
##   Degrees of freedom                                51          51
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.044
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               449.892     408.535
##   Degrees of freedom                                66          66
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.101
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.778       0.768
##   Tucker-Lewis Index (TLI)                       0.713       0.700
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.787
##   Robust Tucker-Lewis Index (TLI)                            0.725
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -9869.689   -9869.689
##   Scaling correction factor                                  1.032
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -9801.552   -9801.552
##   Scaling correction factor                                  1.039
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               19817.378   19817.378
##   Bayesian (BIC)                             19962.598   19962.598
##   Sample-size adjusted Bayesian (SABIC)      19838.908   19838.908
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.074       0.071
##   90 Percent confidence interval - lower         0.059       0.057
##   90 Percent confidence interval - upper         0.089       0.086
##   P-value H_0: RMSEA <= 0.050                    0.005       0.010
##   P-value H_0: RMSEA >= 0.080                    0.265       0.178
##                                                                   
##   Robust RMSEA                                               0.072
##   90 Percent confidence interval - lower                     0.056
##   90 Percent confidence interval - upper                     0.088
##   P-value H_0: Robust RMSEA <= 0.050                         0.013
##   P-value H_0: Robust RMSEA >= 0.080                         0.216
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.065       0.065
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature =~                                                             
##     dsq_humor         1.000                               1.799    0.488
##     dsq_suppressin    1.030    0.495    2.083    0.037    1.853    0.465
##     dsq_sublimatin    1.027    0.504    2.038    0.042    1.847    0.479
##   Neurotic =~                                                           
##     dsq_rctn_frmtn    1.000                               1.877    0.542
##     dsq_idealizatn    0.875    0.262    3.335    0.001    1.642    0.413
##     dsq_psed_ltrsm    0.778    0.194    4.022    0.000    1.461    0.436
##     dsq_undoing       1.183    0.190    6.209    0.000    2.220    0.564
##   Immature =~                                                           
##     dsq_splitting     1.000                               1.477    0.416
##     dsq_displacmnt    1.201    0.282    4.258    0.000    1.773    0.468
##     dsq_pssv_ggrss    1.441    0.314    4.595    0.000    2.128    0.604
##     dsq_somatizatn    1.219    0.276    4.422    0.000    1.801    0.418
##     dsq_projection    1.214    0.323    3.754    0.000    1.793    0.498
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Mature ~~                                                             
##     Neurotic          1.046    0.723    1.446    0.148    0.310    0.310
##     Immature         -0.741    0.559   -1.326    0.185   -0.279   -0.279
##   Neurotic ~~                                                           
##     Immature          1.551    0.397    3.902    0.000    0.559    0.559
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_suppressin    7.426    0.228   32.551    0.000    7.426    1.865
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_rctn_frmtn    9.108    0.199   45.839    0.000    9.108    2.632
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_psed_ltrsm    9.634    0.192   50.267    0.000    9.634    2.878
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_splitting     7.451    0.203   36.640    0.000    7.451    2.100
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_pssv_ggrss    7.349    0.202   36.351    0.000    7.349    2.086
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_projection    8.022    0.206   38.894    0.000    8.022    2.226
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_humor        10.327    1.683    6.137    0.000   10.327    0.761
##    .dsq_suppressin   12.420    1.951    6.367    0.000   12.420    0.783
##    .dsq_sublimatin   11.457    1.788    6.408    0.000   11.457    0.771
##    .dsq_rctn_frmtn    8.451    0.982    8.602    0.000    8.451    0.706
##    .dsq_idealizatn   13.135    1.353    9.709    0.000   13.135    0.830
##    .dsq_psed_ltrsm    9.071    0.928    9.774    0.000    9.071    0.810
##    .dsq_undoing      10.580    1.413    7.487    0.000   10.580    0.682
##    .dsq_splitting    10.409    0.913   11.405    0.000   10.409    0.827
##    .dsq_displacmnt   11.186    1.001   11.179    0.000   11.186    0.781
##    .dsq_pssv_ggrss    7.877    1.035    7.609    0.000    7.877    0.635
##    .dsq_somatizatn   15.312    1.383   11.075    0.000   15.312    0.825
##    .dsq_projection    9.777    1.141    8.566    0.000    9.777    0.752
##     Mature            3.236    1.718    1.884    0.060    1.000    1.000
##     Neurotic          3.524    1.042    3.381    0.001    1.000    1.000
##     Immature          2.181    0.809    2.695    0.007    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_humor         0.239
##     dsq_suppressin    0.217
##     dsq_sublimatin    0.229
##     dsq_rctn_frmtn    0.294
##     dsq_idealizatn    0.170
##     dsq_psed_ltrsm    0.190
##     dsq_undoing       0.318
##     dsq_splitting     0.173
##     dsq_displacmnt    0.219
##     dsq_pssv_ggrss    0.365
##     dsq_somatizatn    0.175
##     dsq_projection    0.248
modindices(fit3_adjkn_XI, sort. = TRUE, minimum.value = 3.84)
##                        lhs op                    rhs     mi    epc sepc.lv sepc.all sepc.nox
## 110       dsq_idealization ~~          dsq_splitting 20.185  3.294   3.294    0.282    0.282
## 103 dsq_reaction_formation ~~          dsq_splitting 15.640 -2.471  -2.471   -0.263   -0.263
## 102 dsq_reaction_formation ~~            dsq_undoing 12.056  3.272   3.272    0.346    0.346
## 49                  Mature =~            dsq_undoing 11.697 -0.653  -1.174   -0.298   -0.298
## 134 dsq_passive_aggression ~~         dsq_projection  9.400  2.373   2.373    0.270    0.270
## 92         dsq_sublimation ~~       dsq_idealization  9.267  2.461   2.461    0.201    0.201
## 65                Immature =~        dsq_sublimation  9.095  0.635   0.938    0.243    0.243
## 56                Neurotic =~        dsq_suppression  9.082 -0.529  -0.992   -0.249   -0.249
## 81         dsq_suppression ~~        dsq_sublimation  8.833  3.909   3.909    0.328    0.328
## 100 dsq_reaction_formation ~~       dsq_idealization  8.303 -2.348  -2.348   -0.223   -0.223
## 119    dsq_pseudo_altruism ~~       dsq_somatization  8.226  2.134   2.134    0.181    0.181
## 57                Neurotic =~        dsq_sublimation  7.734  0.476   0.894    0.232    0.232
## 85         dsq_suppression ~~            dsq_undoing  7.208 -2.198  -2.198   -0.192   -0.192
## 62                Neurotic =~         dsq_projection  6.117 -0.466  -0.874   -0.242   -0.242
## 71               dsq_humor ~~        dsq_sublimation  5.705 -3.075  -3.075   -0.283   -0.283
## 135       dsq_somatization ~~         dsq_projection  5.678 -2.041  -2.041   -0.167   -0.167
## 59                Neurotic =~       dsq_displacement  5.399  0.457   0.858    0.227    0.227
## 74               dsq_humor ~~    dsq_pseudo_altruism  4.379  1.357   1.357    0.140    0.140
## 64                Immature =~        dsq_suppression  4.109 -0.437  -0.646   -0.162   -0.162
## 77               dsq_humor ~~       dsq_displacement  4.083  1.452   1.452    0.135    0.135
## 69                Immature =~            dsq_undoing  4.068  0.559   0.826    0.210    0.210
## 104 dsq_reaction_formation ~~       dsq_displacement  3.972  1.314   1.314    0.135    0.135
## 97         dsq_sublimation ~~ dsq_passive_aggression  3.920  1.366   1.366    0.144    0.144
## 61                Neurotic =~       dsq_somatization  3.858  0.439   0.824    0.191    0.191

5 Post hoc analyses

# Specify CFA models
model_2f <- '
  PA1 =~ dsq_autistic_fantasy + dsq_somatization + dsq_passive_aggression + dsq_displacement 
  + dsq_acting_out + dsq_projection + dsq_undoing + dsq_devaluation + dsq_splitting + dsq_denial
  + dsq_dissociation + dsq_reaction_formation 
  PA2 =~ dsq_suppression + dsq_humor + dsq_rationalization + dsq_anticipation + dsq_sublimation 
  + dsq_pseudo_altruism + dsq_idealization + dsq_isolation
'

# Specify CFA models for Knekt Study (no Rationalization)
model_2f_norat <- '
  PA1 =~ dsq_autistic_fantasy + dsq_somatization + dsq_passive_aggression + dsq_displacement 
  + dsq_acting_out + dsq_projection + dsq_undoing + dsq_devaluation + dsq_splitting + dsq_denial
  + dsq_dissociation + dsq_reaction_formation 
  PA2 =~ dsq_suppression + dsq_humor + dsq_anticipation + dsq_sublimation 
  + dsq_pseudo_altruism + dsq_idealization + dsq_isolation
'

5.1 Multigroup CFA (2-Factor solution)

# Fit models
fit2_comb  <- cfa(model_2f, data = DSQ_Data_mg, group = "StudyID", estimator = "mlr", missing = "fiml")

# Inspect 2-factor
summary(fit2_comb,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 165 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       122
## 
##   Number of observations per group:                   
##     Dekker_2008/Van_2009                           151
##     Dos_Santos_2020                                210
##   Number of missing patterns per group:               
##     Dekker_2008/Van_2009                            18
##     Dos_Santos_2020                                  3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               699.307     642.840
##   Degrees of freedom                               338         338
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.088
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     Dekker_2008/Van_2009                       312.288     312.288
##     Dos_Santos_2020                            330.552     330.552
## 
## Model Test Baseline Model:
## 
##   Test statistic                              1390.926    1256.752
##   Degrees of freedom                               380         380
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.107
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.643       0.652
##   Tucker-Lewis Index (TLI)                       0.598       0.609
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.660
##   Robust Tucker-Lewis Index (TLI)                            0.618
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -18649.159  -18649.159
##   Scaling correction factor                                  1.011
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -18299.505  -18299.505
##   Scaling correction factor                                  1.068
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               37542.317   37542.317
##   Bayesian (BIC)                             38016.760   38016.760
##   Sample-size adjusted Bayesian (SABIC)      37629.712   37629.712
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.077       0.071
##   90 Percent confidence interval - lower         0.069       0.063
##   90 Percent confidence interval - upper         0.085       0.079
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.273       0.026
##                                                                   
##   Robust RMSEA                                               0.076
##   90 Percent confidence interval - lower                     0.067
##   90 Percent confidence interval - upper                     0.085
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.240
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.099       0.099
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [Dekker_2008/Van_2009]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 =~                                                                
##     dsq_tstc_fntsy    1.000                               1.775    0.416
##     dsq_somatizatn    0.707    0.214    3.303    0.001    1.255    0.355
##     dsq_pssv_ggrss    0.982    0.315    3.120    0.002    1.743    0.545
##     dsq_displacmnt    0.688    0.302    2.280    0.023    1.222    0.298
##     dsq_acting_out    0.955    0.361    2.646    0.008    1.695    0.402
##     dsq_projection    1.021    0.281    3.630    0.000    1.812    0.479
##     dsq_undoing       0.803    0.241    3.333    0.001    1.426    0.359
##     dsq_devaluatin    1.202    0.294    4.083    0.000    2.133    0.669
##     dsq_splitting     1.307    0.349    3.746    0.000    2.319    0.609
##     dsq_denial        0.624    0.247    2.522    0.012    1.107    0.338
##     dsq_dissociatn    0.879    0.258    3.401    0.001    1.560    0.423
##     dsq_rctn_frmtn    0.336    0.218    1.542    0.123    0.597    0.158
##   PA2 =~                                                                
##     dsq_suppressin    1.000                               1.715    0.441
##     dsq_humor         1.529    0.475    3.218    0.001    2.622    0.624
##     dsq_rationlztn    0.870    0.254    3.424    0.001    1.492    0.502
##     dsq_anticipatn    1.101    0.340    3.234    0.001    1.888    0.619
##     dsq_sublimatin    1.275    0.311    4.097    0.000    2.187    0.592
##     dsq_psed_ltrsm    0.847    0.269    3.155    0.002    1.453    0.479
##     dsq_idealizatn    0.736    0.266    2.767    0.006    1.261    0.329
##     dsq_isolation     0.212    0.293    0.722    0.470    0.363    0.080
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 ~~                                                                
##     PA2               0.312    0.482    0.648    0.517    0.103    0.103
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy    9.190    0.352   26.088    0.000    9.190    2.153
##    .dsq_somatizatn   11.442    0.289   39.623    0.000   11.442    3.236
##    .dsq_pssv_ggrss    7.748    0.268   28.865    0.000    7.748    2.421
##    .dsq_displacmnt    8.151    0.342   23.839    0.000    8.151    1.992
##    .dsq_acting_out    9.436    0.347   27.182    0.000    9.436    2.239
##    .dsq_projection    9.351    0.313   29.911    0.000    9.351    2.470
##    .dsq_undoing      11.142    0.332   33.523    0.000   11.142    2.805
##    .dsq_devaluatin    9.764    0.262   37.301    0.000    9.764    3.064
##    .dsq_splitting     9.717    0.311   31.276    0.000    9.717    2.552
##    .dsq_denial        6.887    0.269   25.571    0.000    6.887    2.101
##    .dsq_dissociatn    9.586    0.303   31.623    0.000    9.586    2.599
##    .dsq_rctn_frmtn    9.899    0.310   31.946    0.000    9.899    2.629
##    .dsq_suppressin    8.564    0.320   26.759    0.000    8.564    2.204
##    .dsq_humor         9.300    0.346   26.880    0.000    9.300    2.212
##    .dsq_rationlztn    8.846    0.245   36.114    0.000    8.846    2.976
##    .dsq_anticipatn   10.127    0.253   40.092    0.000   10.127    3.321
##    .dsq_sublimatin   10.030    0.308   32.593    0.000   10.030    2.713
##    .dsq_psed_ltrsm   12.697    0.254   50.044    0.000   12.697    4.187
##    .dsq_idealizatn    7.960    0.314   25.323    0.000    7.960    2.078
##    .dsq_isolation     8.592    0.378   22.718    0.000    8.592    1.887
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy   15.072    1.792    8.410    0.000   15.072    0.827
##    .dsq_somatizatn   10.925    1.094    9.987    0.000   10.925    0.874
##    .dsq_pssv_ggrss    7.204    0.987    7.299    0.000    7.204    0.703
##    .dsq_displacmnt   15.259    1.668    9.147    0.000   15.259    0.911
##    .dsq_acting_out   14.882    1.789    8.317    0.000   14.882    0.838
##    .dsq_projection   11.054    1.281    8.626    0.000   11.054    0.771
##    .dsq_undoing      13.745    1.408    9.761    0.000   13.745    0.871
##    .dsq_devaluatin    5.605    0.882    6.352    0.000    5.605    0.552
##    .dsq_splitting     9.123    1.635    5.579    0.000    9.123    0.629
##    .dsq_denial        9.523    1.016    9.372    0.000    9.523    0.886
##    .dsq_dissociatn   11.168    1.504    7.425    0.000   11.168    0.821
##    .dsq_rctn_frmtn   13.822    1.525    9.065    0.000   13.822    0.975
##    .dsq_suppressin   12.157    1.780    6.831    0.000   12.157    0.805
##    .dsq_humor        10.804    1.871    5.774    0.000   10.804    0.611
##    .dsq_rationlztn    6.613    0.893    7.408    0.000    6.613    0.748
##    .dsq_anticipatn    5.734    1.005    5.705    0.000    5.734    0.617
##    .dsq_sublimatin    8.888    1.652    5.380    0.000    8.888    0.650
##    .dsq_psed_ltrsm    7.084    0.990    7.151    0.000    7.084    0.770
##    .dsq_idealizatn   13.086    1.392    9.402    0.000   13.086    0.892
##    .dsq_isolation    20.606    1.767   11.661    0.000   20.606    0.994
##     PA1               3.150    1.469    2.144    0.032    1.000    1.000
##     PA2               2.940    1.366    2.153    0.031    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_tstc_fntsy    0.173
##     dsq_somatizatn    0.126
##     dsq_pssv_ggrss    0.297
##     dsq_displacmnt    0.089
##     dsq_acting_out    0.162
##     dsq_projection    0.229
##     dsq_undoing       0.129
##     dsq_devaluatin    0.448
##     dsq_splitting     0.371
##     dsq_denial        0.114
##     dsq_dissociatn    0.179
##     dsq_rctn_frmtn    0.025
##     dsq_suppressin    0.195
##     dsq_humor         0.389
##     dsq_rationlztn    0.252
##     dsq_anticipatn    0.383
##     dsq_sublimatin    0.350
##     dsq_psed_ltrsm    0.230
##     dsq_idealizatn    0.108
##     dsq_isolation     0.006
## 
## 
## Group 2 [Dos_Santos_2020]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 =~                                                                
##     dsq_tstc_fntsy    1.000                               3.299    0.622
##     dsq_somatizatn    0.510    0.156    3.274    0.001    1.684    0.353
##     dsq_pssv_ggrss    0.772    0.116    6.638    0.000    2.548    0.654
##     dsq_displacmnt    0.496    0.104    4.763    0.000    1.635    0.399
##     dsq_acting_out    0.808    0.132    6.143    0.000    2.665    0.545
##     dsq_projection    0.717    0.112    6.384    0.000    2.367    0.592
##     dsq_undoing       0.359    0.129    2.784    0.005    1.185    0.290
##     dsq_devaluatin    0.466    0.098    4.778    0.000    1.537    0.475
##     dsq_splitting     0.412    0.108    3.818    0.000    1.358    0.330
##     dsq_denial        0.227    0.099    2.298    0.022    0.748    0.223
##     dsq_dissociatn    0.052    0.105    0.493    0.622    0.170    0.054
##     dsq_rctn_frmtn   -0.167    0.133   -1.260    0.208   -0.551   -0.137
##   PA2 =~                                                                
##     dsq_suppressin    1.000                               1.665    0.411
##     dsq_humor         1.396    0.424    3.290    0.001    2.325    0.517
##     dsq_rationlztn    1.728    0.501    3.452    0.001    2.879    0.705
##     dsq_anticipatn    1.290    0.319    4.037    0.000    2.148    0.505
##     dsq_sublimatin    0.956    0.310    3.083    0.002    1.593    0.400
##     dsq_psed_ltrsm    0.477    0.281    1.700    0.089    0.794    0.214
##     dsq_idealizatn    0.905    0.289    3.128    0.002    1.506    0.371
##     dsq_isolation    -0.140    0.346   -0.405    0.685   -0.234   -0.048
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 ~~                                                                
##     PA2              -0.188    0.913   -0.205    0.837   -0.034   -0.034
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy   10.323    0.376   27.428    0.000   10.323    1.946
##    .dsq_somatizatn   11.558    0.387   29.860    0.000   11.558    2.423
##    .dsq_pssv_ggrss    8.766    0.277   31.687    0.000    8.766    2.250
##    .dsq_displacmnt   10.040    0.291   34.549    0.000   10.040    2.451
##    .dsq_acting_out   10.731    0.348   30.880    0.000   10.731    2.193
##    .dsq_projection    8.163    0.283   28.859    0.000    8.163    2.041
##    .dsq_undoing       9.460    0.290   32.579    0.000    9.460    2.313
##    .dsq_devaluatin    7.186    0.230   31.213    0.000    7.186    2.219
##    .dsq_splitting    10.012    0.292   34.289    0.000   10.012    2.434
##    .dsq_denial        5.391    0.239   22.520    0.000    5.391    1.605
##    .dsq_dissociatn    5.259    0.222   23.657    0.000    5.259    1.682
##    .dsq_rctn_frmtn    8.950    0.286   31.341    0.000    8.950    2.223
##    .dsq_suppressin    6.762    0.288   23.482    0.000    6.762    1.669
##    .dsq_humor         8.247    0.319   25.827    0.000    8.247    1.832
##    .dsq_rationlztn    8.439    0.290   29.132    0.000    8.439    2.066
##    .dsq_anticipatn   11.812    0.302   39.108    0.000   11.812    2.779
##    .dsq_sublimatin    9.803    0.283   34.670    0.000    9.803    2.463
##    .dsq_psed_ltrsm   11.030    0.264   41.771    0.000   11.030    2.967
##    .dsq_idealizatn    8.095    0.288   28.071    0.000    8.095    1.995
##    .dsq_isolation     9.833    0.349   28.208    0.000    9.833    2.004
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy   17.270    2.301    7.506    0.000   17.270    0.613
##    .dsq_somatizatn   19.921    2.251    8.850    0.000   19.921    0.875
##    .dsq_pssv_ggrss    8.690    1.289    6.743    0.000    8.690    0.572
##    .dsq_displacmnt   14.114    1.296   10.887    0.000   14.114    0.841
##    .dsq_acting_out   16.832    1.807    9.313    0.000   16.832    0.703
##    .dsq_projection   10.387    1.381    7.523    0.000   10.387    0.650
##    .dsq_undoing      15.330    1.584    9.678    0.000   15.330    0.916
##    .dsq_devaluatin    8.127    0.870    9.343    0.000    8.127    0.775
##    .dsq_splitting    15.079    1.606    9.388    0.000   15.079    0.891
##    .dsq_denial       10.718    0.981   10.923    0.000   10.718    0.950
##    .dsq_dissociatn    9.748    0.946   10.306    0.000    9.748    0.997
##    .dsq_rctn_frmtn   15.902    1.432   11.106    0.000   15.902    0.981
##    .dsq_suppressin   13.650    2.022    6.749    0.000   13.650    0.831
##    .dsq_humor        14.853    1.950    7.616    0.000   14.853    0.733
##    .dsq_rationlztn    8.395    1.831    4.586    0.000    8.395    0.503
##    .dsq_anticipatn   13.458    1.665    8.080    0.000   13.458    0.745
##    .dsq_sublimatin   13.299    1.555    8.552    0.000   13.299    0.840
##    .dsq_psed_ltrsm   13.186    1.315   10.031    0.000   13.186    0.954
##    .dsq_idealizatn   14.201    1.770    8.022    0.000   14.201    0.862
##    .dsq_isolation    24.014    1.747   13.749    0.000   24.014    0.998
##     PA1              10.883    2.354    4.623    0.000    1.000    1.000
##     PA2               2.774    1.310    2.118    0.034    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_tstc_fntsy    0.387
##     dsq_somatizatn    0.125
##     dsq_pssv_ggrss    0.428
##     dsq_displacmnt    0.159
##     dsq_acting_out    0.297
##     dsq_projection    0.350
##     dsq_undoing       0.084
##     dsq_devaluatin    0.225
##     dsq_splitting     0.109
##     dsq_denial        0.050
##     dsq_dissociatn    0.003
##     dsq_rctn_frmtn    0.019
##     dsq_suppressin    0.169
##     dsq_humor         0.267
##     dsq_rationlztn    0.497
##     dsq_anticipatn    0.255
##     dsq_sublimatin    0.160
##     dsq_psed_ltrsm    0.046
##     dsq_idealizatn    0.138
##     dsq_isolation     0.002

5.1.1 Model Comparison

# Likelihood Ratio Tests (Nested)
anova(fit1_comb, fit2_comb)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():  
##    scaling factor is negative
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##            Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit2_comb 338 37542 38017 699.31                              
## fit1_comb 340 37774 38241 935.28                  2
anova(fit1_comb, fit3_comb)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():  
##    scaling factor is negative
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##            Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit3_comb 334 37575 38065 724.23                              
## fit1_comb 340 37774 38241 935.28                  6
anova(fit1_comb, fit4_comb)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##            Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit4_comb 328 37471 37984 608.10                                  
## fit1_comb 340 37774 38241 935.28     732.49      12  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# BIC (Non-Nested)
fitMeasures(fit2_comb, "bic")
##      bic 
## 38016.76
fitMeasures(fit3_comb, "bic")
##      bic 
## 38065.24
fitMeasures(fit4_comb, "bic")
##      bic 
## 37984.45

5.2 Per Study CFA (2-Factor solution)

5.2.1 Dekker

fit2_dekker <- cfa(model_2f, data = dekker_df, estimator = "mlr", missing = "fiml")

# Inspect 2-factor
summary(fit2_dekker,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 80 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        61
## 
##   Number of observations                           151
##   Number of missing patterns                        18
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               339.719     321.488
##   Degrees of freedom                               169         169
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.057
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               666.331     620.879
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.073
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.642       0.646
##   Tucker-Lewis Index (TLI)                       0.597       0.602
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.649
##   Robust Tucker-Lewis Index (TLI)                            0.605
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7786.126   -7786.126
##   Scaling correction factor                                  0.992
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -7616.266   -7616.266
##   Scaling correction factor                                  1.040
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               15694.252   15694.252
##   Bayesian (BIC)                             15878.306   15878.306
##   Sample-size adjusted Bayesian (SABIC)      15685.248   15685.248
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.082       0.077
##   90 Percent confidence interval - lower         0.069       0.065
##   90 Percent confidence interval - upper         0.094       0.090
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.603       0.371
##                                                                   
##   Robust RMSEA                                               0.082
##   90 Percent confidence interval - lower                     0.069
##   90 Percent confidence interval - upper                     0.096
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.618
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.095       0.095
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 =~                                                                
##     dsq_tstc_fntsy    1.000                               1.775    0.416
##     dsq_somatizatn    0.707    0.214    3.304    0.001    1.255    0.355
##     dsq_pssv_ggrss    0.982    0.315    3.120    0.002    1.743    0.545
##     dsq_displacmnt    0.688    0.302    2.280    0.023    1.222    0.298
##     dsq_acting_out    0.955    0.361    2.646    0.008    1.695    0.402
##     dsq_projection    1.021    0.281    3.630    0.000    1.812    0.479
##     dsq_undoing       0.803    0.241    3.333    0.001    1.426    0.359
##     dsq_devaluatin    1.202    0.294    4.084    0.000    2.133    0.669
##     dsq_splitting     1.307    0.349    3.746    0.000    2.319    0.609
##     dsq_denial        0.624    0.247    2.522    0.012    1.107    0.338
##     dsq_dissociatn    0.879    0.258    3.401    0.001    1.560    0.423
##     dsq_rctn_frmtn    0.336    0.218    1.542    0.123    0.597    0.158
##   PA2 =~                                                                
##     dsq_suppressin    1.000                               1.715    0.441
##     dsq_humor         1.529    0.475    3.218    0.001    2.622    0.624
##     dsq_rationlztn    0.870    0.254    3.424    0.001    1.492    0.502
##     dsq_anticipatn    1.101    0.340    3.234    0.001    1.888    0.619
##     dsq_sublimatin    1.275    0.311    4.097    0.000    2.187    0.592
##     dsq_psed_ltrsm    0.847    0.269    3.155    0.002    1.453    0.479
##     dsq_idealizatn    0.736    0.266    2.767    0.006    1.261    0.329
##     dsq_isolation     0.212    0.293    0.722    0.470    0.363    0.080
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 ~~                                                                
##     PA2               0.312    0.482    0.648    0.517    0.103    0.103
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy    9.190    0.352   26.088    0.000    9.190    2.153
##    .dsq_somatizatn   11.442    0.289   39.623    0.000   11.442    3.236
##    .dsq_pssv_ggrss    7.748    0.268   28.865    0.000    7.748    2.421
##    .dsq_displacmnt    8.151    0.342   23.839    0.000    8.151    1.992
##    .dsq_acting_out    9.436    0.347   27.182    0.000    9.436    2.239
##    .dsq_projection    9.351    0.313   29.911    0.000    9.351    2.470
##    .dsq_undoing      11.142    0.332   33.523    0.000   11.142    2.805
##    .dsq_devaluatin    9.764    0.262   37.301    0.000    9.764    3.064
##    .dsq_splitting     9.717    0.311   31.276    0.000    9.717    2.552
##    .dsq_denial        6.887    0.269   25.571    0.000    6.887    2.101
##    .dsq_dissociatn    9.586    0.303   31.623    0.000    9.586    2.599
##    .dsq_rctn_frmtn    9.899    0.310   31.946    0.000    9.899    2.629
##    .dsq_suppressin    8.564    0.320   26.759    0.000    8.564    2.204
##    .dsq_humor         9.300    0.346   26.880    0.000    9.300    2.212
##    .dsq_rationlztn    8.846    0.245   36.114    0.000    8.846    2.976
##    .dsq_anticipatn   10.127    0.253   40.092    0.000   10.127    3.321
##    .dsq_sublimatin   10.030    0.308   32.593    0.000   10.030    2.713
##    .dsq_psed_ltrsm   12.697    0.254   50.044    0.000   12.697    4.187
##    .dsq_idealizatn    7.960    0.314   25.323    0.000    7.960    2.078
##    .dsq_isolation     8.592    0.378   22.718    0.000    8.592    1.887
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy   15.072    1.792    8.410    0.000   15.072    0.827
##    .dsq_somatizatn   10.925    1.094    9.987    0.000   10.925    0.874
##    .dsq_pssv_ggrss    7.204    0.987    7.299    0.000    7.204    0.703
##    .dsq_displacmnt   15.259    1.668    9.147    0.000   15.259    0.911
##    .dsq_acting_out   14.882    1.789    8.317    0.000   14.882    0.838
##    .dsq_projection   11.054    1.281    8.626    0.000   11.054    0.771
##    .dsq_undoing      13.745    1.408    9.761    0.000   13.745    0.871
##    .dsq_devaluatin    5.605    0.882    6.352    0.000    5.605    0.552
##    .dsq_splitting     9.123    1.635    5.579    0.000    9.123    0.629
##    .dsq_denial        9.523    1.016    9.372    0.000    9.523    0.886
##    .dsq_dissociatn   11.168    1.504    7.425    0.000   11.168    0.821
##    .dsq_rctn_frmtn   13.822    1.525    9.065    0.000   13.822    0.975
##    .dsq_suppressin   12.157    1.780    6.831    0.000   12.157    0.805
##    .dsq_humor        10.804    1.871    5.774    0.000   10.804    0.611
##    .dsq_rationlztn    6.613    0.893    7.408    0.000    6.613    0.748
##    .dsq_anticipatn    5.734    1.005    5.705    0.000    5.734    0.617
##    .dsq_sublimatin    8.888    1.652    5.380    0.000    8.888    0.650
##    .dsq_psed_ltrsm    7.084    0.991    7.151    0.000    7.084    0.770
##    .dsq_idealizatn   13.086    1.392    9.402    0.000   13.086    0.892
##    .dsq_isolation    20.606    1.767   11.661    0.000   20.606    0.994
##     PA1               3.150    1.469    2.144    0.032    1.000    1.000
##     PA2               2.940    1.366    2.153    0.031    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_tstc_fntsy    0.173
##     dsq_somatizatn    0.126
##     dsq_pssv_ggrss    0.297
##     dsq_displacmnt    0.089
##     dsq_acting_out    0.162
##     dsq_projection    0.229
##     dsq_undoing       0.129
##     dsq_devaluatin    0.448
##     dsq_splitting     0.371
##     dsq_denial        0.114
##     dsq_dissociatn    0.179
##     dsq_rctn_frmtn    0.025
##     dsq_suppressin    0.195
##     dsq_humor         0.389
##     dsq_rationlztn    0.252
##     dsq_anticipatn    0.383
##     dsq_sublimatin    0.350
##     dsq_psed_ltrsm    0.230
##     dsq_idealizatn    0.108
##     dsq_isolation     0.006

5.2.1.1 Model Comparison

# Likelihood Ratio Tests (Nested)
anova(fit1_dekker, fit2_dekker)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():  
##    scaling factor is negative
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##              Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit2_dekker 169 15694 15878 339.72                              
## fit1_dekker 170 15793 15974 440.11                  1
anova(fit1_dekker, fit3_dekker)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##              Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit3_dekker 167 15708 15898 349.66                                  
## fit1_dekker 170 15793 15974 440.11      49.38       3  1.083e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(fit1_dekker, fit4_dekker)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##              Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit4_dekker 164 15685 15884 320.06                                  
## fit1_dekker 170 15793 15974 440.11     104.13       6  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# BIC (Non-Nested)
fitMeasures(fit2_dekker, "bic")
##      bic 
## 15878.31
fitMeasures(fit3_dekker, "bic")
##      bic 
## 15898.29
fitMeasures(fit4_dekker, "bic")
##      bic 
## 15883.74

5.2.2 Dos Santos

fit2_ds <- cfa(model_2f, data = ds_df, estimator = "mlr", missing = "fiml")

summary(fit2_ds,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 91 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        61
## 
##   Number of observations                           210
##   Number of missing patterns                         3
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               359.587     321.355
##   Degrees of freedom                               169         169
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.119
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               724.594     635.432
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.140
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.643       0.658
##   Tucker-Lewis Index (TLI)                       0.599       0.615
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.671
##   Robust Tucker-Lewis Index (TLI)                            0.630
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10863.032  -10863.032
##   Scaling correction factor                                  1.031
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -10683.239  -10683.239
##   Scaling correction factor                                  1.096
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               21848.065   21848.065
##   Bayesian (BIC)                             22052.239   22052.239
##   Sample-size adjusted Bayesian (SABIC)      21858.955   21858.955
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.073       0.066
##   90 Percent confidence interval - lower         0.063       0.055
##   90 Percent confidence interval - upper         0.084       0.076
##   P-value H_0: RMSEA <= 0.050                    0.000       0.008
##   P-value H_0: RMSEA >= 0.080                    0.150       0.009
##                                                                   
##   Robust RMSEA                                               0.071
##   90 Percent confidence interval - lower                     0.059
##   90 Percent confidence interval - upper                     0.083
##   P-value H_0: Robust RMSEA <= 0.050                         0.004
##   P-value H_0: Robust RMSEA >= 0.080                         0.122
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.102       0.102
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 =~                                                                
##     dsq_tstc_fntsy    1.000                               3.299    0.622
##     dsq_somatizatn    0.510    0.156    3.274    0.001    1.684    0.353
##     dsq_pssv_ggrss    0.772    0.116    6.638    0.000    2.548    0.654
##     dsq_displacmnt    0.496    0.104    4.763    0.000    1.635    0.399
##     dsq_acting_out    0.808    0.132    6.143    0.000    2.665    0.545
##     dsq_projection    0.717    0.112    6.384    0.000    2.367    0.592
##     dsq_undoing       0.359    0.129    2.784    0.005    1.185    0.290
##     dsq_devaluatin    0.466    0.098    4.778    0.000    1.537    0.475
##     dsq_splitting     0.412    0.108    3.818    0.000    1.358    0.330
##     dsq_denial        0.227    0.099    2.298    0.022    0.748    0.223
##     dsq_dissociatn    0.052    0.105    0.493    0.622    0.170    0.054
##     dsq_rctn_frmtn   -0.167    0.133   -1.260    0.208   -0.551   -0.137
##   PA2 =~                                                                
##     dsq_suppressin    1.000                               1.665    0.411
##     dsq_humor         1.396    0.424    3.290    0.001    2.325    0.517
##     dsq_rationlztn    1.728    0.501    3.452    0.001    2.879    0.705
##     dsq_anticipatn    1.290    0.319    4.037    0.000    2.148    0.505
##     dsq_sublimatin    0.956    0.310    3.083    0.002    1.593    0.400
##     dsq_psed_ltrsm    0.477    0.281    1.700    0.089    0.794    0.214
##     dsq_idealizatn    0.905    0.289    3.128    0.002    1.506    0.371
##     dsq_isolation    -0.140    0.346   -0.405    0.685   -0.234   -0.048
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 ~~                                                                
##     PA2              -0.188    0.913   -0.205    0.837   -0.034   -0.034
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy   10.323    0.376   27.428    0.000   10.323    1.946
##    .dsq_somatizatn   11.558    0.387   29.860    0.000   11.558    2.423
##    .dsq_pssv_ggrss    8.766    0.277   31.687    0.000    8.766    2.250
##    .dsq_displacmnt   10.040    0.291   34.549    0.000   10.040    2.451
##    .dsq_acting_out   10.731    0.348   30.880    0.000   10.731    2.193
##    .dsq_projection    8.163    0.283   28.859    0.000    8.163    2.041
##    .dsq_undoing       9.460    0.290   32.579    0.000    9.460    2.313
##    .dsq_devaluatin    7.186    0.230   31.213    0.000    7.186    2.219
##    .dsq_splitting    10.012    0.292   34.289    0.000   10.012    2.434
##    .dsq_denial        5.391    0.239   22.520    0.000    5.391    1.605
##    .dsq_dissociatn    5.259    0.222   23.657    0.000    5.259    1.682
##    .dsq_rctn_frmtn    8.950    0.286   31.341    0.000    8.950    2.223
##    .dsq_suppressin    6.762    0.288   23.482    0.000    6.762    1.669
##    .dsq_humor         8.247    0.319   25.827    0.000    8.247    1.832
##    .dsq_rationlztn    8.439    0.290   29.132    0.000    8.439    2.066
##    .dsq_anticipatn   11.812    0.302   39.108    0.000   11.812    2.779
##    .dsq_sublimatin    9.803    0.283   34.670    0.000    9.803    2.463
##    .dsq_psed_ltrsm   11.030    0.264   41.771    0.000   11.030    2.967
##    .dsq_idealizatn    8.095    0.288   28.071    0.000    8.095    1.995
##    .dsq_isolation     9.833    0.349   28.208    0.000    9.833    2.004
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy   17.270    2.301    7.506    0.000   17.270    0.613
##    .dsq_somatizatn   19.921    2.251    8.850    0.000   19.921    0.875
##    .dsq_pssv_ggrss    8.690    1.289    6.743    0.000    8.690    0.572
##    .dsq_displacmnt   14.114    1.296   10.887    0.000   14.114    0.841
##    .dsq_acting_out   16.832    1.807    9.313    0.000   16.832    0.703
##    .dsq_projection   10.387    1.381    7.523    0.000   10.387    0.650
##    .dsq_undoing      15.330    1.584    9.678    0.000   15.330    0.916
##    .dsq_devaluatin    8.127    0.870    9.343    0.000    8.127    0.775
##    .dsq_splitting    15.079    1.606    9.388    0.000   15.079    0.891
##    .dsq_denial       10.718    0.981   10.923    0.000   10.718    0.950
##    .dsq_dissociatn    9.748    0.946   10.306    0.000    9.748    0.997
##    .dsq_rctn_frmtn   15.902    1.432   11.106    0.000   15.902    0.981
##    .dsq_suppressin   13.650    2.022    6.749    0.000   13.650    0.831
##    .dsq_humor        14.853    1.950    7.616    0.000   14.853    0.733
##    .dsq_rationlztn    8.395    1.831    4.586    0.000    8.395    0.503
##    .dsq_anticipatn   13.458    1.665    8.080    0.000   13.458    0.745
##    .dsq_sublimatin   13.299    1.555    8.552    0.000   13.299    0.840
##    .dsq_psed_ltrsm   13.186    1.315   10.031    0.000   13.186    0.954
##    .dsq_idealizatn   14.201    1.770    8.022    0.000   14.201    0.862
##    .dsq_isolation    24.014    1.747   13.749    0.000   24.014    0.998
##     PA1              10.883    2.354    4.623    0.000    1.000    1.000
##     PA2               2.774    1.310    2.118    0.034    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_tstc_fntsy    0.387
##     dsq_somatizatn    0.125
##     dsq_pssv_ggrss    0.428
##     dsq_displacmnt    0.159
##     dsq_acting_out    0.297
##     dsq_projection    0.350
##     dsq_undoing       0.084
##     dsq_devaluatin    0.225
##     dsq_splitting     0.109
##     dsq_denial        0.050
##     dsq_dissociatn    0.003
##     dsq_rctn_frmtn    0.019
##     dsq_suppressin    0.169
##     dsq_humor         0.267
##     dsq_rationlztn    0.497
##     dsq_anticipatn    0.255
##     dsq_sublimatin    0.160
##     dsq_psed_ltrsm    0.046
##     dsq_idealizatn    0.138
##     dsq_isolation     0.002

5.2.2.1 Model Comparison

# Likelihood Ratio Tests (Nested)
anova(fit1_ds, fit2_ds)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():  
##    scaling factor is negative
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit2_ds 169 21848 22052 359.59                              
## fit1_ds 170 21982 22183 495.16                  1
anova(fit1_ds, fit3_ds)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():  
##    scaling factor is negative
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit3_ds 167 21867 22078 374.57                              
## fit1_ds 170 21982 22183 495.16                  3
anova(fit1_ds, fit4_ds)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():  
##    scaling factor is negative
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit4_ds 164 21787 22007 288.04                              
## fit1_ds 170 21982 22183 495.16                  6
# BIC (Non-Nested)
fitMeasures(fit2_ds, "bic")
##      bic 
## 22052.24
fitMeasures(fit3_ds, "bic")
##      bic 
## 22077.91
fitMeasures(fit4_ds, "bic")
##      bic 
## 22007.43

5.2.3 Knekt

fit2_kn <- cfa(model_2f_norat, data = kn_df, estimator = "mlr", missing = "fiml")

summary(fit2_kn,
        standardized = TRUE,
        fit.measures = TRUE,
        rsquare      = TRUE)
## lavaan 0.6-19 ended normally after 134 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        58
## 
##   Number of observations                           306
##   Number of missing patterns                        12
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               458.252     445.277
##   Degrees of freedom                               151         151
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.029
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                               774.640     708.842
##   Degrees of freedom                               171         171
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.093
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.491       0.453
##   Tucker-Lewis Index (TLI)                       0.424       0.380
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.500
##   Robust Tucker-Lewis Index (TLI)                            0.433
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15562.195  -15562.195
##   Scaling correction factor                                  1.119
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -15333.068  -15333.068
##   Scaling correction factor                                  1.054
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               31240.389   31240.389
##   Bayesian (BIC)                             31456.357   31456.357
##   Sample-size adjusted Bayesian (SABIC)      31272.408   31272.408
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.082       0.080
##   90 Percent confidence interval - lower         0.073       0.071
##   90 Percent confidence interval - upper         0.090       0.088
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.626       0.494
##                                                                   
##   Robust RMSEA                                               0.080
##   90 Percent confidence interval - lower                     0.071
##   90 Percent confidence interval - upper                     0.089
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.521
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.088       0.088
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 =~                                                                
##     dsq_tstc_fntsy    1.000                               1.338    0.257
##     dsq_somatizatn    1.262    0.527    2.396    0.017    1.689    0.392
##     dsq_pssv_ggrss    1.524    0.473    3.224    0.001    2.038    0.579
##     dsq_displacmnt    1.286    0.494    2.605    0.009    1.720    0.454
##     dsq_acting_out    0.535    0.303    1.763    0.078    0.716    0.183
##     dsq_projection    1.235    0.450    2.747    0.006    1.652    0.458
##     dsq_undoing       1.352    0.510    2.652    0.008    1.808    0.459
##     dsq_devaluatin    0.716    0.233    3.076    0.002    0.958    0.322
##     dsq_splitting     1.026    0.417    2.461    0.014    1.373    0.387
##     dsq_denial        0.701    0.249    2.817    0.005    0.938    0.323
##     dsq_dissociatn    0.328    0.189    1.735    0.083    0.438    0.173
##     dsq_rctn_frmtn    0.913    0.418    2.184    0.029    1.222    0.353
##   PA2 =~                                                                
##     dsq_suppressin    1.000                               0.686    0.172
##     dsq_humor         1.300    1.207    1.077    0.282    0.892    0.242
##     dsq_anticipatn    1.097    1.909    0.574    0.566    0.753    0.234
##     dsq_sublimatin    2.389    2.502    0.955    0.340    1.640    0.425
##     dsq_psed_ltrsm    2.453    4.199    0.584    0.559    1.684    0.503
##     dsq_idealizatn    2.872    5.148    0.558    0.577    1.971    0.495
##     dsq_isolation    -0.976    1.733   -0.563    0.573   -0.670   -0.151
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   PA1 ~~                                                                
##     PA2               0.313    0.283    1.107    0.268    0.341    0.341
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy   11.665    0.299   39.039    0.000   11.665    2.239
##    .dsq_somatizatn   10.118    0.246   41.088    0.000   10.118    2.349
##    .dsq_pssv_ggrss    7.341    0.202   36.344    0.000    7.341    2.085
##    .dsq_displacmnt    8.673    0.216   40.077    0.000    8.673    2.291
##    .dsq_acting_out   10.797    0.224   48.218    0.000   10.797    2.766
##    .dsq_projection    8.023    0.206   38.872    0.000    8.023    2.226
##    .dsq_undoing       9.314    0.225   41.370    0.000    9.314    2.365
##    .dsq_devaluatin    7.258    0.170   42.612    0.000    7.258    2.436
##    .dsq_splitting     7.453    0.203   36.651    0.000    7.453    2.100
##    .dsq_denial        5.415    0.166   32.646    0.000    5.415    1.866
##    .dsq_dissociatn    4.413    0.145   30.346    0.000    4.413    1.744
##    .dsq_rctn_frmtn    9.110    0.199   45.863    0.000    9.110    2.634
##    .dsq_suppressin    7.431    0.228   32.561    0.000    7.431    1.866
##    .dsq_humor        11.523    0.211   54.732    0.000   11.523    3.129
##    .dsq_anticipatn   10.706    0.184   58.190    0.000   10.706    3.326
##    .dsq_sublimatin    9.549    0.220   43.320    0.000    9.549    2.476
##    .dsq_psed_ltrsm    9.635    0.192   50.250    0.000    9.635    2.878
##    .dsq_idealizatn    6.304    0.227   27.714    0.000    6.304    1.584
##    .dsq_isolation     8.102    0.254   31.881    0.000    8.102    1.830
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .dsq_tstc_fntsy   25.367    1.905   13.318    0.000   25.367    0.934
##    .dsq_somatizatn   15.703    1.457   10.781    0.000   15.703    0.846
##    .dsq_pssv_ggrss    8.246    1.112    7.413    0.000    8.246    0.665
##    .dsq_displacmnt   11.372    0.958   11.865    0.000   11.372    0.793
##    .dsq_acting_out   14.726    0.975   15.102    0.000   14.726    0.966
##    .dsq_projection   10.264    1.259    8.151    0.000   10.264    0.790
##    .dsq_undoing      12.239    1.326    9.227    0.000   12.239    0.789
##    .dsq_devaluatin    7.960    0.757   10.513    0.000    7.960    0.897
##    .dsq_splitting    10.706    0.936   11.435    0.000   10.706    0.850
##    .dsq_denial        7.539    0.600   12.566    0.000    7.539    0.895
##    .dsq_dissociatn    6.214    0.538   11.542    0.000    6.214    0.970
##    .dsq_rctn_frmtn   10.473    1.008   10.394    0.000   10.473    0.875
##    .dsq_suppressin   15.380    1.737    8.856    0.000   15.380    0.970
##    .dsq_humor        12.767    1.500    8.514    0.000   12.767    0.941
##    .dsq_anticipatn    9.791    0.887   11.038    0.000    9.791    0.945
##    .dsq_sublimatin   12.180    2.792    4.362    0.000   12.180    0.819
##    .dsq_psed_ltrsm    8.372    1.517    5.519    0.000    8.372    0.747
##    .dsq_idealizatn   11.947    2.683    4.452    0.000   11.947    0.755
##    .dsq_isolation    19.147    1.188   16.119    0.000   19.147    0.977
##     PA1               1.790    1.143    1.565    0.118    1.000    1.000
##     PA2               0.471    1.450    0.325    0.745    1.000    1.000
## 
## R-Square:
##                    Estimate
##     dsq_tstc_fntsy    0.066
##     dsq_somatizatn    0.154
##     dsq_pssv_ggrss    0.335
##     dsq_displacmnt    0.207
##     dsq_acting_out    0.034
##     dsq_projection    0.210
##     dsq_undoing       0.211
##     dsq_devaluatin    0.103
##     dsq_splitting     0.150
##     dsq_denial        0.105
##     dsq_dissociatn    0.030
##     dsq_rctn_frmtn    0.125
##     dsq_suppressin    0.030
##     dsq_humor         0.059
##     dsq_anticipatn    0.055
##     dsq_sublimatin    0.181
##     dsq_psed_ltrsm    0.253
##     dsq_idealizatn    0.245
##     dsq_isolation     0.023

5.2.3.1 Model Comparison

# Likelihood Ratio Tests (Nested)
anova(fit1_kn, fit2_kn)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)  
## fit2_kn 151 31240 31456 458.25                                
## fit1_kn 152 31261 31473 480.58     4.6856       1    0.03042 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(fit1_kn, fit3_kn)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit3_kn 149 31178 31402 392.12                                  
## fit1_kn 152 31261 31473 480.58     63.488       3  1.056e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(fit1_kn, fit4_kn)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan->lavTestLRT():  
##    lavaan NOTE: The "Chisq" column contains standard test statistics, not the robust test that should be reported per 
##    model. A robust difference test is a function of two standard (not robust) statistics.
##          Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## fit4_kn 146 31179 31414 387.27                                  
## fit1_kn 152 31261 31473 480.58     63.062       6  1.072e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# BIC (Non-Nested)
fitMeasures(fit2_kn, "bic")
##      bic 
## 31456.36
fitMeasures(fit3_kn, "bic")
##      bic 
## 31401.67
fitMeasures(fit4_kn, "bic")
##      bic 
## 31413.99