library('lavaan')
## This is lavaan 0.6-16
## lavaan is FREE software! Please report any bugs.
  spasd_spins_yj_z_df <- read.csv('spasd_spins_cfa_input.csv')

 # model 1: scog vars across all groups
      
    CFA_scog_model1 <- 'simulation =~ er40_total + rmet_total + mean_ea + tasit3_lies
                        mentalizing =~ tasit2_ssar + tasit2_psar + tasit3_sar'   
    
    CFA_scog_model1_fit <- cfa(CFA_scog_model1, data = spasd_spins_yj_z_df[,c(4:26)], std.lv=TRUE, estimator = "MLR", 
                               missing = "ml") 
    
    cfa_results <- summary(CFA_scog_model1_fit, fit.measures = TRUE, modindices = TRUE, standardized = TRUE, rsquare =
                             TRUE)
    
 # manual testing for measurement invariance 
    
    # configural - is factor structure model equal across groups (same as look at model fit in each group)
    
      CFA_scog_model1_grp_fit <- cfa(CFA_scog_model1, data = spasd_spins_yj_z_df, group = 'group', std.lv=TRUE,
                                     estimator = "MLR", missing = "ml") 
      
      summary(CFA_scog_model1_grp_fit, fit.measures = TRUE, modindices = TRUE, standardized = TRUE, rsquare = TRUE)
## lavaan 0.6.16 ended normally after 64 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
## 
##   Number of observations per group:                   
##     ASD                                            100
##     Control                                        209
##     SSD                                            276
##   Number of missing patterns per group:               
##     ASD                                              4
##     Control                                          6
##     SSD                                             20
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                                68.870      70.585
##   Degrees of freedom                                39          39
##   P-value (Chi-square)                           0.002       0.001
##   Scaling correction factor                                  0.976
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     ASD                                         22.175      22.727
##     Control                                     16.782      17.200
##     SSD                                         29.913      30.657
## 
## Model Test Baseline Model:
## 
##   Test statistic                               973.724     901.247
##   Degrees of freedom                                63          63
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.080
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.967       0.962
##   Tucker-Lewis Index (TLI)                       0.947       0.939
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.957
##   Robust Tucker-Lewis Index (TLI)                            0.930
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4307.123   -4307.123
##   Scaling correction factor                                  1.243
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -4272.688   -4272.688
##   Scaling correction factor                                  1.143
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                                8746.247    8746.247
##   Bayesian (BIC)                              9034.773    9034.773
##   Sample-size adjusted Bayesian (SABIC)       8825.247    8825.247
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.063       0.064
##   90 Percent confidence interval - lower         0.037       0.039
##   90 Percent confidence interval - upper         0.087       0.088
##   P-value H_0: RMSEA <= 0.050                    0.186       0.157
##   P-value H_0: RMSEA >= 0.080                    0.123       0.152
##                                                                   
##   Robust RMSEA                                               0.076
##   90 Percent confidence interval - lower                     0.000
##   90 Percent confidence interval - upper                     0.130
##   P-value H_0: Robust RMSEA <= 0.050                         0.242
##   P-value H_0: Robust RMSEA >= 0.080                         0.479
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.064       0.064
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [ASD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_total        0.425    0.163    2.615    0.009    0.425    0.431
##     rmet_total        0.773    0.139    5.561    0.000    0.773    0.829
##     mean_ea          -0.106    0.194   -0.546    0.585   -0.106   -0.113
##     tasit3_lies       0.363    0.114    3.198    0.001    0.363    0.345
##   mentalizing =~                                                        
##     tasit2_ssar       0.690    0.123    5.627    0.000    0.690    0.775
##     tasit2_psar       0.765    0.110    6.958    0.000    0.765    0.830
##     tasit3_sar        0.598    0.095    6.319    0.000    0.598    0.751
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.809    0.149    5.414    0.000    0.809    0.809
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.066    0.101   -0.650    0.516   -0.066   -0.067
##    .rmet_total        0.149    0.093    1.597    0.110    0.149    0.160
##    .mean_ea           0.073    0.230    0.318    0.750    0.073    0.079
##    .tasit3_lies      -0.328    0.105   -3.115    0.002   -0.328   -0.311
##    .tasit2_ssar       0.141    0.091    1.555    0.120    0.141    0.158
##    .tasit2_psar       0.111    0.092    1.209    0.227    0.111    0.121
##    .tasit3_sar        0.290    0.080    3.642    0.000    0.290    0.364
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.794    0.133    5.990    0.000    0.794    0.815
##    .rmet_total        0.271    0.182    1.491    0.136    0.271    0.313
##    .mean_ea           0.855    0.461    1.852    0.064    0.855    0.987
##    .tasit3_lies       0.977    0.155    6.295    0.000    0.977    0.881
##    .tasit2_ssar       0.316    0.086    3.682    0.000    0.316    0.399
##    .tasit2_psar       0.263    0.100    2.640    0.008    0.263    0.310
##    .tasit3_sar        0.277    0.055    5.008    0.000    0.277    0.436
##     simulation        1.000                               1.000    1.000
##     mentalizing       1.000                               1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.185
##     rmet_total        0.687
##     mean_ea           0.013
##     tasit3_lies       0.119
##     tasit2_ssar       0.601
##     tasit2_psar       0.690
##     tasit3_sar        0.564
## 
## 
## Group 2 [Control]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_total        0.311    0.094    3.308    0.001    0.311    0.359
##     rmet_total        0.630    0.109    5.799    0.000    0.630    0.764
##     mean_ea           0.274    0.205    1.338    0.181    0.274    0.235
##     tasit3_lies       0.290    0.087    3.340    0.001    0.290    0.336
##   mentalizing =~                                                        
##     tasit2_ssar       0.263    0.062    4.239    0.000    0.263    0.543
##     tasit2_psar       0.470    0.068    6.899    0.000    0.470    0.724
##     tasit3_sar        0.463    0.074    6.243    0.000    0.463    0.602
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.606    0.111    5.445    0.000    0.606    0.606
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.255    0.060    4.226    0.000    0.255    0.294
##    .rmet_total        0.333    0.057    5.841    0.000    0.333    0.405
##    .mean_ea           0.684    0.197    3.473    0.001    0.684    0.586
##    .tasit3_lies       0.373    0.060    6.217    0.000    0.373    0.432
##    .tasit2_ssar       0.468    0.033   13.971    0.000    0.468    0.966
##    .tasit2_psar       0.424    0.045    9.443    0.000    0.424    0.653
##    .tasit3_sar        0.419    0.053    7.875    0.000    0.419    0.545
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.657    0.077    8.584    0.000    0.657    0.871
##    .rmet_total        0.282    0.114    2.471    0.013    0.282    0.416
##    .mean_ea           1.291    0.288    4.485    0.000    1.291    0.945
##    .tasit3_lies       0.662    0.109    6.077    0.000    0.662    0.887
##    .tasit2_ssar       0.165    0.021    8.051    0.000    0.165    0.705
##    .tasit2_psar       0.200    0.051    3.899    0.000    0.200    0.475
##    .tasit3_sar        0.377    0.101    3.729    0.000    0.377    0.637
##     simulation        1.000                               1.000    1.000
##     mentalizing       1.000                               1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.129
##     rmet_total        0.584
##     mean_ea           0.055
##     tasit3_lies       0.113
##     tasit2_ssar       0.295
##     tasit2_psar       0.525
##     tasit3_sar        0.363
## 
## 
## Group 3 [SSD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_total        0.638    0.075    8.494    0.000    0.638    0.601
##     rmet_total        0.924    0.064   14.324    0.000    0.924    0.867
##     mean_ea           0.218    0.082    2.668    0.008    0.218    0.269
##     tasit3_lies       0.525    0.062    8.506    0.000    0.525    0.531
##   mentalizing =~                                                        
##     tasit2_ssar       0.947    0.059   15.975    0.000    0.947    0.820
##     tasit2_psar       0.863    0.061   14.186    0.000    0.863    0.762
##     tasit3_sar        0.900    0.051   17.777    0.000    0.900    0.850
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.686    0.048   14.447    0.000    0.686    0.686
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.200    0.065   -3.054    0.002   -0.200   -0.188
##    .rmet_total       -0.337    0.065   -5.198    0.000   -0.337   -0.316
##    .mean_ea          -0.198    0.085   -2.341    0.019   -0.198   -0.245
##    .tasit3_lies      -0.170    0.060   -2.836    0.005   -0.170   -0.172
##    .tasit2_ssar      -0.447    0.070   -6.339    0.000   -0.447   -0.387
##    .tasit2_psar      -0.424    0.070   -6.088    0.000   -0.424   -0.375
##    .tasit3_sar       -0.462    0.064   -7.185    0.000   -0.462   -0.436
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.721    0.100    7.241    0.000    0.721    0.639
##    .rmet_total        0.282    0.078    3.638    0.000    0.282    0.248
##    .mean_ea           0.609    0.125    4.863    0.000    0.609    0.928
##    .tasit3_lies       0.700    0.060   11.594    0.000    0.700    0.718
##    .tasit2_ssar       0.437    0.057    7.651    0.000    0.437    0.328
##    .tasit2_psar       0.537    0.063    8.493    0.000    0.537    0.419
##    .tasit3_sar        0.311    0.047    6.604    0.000    0.311    0.277
##     simulation        1.000                               1.000    1.000
##     mentalizing       1.000                               1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.361
##     rmet_total        0.752
##     mean_ea           0.072
##     tasit3_lies       0.282
##     tasit2_ssar       0.672
##     tasit2_psar       0.581
##     tasit3_sar        0.723
## 
## Modification Indices:
## 
##            lhs op         rhs block group level    mi    epc sepc.lv sepc.all
## 1   simulation =~ tasit2_ssar     1     1     1 2.324 -0.316  -0.316   -0.355
## 2   simulation =~ tasit2_psar     1     1     1 0.077  0.063   0.063    0.068
## 3   simulation =~  tasit3_sar     1     1     1 1.592  0.230   0.230    0.289
## 4  mentalizing =~  er40_total     1     1     1 2.584  0.590   0.590    0.598
## 5  mentalizing =~  rmet_total     1     1     1 0.721 -0.932  -0.932   -1.000
## 6  mentalizing =~     mean_ea     1     1     1 1.515 -0.719  -0.719   -0.772
## 7  mentalizing =~ tasit3_lies     1     1     1 1.702 -0.416  -0.416   -0.395
## 8   er40_total ~~  rmet_total     1     1     1 1.385 -0.145  -0.145   -0.312
## 9   er40_total ~~     mean_ea     1     1     1 3.319  0.376   0.376    0.457
## 10  er40_total ~~ tasit3_lies     1     1     1 0.247 -0.047  -0.047   -0.054
## 11  er40_total ~~ tasit2_ssar     1     1     1 0.000  0.000   0.000    0.001
## 12  er40_total ~~ tasit2_psar     1     1     1 0.373 -0.038  -0.038   -0.082
## 13  er40_total ~~  tasit3_sar     1     1     1 3.537  0.105   0.105    0.224
## 14  rmet_total ~~     mean_ea     1     1     1 0.023 -0.027  -0.027   -0.057
## 15  rmet_total ~~ tasit3_lies     1     1     1 2.748  0.172   0.172    0.335
## 16  rmet_total ~~ tasit2_ssar     1     1     1 1.415 -0.063  -0.063   -0.216
## 17  rmet_total ~~ tasit2_psar     1     1     1 0.009  0.005   0.005    0.020
## 18  rmet_total ~~  tasit3_sar     1     1     1 0.891  0.045   0.045    0.162
## 19     mean_ea ~~ tasit3_lies     1     1     1 1.278  0.256   0.256    0.280
## 20     mean_ea ~~ tasit2_ssar     1     1     1 0.526  0.107   0.107    0.206
## 21     mean_ea ~~ tasit2_psar     1     1     1 1.292 -0.161  -0.161   -0.339
## 22     mean_ea ~~  tasit3_sar     1     1     1 0.544 -0.097  -0.097   -0.200
## 23 tasit3_lies ~~ tasit2_ssar     1     1     1 0.393 -0.041  -0.041   -0.074
## 24 tasit3_lies ~~ tasit2_psar     1     1     1 1.027  0.066   0.066    0.130
## 25 tasit3_lies ~~  tasit3_sar     1     1     1 2.929 -0.102  -0.102   -0.197
## 26 tasit2_ssar ~~ tasit2_psar     1     1     1 1.592  0.087   0.087    0.302
## 27 tasit2_ssar ~~  tasit3_sar     1     1     1 0.077  0.014   0.014    0.049
## 28 tasit2_psar ~~  tasit3_sar     1     1     1 2.324 -0.090  -0.090   -0.332
## 29  simulation =~ tasit2_ssar     2     2     1 0.442 -0.042  -0.042   -0.088
## 30  simulation =~ tasit2_psar     2     2     1 0.109 -0.035  -0.035   -0.054
## 31  simulation =~  tasit3_sar     2     2     1 0.945  0.104   0.104    0.135
## 32 mentalizing =~  er40_total     2     2     1 1.333 -0.157  -0.157   -0.181
## 33 mentalizing =~  rmet_total     2     2     1 3.914  0.652   0.652    0.792
## 34 mentalizing =~     mean_ea     2     2     1 0.042 -0.070  -0.070   -0.060
## 35 mentalizing =~ tasit3_lies     2     2     1 0.190 -0.056  -0.056   -0.065
## 36  er40_total ~~  rmet_total     2     2     1 0.447 -0.060  -0.060   -0.140
## 37  er40_total ~~     mean_ea     2     2     1 0.814 -0.144  -0.144   -0.156
## 38  er40_total ~~ tasit3_lies     2     2     1 6.641  0.134   0.134    0.204
## 39  er40_total ~~ tasit2_ssar     2     2     1 0.704 -0.022  -0.022   -0.065
## 40  er40_total ~~ tasit2_psar     2     2     1 4.507 -0.072  -0.072   -0.199
## 41  er40_total ~~  tasit3_sar     2     2     1 4.538  0.086   0.086    0.172
## 42  rmet_total ~~     mean_ea     2     2     1 1.158  0.199   0.199    0.329
## 43  rmet_total ~~ tasit3_lies     2     2     1 2.066 -0.119  -0.119   -0.276
## 44  rmet_total ~~ tasit2_ssar     2     2     1 0.117 -0.008  -0.008   -0.039
## 45  rmet_total ~~ tasit2_psar     2     2     1 0.671  0.031   0.031    0.130
## 46  rmet_total ~~  tasit3_sar     2     2     1 0.064  0.010   0.010    0.031
## 47     mean_ea ~~ tasit3_lies     2     2     1 0.527 -0.114  -0.114   -0.123
## 48     mean_ea ~~ tasit2_ssar     2     2     1 0.104  0.026   0.026    0.057
## 49     mean_ea ~~ tasit2_psar     2     2     1 0.226 -0.049  -0.049   -0.096
## 50     mean_ea ~~  tasit3_sar     2     2     1 0.003  0.007   0.007    0.009
## 51 tasit3_lies ~~ tasit2_ssar     2     2     1 0.016  0.003   0.003    0.010
## 52 tasit3_lies ~~ tasit2_psar     2     2     1 0.057  0.008   0.008    0.022
## 53 tasit3_lies ~~  tasit3_sar     2     2     1 0.738 -0.034  -0.034   -0.069
## 54 tasit2_ssar ~~ tasit2_psar     2     2     1 0.945  0.029   0.029    0.159
## 55 tasit2_ssar ~~  tasit3_sar     2     2     1 0.109 -0.009  -0.009   -0.038
## 56 tasit2_psar ~~  tasit3_sar     2     2     1 0.442 -0.037  -0.037   -0.134
## 57  simulation =~ tasit2_ssar     3     3     1 0.299 -0.054  -0.054   -0.046
## 58  simulation =~ tasit2_psar     3     3     1 6.064  0.235   0.235    0.208
## 59  simulation =~  tasit3_sar     3     3     1 2.964 -0.157  -0.157   -0.148
## 60 mentalizing =~  er40_total     3     3     1 0.297 -0.066  -0.066   -0.062
## 61 mentalizing =~  rmet_total     3     3     1 1.524  0.232   0.232    0.218
## 62 mentalizing =~     mean_ea     3     3     1 0.003 -0.007  -0.007   -0.009
## 63 mentalizing =~ tasit3_lies     3     3     1 0.386 -0.065  -0.065   -0.066
## 64  er40_total ~~  rmet_total     3     3     1 0.948 -0.086  -0.086   -0.191
## 65  er40_total ~~     mean_ea     3     3     1 1.618  0.096   0.096    0.145
## 66  er40_total ~~ tasit3_lies     3     3     1 1.625  0.069   0.069    0.097
## 67  er40_total ~~ tasit2_ssar     3     3     1 1.637  0.057   0.057    0.101
## 68  er40_total ~~ tasit2_psar     3     3     1 0.231 -0.022  -0.022   -0.036
## 69  er40_total ~~  tasit3_sar     3     3     1 1.411 -0.047  -0.047   -0.100
## 70  rmet_total ~~     mean_ea     3     3     1 0.001  0.003   0.003    0.007
## 71  rmet_total ~~ tasit3_lies     3     3     1 0.047 -0.015  -0.015   -0.035
## 72  rmet_total ~~ tasit2_ssar     3     3     1 0.771 -0.036  -0.036   -0.102
## 73  rmet_total ~~ tasit2_psar     3     3     1 0.391  0.026   0.026    0.066
## 74  rmet_total ~~  tasit3_sar     3     3     1 0.666  0.030   0.030    0.103
## 75     mean_ea ~~ tasit3_lies     3     3     1 2.056 -0.101  -0.101   -0.154
## 76     mean_ea ~~ tasit2_ssar     3     3     1 3.355 -0.113  -0.113   -0.219
## 77     mean_ea ~~ tasit2_psar     3     3     1 3.184  0.117   0.117    0.205
## 78     mean_ea ~~  tasit3_sar     3     3     1 0.059  0.014   0.014    0.031
## 79 tasit3_lies ~~ tasit2_ssar     3     3     1 0.044 -0.009  -0.009   -0.016
## 80 tasit3_lies ~~ tasit2_psar     3     3     1 8.841  0.131   0.131    0.213
## 81 tasit3_lies ~~  tasit3_sar     3     3     1 7.315 -0.102  -0.102   -0.217
## 82 tasit2_ssar ~~ tasit2_psar     3     3     1 2.964 -0.110  -0.110   -0.227
## 83 tasit2_ssar ~~  tasit3_sar     3     3     1 6.065  0.179   0.179    0.485
## 84 tasit2_psar ~~  tasit3_sar     3     3     1 0.299 -0.034  -0.034   -0.083
##    sepc.nox
## 1    -0.355
## 2     0.068
## 3     0.289
## 4     0.598
## 5    -1.000
## 6    -0.772
## 7    -0.395
## 8    -0.312
## 9     0.457
## 10   -0.054
## 11    0.001
## 12   -0.082
## 13    0.224
## 14   -0.057
## 15    0.335
## 16   -0.216
## 17    0.020
## 18    0.162
## 19    0.280
## 20    0.206
## 21   -0.339
## 22   -0.200
## 23   -0.074
## 24    0.130
## 25   -0.197
## 26    0.302
## 27    0.049
## 28   -0.332
## 29   -0.088
## 30   -0.054
## 31    0.135
## 32   -0.181
## 33    0.792
## 34   -0.060
## 35   -0.065
## 36   -0.140
## 37   -0.156
## 38    0.204
## 39   -0.065
## 40   -0.199
## 41    0.172
## 42    0.329
## 43   -0.276
## 44   -0.039
## 45    0.130
## 46    0.031
## 47   -0.123
## 48    0.057
## 49   -0.096
## 50    0.009
## 51    0.010
## 52    0.022
## 53   -0.069
## 54    0.159
## 55   -0.038
## 56   -0.134
## 57   -0.046
## 58    0.208
## 59   -0.148
## 60   -0.062
## 61    0.218
## 62   -0.009
## 63   -0.066
## 64   -0.191
## 65    0.145
## 66    0.097
## 67    0.101
## 68   -0.036
## 69   -0.100
## 70    0.007
## 71   -0.035
## 72   -0.102
## 73    0.066
## 74    0.103
## 75   -0.154
## 76   -0.219
## 77    0.205
## 78    0.031
## 79   -0.016
## 80    0.213
## 81   -0.217
## 82   -0.227
## 83    0.485
## 84   -0.083
    # metric - are factor loadings equal across groups
      
      CFA_sc_model1_grp_fit2 <- cfa(model= CFA_scog_model1,data = spasd_spins_yj_z_df,group = "group",
                                    group.equal=c("loadings"),estimator = "MLR", missing = "ml")
      
      summary(CFA_sc_model1_grp_fit2, fit.measures = TRUE, modindices = TRUE, standardized = TRUE, rsquare = TRUE)
## lavaan 0.6.16 ended normally after 63 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
##   Number of equality constraints                    10
## 
##   Number of observations per group:                   
##     ASD                                            100
##     Control                                        209
##     SSD                                            276
##   Number of missing patterns per group:               
##     ASD                                              4
##     Control                                          6
##     SSD                                             20
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                                90.697      88.980
##   Degrees of freedom                                49          49
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.019
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     ASD                                         26.555      26.052
##     Control                                     31.038      30.450
##     SSD                                         33.105      32.478
## 
## Model Test Baseline Model:
## 
##   Test statistic                               973.724     901.247
##   Degrees of freedom                                63          63
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.080
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.954       0.952
##   Tucker-Lewis Index (TLI)                       0.941       0.939
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.948
##   Robust Tucker-Lewis Index (TLI)                            0.933
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4318.037   -4318.037
##   Scaling correction factor                                  1.062
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -4272.688   -4272.688
##   Scaling correction factor                                  1.143
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                                8748.074    8748.074
##   Bayesian (BIC)                              8992.884    8992.884
##   Sample-size adjusted Bayesian (SABIC)       8815.104    8815.104
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.066       0.065
##   90 Percent confidence interval - lower         0.044       0.043
##   90 Percent confidence interval - upper         0.087       0.086
##   P-value H_0: RMSEA <= 0.050                    0.105       0.124
##   P-value H_0: RMSEA >= 0.080                    0.145       0.120
##                                                                   
##   Robust RMSEA                                               0.074
##   90 Percent confidence interval - lower                     0.000
##   90 Percent confidence interval - upper                     0.119
##   P-value H_0: Robust RMSEA <= 0.050                         0.217
##   P-value H_0: Robust RMSEA >= 0.080                         0.440
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.076       0.076
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [ASD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.472    0.474
##     rmt_ttl (.p2.)    1.546    0.194    7.972    0.000    0.730    0.793
##     mean_ea (.p3.)    0.315    0.135    2.324    0.020    0.149    0.152
##     tst3_ls (.p4.)    0.844    0.102    8.284    0.000    0.399    0.374
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.667    0.760
##     tst2_ps (.p6.)    1.044    0.076   13.733    0.000    0.696    0.784
##     tst3_sr (.p7.)    1.001    0.067   14.851    0.000    0.668    0.800
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.262    0.088    2.981    0.003    0.832    0.832
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.067    0.101   -0.669    0.504   -0.067   -0.068
##    .rmet_total        0.149    0.093    1.597    0.110    0.149    0.162
##    .mean_ea           0.093    0.235    0.397    0.691    0.093    0.095
##    .tasit3_lies      -0.328    0.105   -3.115    0.002   -0.328   -0.307
##    .tasit2_ssar       0.142    0.090    1.581    0.114    0.142    0.162
##    .tasit2_psar       0.111    0.092    1.209    0.226    0.111    0.125
##    .tasit3_sar        0.290    0.080    3.643    0.000    0.290    0.348
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.770    0.125    6.157    0.000    0.770    0.775
##    .rmet_total        0.314    0.099    3.180    0.001    0.314    0.371
##    .mean_ea           0.936    0.437    2.144    0.032    0.936    0.977
##    .tasit3_lies       0.979    0.153    6.385    0.000    0.979    0.860
##    .tasit2_ssar       0.325    0.085    3.847    0.000    0.325    0.422
##    .tasit2_psar       0.305    0.098    3.117    0.002    0.305    0.386
##    .tasit3_sar        0.251    0.053    4.692    0.000    0.251    0.360
##     simulation        0.223    0.069    3.214    0.001    1.000    1.000
##     mentalizing       0.445    0.136    3.279    0.001    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.225
##     rmet_total        0.629
##     mean_ea           0.023
##     tasit3_lies       0.140
##     tasit2_ssar       0.578
##     tasit2_psar       0.614
##     tasit3_sar        0.640
## 
## 
## Group 2 [Control]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.371    0.422
##     rmt_ttl (.p2.)    1.546    0.194    7.972    0.000    0.573    0.698
##     mean_ea (.p3.)    0.315    0.135    2.324    0.020    0.117    0.100
##     tst3_ls (.p4.)    0.844    0.102    8.284    0.000    0.313    0.363
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.358    0.699
##     tst2_ps (.p6.)    1.044    0.076   13.733    0.000    0.374    0.598
##     tst3_sr (.p7.)    1.001    0.067   14.851    0.000    0.359    0.483
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.079    0.026    3.079    0.002    0.597    0.597
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.255    0.060    4.220    0.000    0.255    0.290
##    .rmet_total        0.333    0.057    5.842    0.000    0.333    0.406
##    .mean_ea           0.651    0.189    3.453    0.001    0.651    0.561
##    .tasit3_lies       0.373    0.060    6.227    0.000    0.373    0.433
##    .tasit2_ssar       0.468    0.033   13.971    0.000    0.468    0.912
##    .tasit2_psar       0.424    0.045    9.443    0.000    0.424    0.677
##    .tasit3_sar        0.419    0.053    7.875    0.000    0.419    0.564
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.633    0.073    8.650    0.000    0.633    0.822
##    .rmet_total        0.345    0.069    4.965    0.000    0.345    0.512
##    .mean_ea           1.333    0.288    4.631    0.000    1.333    0.990
##    .tasit3_lies       0.645    0.103    6.278    0.000    0.645    0.868
##    .tasit2_ssar       0.134    0.021    6.501    0.000    0.134    0.511
##    .tasit2_psar       0.251    0.049    5.142    0.000    0.251    0.642
##    .tasit3_sar        0.422    0.087    4.843    0.000    0.422    0.766
##     simulation        0.137    0.039    3.540    0.000    1.000    1.000
##     mentalizing       0.129    0.036    3.618    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.178
##     rmet_total        0.488
##     mean_ea           0.010
##     tasit3_lies       0.132
##     tasit2_ssar       0.489
##     tasit2_psar       0.358
##     tasit3_sar        0.234
## 
## 
## Group 3 [SSD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.610    0.580
##     rmt_ttl (.p2.)    1.546    0.194    7.972    0.000    0.944    0.881
##     mean_ea (.p3.)    0.315    0.135    2.324    0.020    0.192    0.238
##     tst3_ls (.p4.)    0.844    0.102    8.284    0.000    0.515    0.523
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.893    0.794
##     tst2_ps (.p6.)    1.044    0.076   13.733    0.000    0.932    0.794
##     tst3_sr (.p7.)    1.001    0.067   14.851    0.000    0.894    0.846
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.374    0.063    5.938    0.000    0.687    0.687
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.199    0.065   -3.048    0.002   -0.199   -0.189
##    .rmet_total       -0.338    0.065   -5.203    0.000   -0.338   -0.315
##    .mean_ea          -0.205    0.084   -2.451    0.014   -0.205   -0.254
##    .tasit3_lies      -0.170    0.060   -2.839    0.005   -0.170   -0.172
##    .tasit2_ssar      -0.445    0.070   -6.326    0.000   -0.445   -0.396
##    .tasit2_psar      -0.429    0.070   -6.138    0.000   -0.429   -0.365
##    .tasit3_sar       -0.462    0.064   -7.188    0.000   -0.462   -0.438
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.735    0.097    7.606    0.000    0.735    0.664
##    .rmet_total        0.256    0.076    3.361    0.001    0.256    0.223
##    .mean_ea           0.611    0.126    4.872    0.000    0.611    0.943
##    .tasit3_lies       0.705    0.059   12.021    0.000    0.705    0.727
##    .tasit2_ssar       0.468    0.058    8.098    0.000    0.468    0.370
##    .tasit2_psar       0.510    0.062    8.205    0.000    0.510    0.370
##    .tasit3_sar        0.317    0.047    6.743    0.000    0.317    0.284
##     simulation        0.372    0.086    4.349    0.000    1.000    1.000
##     mentalizing       0.797    0.111    7.183    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.336
##     rmet_total        0.777
##     mean_ea           0.057
##     tasit3_lies       0.273
##     tasit2_ssar       0.630
##     tasit2_psar       0.630
##     tasit3_sar        0.716
## 
## Modification Indices:
## 
##            lhs op         rhs block group level     mi    epc sepc.lv sepc.all
## 1   simulation =~  er40_total     1     1     1  0.063 -0.068  -0.032   -0.032
## 2  mentalizing =~ tasit2_ssar     1     1     1  0.134  0.049   0.033    0.037
## 3   simulation =~  er40_total     2     2     1  0.483 -0.191  -0.071   -0.081
## 4  mentalizing =~ tasit2_ssar     2     2     1 16.318 -0.732  -0.263   -0.512
## 5   simulation =~  er40_total     3     3     1  0.537  0.156   0.095    0.090
## 6  mentalizing =~ tasit2_ssar     3     3     1  5.296  0.271   0.242    0.215
## 7   simulation =~ tasit2_ssar     1     1     1  0.047 -0.040  -0.019   -0.022
## 8   simulation =~ tasit2_psar     1     1     1  1.621  0.237   0.112    0.126
## 9   simulation =~  tasit3_sar     1     1     1  1.075 -0.180  -0.085   -0.102
## 10 mentalizing =~  er40_total     1     1     1  0.024  0.026   0.018    0.018
## 11 mentalizing =~  rmet_total     1     1     1  0.590  0.170   0.113    0.123
## 12 mentalizing =~     mean_ea     1     1     1  4.369 -0.823  -0.549   -0.560
## 13 mentalizing =~ tasit3_lies     1     1     1  0.955 -0.175  -0.116   -0.109
## 14  er40_total ~~  rmet_total     1     1     1  1.479 -0.126  -0.126   -0.256
## 15  er40_total ~~     mean_ea     1     1     1  2.823  0.359   0.359    0.423
## 16  er40_total ~~ tasit3_lies     1     1     1  0.389 -0.059  -0.059   -0.067
## 17  er40_total ~~ tasit2_ssar     1     1     1  0.070 -0.016  -0.016   -0.032
## 18  er40_total ~~ tasit2_psar     1     1     1  0.434 -0.040  -0.040   -0.082
## 19  er40_total ~~  tasit3_sar     1     1     1  2.865  0.094   0.094    0.215
## 20  rmet_total ~~     mean_ea     1     1     1  0.557 -0.126  -0.126   -0.232
## 21  rmet_total ~~ tasit3_lies     1     1     1  2.314  0.135   0.135    0.243
## 22  rmet_total ~~ tasit2_ssar     1     1     1  0.884 -0.047  -0.047   -0.148
## 23  rmet_total ~~ tasit2_psar     1     1     1  0.499  0.036   0.036    0.115
## 24  rmet_total ~~  tasit3_sar     1     1     1  0.277  0.025   0.025    0.089
## 25     mean_ea ~~ tasit3_lies     1     1     1  0.806  0.213   0.213    0.223
## 26     mean_ea ~~ tasit2_ssar     1     1     1  0.090  0.047   0.047    0.085
## 27     mean_ea ~~ tasit2_psar     1     1     1  1.659 -0.193  -0.193   -0.360
## 28     mean_ea ~~  tasit3_sar     1     1     1  1.036 -0.141  -0.141   -0.290
## 29 tasit3_lies ~~ tasit2_ssar     1     1     1  0.384 -0.041  -0.041   -0.072
## 30 tasit3_lies ~~ tasit2_psar     1     1     1  0.857  0.060   0.060    0.110
## 31 tasit3_lies ~~  tasit3_sar     1     1     1  3.288 -0.109  -0.109   -0.220
## 32 tasit2_ssar ~~ tasit2_psar     1     1     1  3.787  0.100   0.100    0.317
## 33 tasit2_ssar ~~  tasit3_sar     1     1     1  0.218 -0.023  -0.023   -0.080
## 34 tasit2_psar ~~  tasit3_sar     1     1     1  2.172 -0.075  -0.075   -0.273
## 35  simulation =~ tasit2_ssar     2     2     1 12.037 -0.469  -0.174   -0.339
## 36  simulation =~ tasit2_psar     2     2     1  3.382  0.279   0.103    0.165
## 37  simulation =~  tasit3_sar     2     2     1  5.207  0.401   0.148    0.200
## 38 mentalizing =~  er40_total     2     2     1  1.966 -0.308  -0.110   -0.126
## 39 mentalizing =~  rmet_total     2     2     1  1.961  0.395   0.142    0.173
## 40 mentalizing =~     mean_ea     2     2     1  0.186  0.279   0.100    0.086
## 41 mentalizing =~ tasit3_lies     2     2     1  0.143 -0.081  -0.029   -0.034
## 42  er40_total ~~  rmet_total     2     2     1  0.604 -0.050  -0.050   -0.108
## 43  er40_total ~~     mean_ea     2     2     1  0.724 -0.135  -0.135   -0.147
## 44  er40_total ~~ tasit3_lies     2     2     1  4.483  0.104   0.104    0.163
## 45  er40_total ~~ tasit2_ssar     2     2     1  1.664 -0.034  -0.034   -0.117
## 46  er40_total ~~ tasit2_psar     2     2     1  3.043 -0.057  -0.057   -0.143
## 47  er40_total ~~  tasit3_sar     2     2     1  3.223  0.072   0.072    0.139
## 48  rmet_total ~~     mean_ea     2     2     1  1.947  0.195   0.195    0.287
## 49  rmet_total ~~ tasit3_lies     2     2     1  0.697 -0.046  -0.046   -0.098
## 50  rmet_total ~~ tasit2_ssar     2     2     1  1.745 -0.034  -0.034   -0.159
## 51  rmet_total ~~ tasit2_psar     2     2     1  4.257  0.063   0.063    0.214
## 52  rmet_total ~~  tasit3_sar     2     2     1  1.377  0.043   0.043    0.112
## 53     mean_ea ~~ tasit3_lies     2     2     1  0.442 -0.103  -0.103   -0.111
## 54     mean_ea ~~ tasit2_ssar     2     2     1  0.048  0.018   0.018    0.043
## 55     mean_ea ~~ tasit2_psar     2     2     1  0.074 -0.028  -0.028   -0.049
## 56     mean_ea ~~  tasit3_sar     2     2     1  0.028  0.021   0.021    0.029
## 57 tasit3_lies ~~ tasit2_ssar     2     2     1  0.062 -0.006  -0.006   -0.022
## 58 tasit3_lies ~~ tasit2_psar     2     2     1  0.037  0.006   0.006    0.015
## 59 tasit3_lies ~~  tasit3_sar     2     2     1  0.730 -0.034  -0.034   -0.065
## 60 tasit2_ssar ~~ tasit2_psar     2     2     1  0.560 -0.019  -0.019   -0.105
## 61 tasit2_ssar ~~  tasit3_sar     2     2     1  2.258 -0.038  -0.038   -0.158
## 62 tasit2_psar ~~  tasit3_sar     2     2     1  6.092  0.071   0.071    0.216
## 63  simulation =~ tasit2_ssar     3     3     1  0.814  0.110   0.067    0.060
## 64  simulation =~ tasit2_psar     3     3     1  0.150  0.049   0.030    0.026
## 65  simulation =~  tasit3_sar     3     3     1  1.489 -0.141  -0.086   -0.081
## 66 mentalizing =~  er40_total     3     3     1  0.016  0.012   0.011    0.011
## 67 mentalizing =~  rmet_total     3     3     1  0.008 -0.012  -0.010   -0.010
## 68 mentalizing =~     mean_ea     3     3     1  0.187  0.061   0.055    0.068
## 69 mentalizing =~ tasit3_lies     3     3     1  0.018 -0.012  -0.011   -0.011
## 70  er40_total ~~  rmet_total     3     3     1  0.541 -0.059  -0.059   -0.137
## 71  er40_total ~~     mean_ea     3     3     1  1.697  0.098   0.098    0.146
## 72  er40_total ~~ tasit3_lies     3     3     1  2.067  0.075   0.075    0.105
## 73  er40_total ~~ tasit2_ssar     3     3     1  1.887  0.061   0.061    0.104
## 74  er40_total ~~ tasit2_psar     3     3     1  0.199 -0.021  -0.021   -0.034
## 75  er40_total ~~  tasit3_sar     3     3     1  1.083 -0.041  -0.041   -0.086
## 76  rmet_total ~~     mean_ea     3     3     1  0.002  0.003   0.003    0.008
## 77  rmet_total ~~ tasit3_lies     3     3     1  0.246 -0.033  -0.033   -0.078
## 78  rmet_total ~~ tasit2_ssar     3     3     1  0.486 -0.028  -0.028   -0.081
## 79  rmet_total ~~ tasit2_psar     3     3     1  0.053  0.010   0.010    0.027
## 80  rmet_total ~~  tasit3_sar     3     3     1  0.444  0.025   0.025    0.087
## 81     mean_ea ~~ tasit3_lies     3     3     1  1.776 -0.093  -0.093   -0.142
## 82     mean_ea ~~ tasit2_ssar     3     3     1  3.084 -0.109  -0.109   -0.203
## 83     mean_ea ~~ tasit2_psar     3     3     1  3.295  0.119   0.119    0.214
## 84     mean_ea ~~  tasit3_sar     3     3     1  0.017  0.007   0.007    0.017
## 85 tasit3_lies ~~ tasit2_ssar     3     3     1  0.044 -0.009  -0.009   -0.015
## 86 tasit3_lies ~~ tasit2_psar     3     3     1  9.243  0.134   0.134    0.224
## 87 tasit3_lies ~~  tasit3_sar     3     3     1  7.589 -0.103  -0.103   -0.219
## 88 tasit2_ssar ~~ tasit2_psar     3     3     1  3.005 -0.101  -0.101   -0.207
## 89 tasit2_ssar ~~  tasit3_sar     3     3     1 11.516  0.193   0.193    0.500
## 90 tasit2_psar ~~  tasit3_sar     3     3     1  2.675 -0.097  -0.097   -0.242
##    sepc.nox
## 1    -0.032
## 2     0.037
## 3    -0.081
## 4    -0.512
## 5     0.090
## 6     0.215
## 7    -0.022
## 8     0.126
## 9    -0.102
## 10    0.018
## 11    0.123
## 12   -0.560
## 13   -0.109
## 14   -0.256
## 15    0.423
## 16   -0.067
## 17   -0.032
## 18   -0.082
## 19    0.215
## 20   -0.232
## 21    0.243
## 22   -0.148
## 23    0.115
## 24    0.089
## 25    0.223
## 26    0.085
## 27   -0.360
## 28   -0.290
## 29   -0.072
## 30    0.110
## 31   -0.220
## 32    0.317
## 33   -0.080
## 34   -0.273
## 35   -0.339
## 36    0.165
## 37    0.200
## 38   -0.126
## 39    0.173
## 40    0.086
## 41   -0.034
## 42   -0.108
## 43   -0.147
## 44    0.163
## 45   -0.117
## 46   -0.143
## 47    0.139
## 48    0.287
## 49   -0.098
## 50   -0.159
## 51    0.214
## 52    0.112
## 53   -0.111
## 54    0.043
## 55   -0.049
## 56    0.029
## 57   -0.022
## 58    0.015
## 59   -0.065
## 60   -0.105
## 61   -0.158
## 62    0.216
## 63    0.060
## 64    0.026
## 65   -0.081
## 66    0.011
## 67   -0.010
## 68    0.068
## 69   -0.011
## 70   -0.137
## 71    0.146
## 72    0.105
## 73    0.104
## 74   -0.034
## 75   -0.086
## 76    0.008
## 77   -0.078
## 78   -0.081
## 79    0.027
## 80    0.087
## 81   -0.142
## 82   -0.203
## 83    0.214
## 84    0.017
## 85   -0.015
## 86    0.224
## 87   -0.219
## 88   -0.207
## 89    0.500
## 90   -0.242
      anova(CFA_scog_model1_grp_fit,CFA_sc_model1_grp_fit2 )
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## 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)  
## CFA_scog_model1_grp_fit 39 8746.2 9034.8 68.870                                
## CFA_sc_model1_grp_fit2  49 8748.1 8992.9 90.697     18.353      10     0.0493 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
      modindices(CFA_sc_model1_grp_fit2, sort = TRUE, maximum.number = 10)
##             lhs op         rhs block group level     mi    epc sepc.lv sepc.all
## 31  mentalizing =~ tasit2_ssar     2     2     1 16.318 -0.732  -0.263   -0.512
## 117  simulation =~ tasit2_ssar     2     2     1 12.037 -0.469  -0.174   -0.339
## 171 tasit2_ssar ~~  tasit3_sar     3     3     1 11.516  0.193   0.193    0.500
## 168 tasit3_lies ~~ tasit2_psar     3     3     1  9.243  0.134   0.134    0.224
## 169 tasit3_lies ~~  tasit3_sar     3     3     1  7.589 -0.103  -0.103   -0.219
## 144 tasit2_psar ~~  tasit3_sar     2     2     1  6.092  0.071   0.071    0.216
## 57  mentalizing =~ tasit2_ssar     3     3     1  5.296  0.271   0.242    0.215
## 119  simulation =~  tasit3_sar     2     2     1  5.207  0.401   0.148    0.200
## 126  er40_total ~~ tasit3_lies     2     2     1  4.483  0.104   0.104    0.163
## 94  mentalizing =~     mean_ea     1     1     1  4.369 -0.823  -0.549   -0.560
##     sepc.nox
## 31    -0.512
## 117   -0.339
## 171    0.500
## 168    0.224
## 169   -0.219
## 144    0.216
## 57     0.215
## 119    0.200
## 126    0.163
## 94    -0.560
      # metric - partial isolating mean_ea
        CFA_sc_model1_grp_fit2_part <- cfa(model= CFA_scog_model1,data = spasd_spins_yj_z_df, group =
                                             "group",group.equal=c("loadings"),estimator = "MLR", missing = "ml",
                                           group.partial = c("simulation=~mean_ea"))
        
        summary(CFA_sc_model1_grp_fit2_part, fit.measures = TRUE, modindices = TRUE, standardized = TRUE, rsquare = TRUE)
## lavaan 0.6.16 ended normally after 84 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
##   Number of equality constraints                     8
## 
##   Number of observations per group:                   
##     ASD                                            100
##     Control                                        209
##     SSD                                            276
##   Number of missing patterns per group:               
##     ASD                                              4
##     Control                                          6
##     SSD                                             20
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                                88.629      87.935
##   Degrees of freedom                                47          47
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.008
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     ASD                                         24.951      24.756
##     Control                                     30.590      30.350
##     SSD                                         33.088      32.829
## 
## Model Test Baseline Model:
## 
##   Test statistic                               973.724     901.247
##   Degrees of freedom                                63          63
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.080
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.954       0.951
##   Tucker-Lewis Index (TLI)                       0.939       0.935
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.942
##   Robust Tucker-Lewis Index (TLI)                            0.922
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4317.003   -4317.003
##   Scaling correction factor                                  1.101
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -4272.688   -4272.688
##   Scaling correction factor                                  1.143
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                                8750.006    8750.006
##   Bayesian (BIC)                              9003.559    9003.559
##   Sample-size adjusted Bayesian (SABIC)       8819.430    8819.430
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.067       0.067
##   90 Percent confidence interval - lower         0.045       0.045
##   90 Percent confidence interval - upper         0.089       0.088
##   P-value H_0: RMSEA <= 0.050                    0.091       0.098
##   P-value H_0: RMSEA >= 0.080                    0.175       0.163
##                                                                   
##   Robust RMSEA                                               0.080
##   90 Percent confidence interval - lower                     0.016
##   90 Percent confidence interval - upper                     0.124
##   P-value H_0: Robust RMSEA <= 0.050                         0.160
##   P-value H_0: Robust RMSEA >= 0.080                         0.523
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.072       0.072
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [ASD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.472    0.473
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.732    0.794
##     mean_ea          -0.220    0.416   -0.528    0.597   -0.104   -0.111
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.398    0.373
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.666    0.759
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.696    0.784
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.668    0.800
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.264    0.088    2.995    0.003    0.839    0.839
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.067    0.101   -0.668    0.504   -0.067   -0.067
##    .rmet_total        0.149    0.093    1.597    0.110    0.149    0.161
##    .mean_ea           0.075    0.229    0.325    0.745    0.075    0.080
##    .tasit3_lies      -0.328    0.105   -3.115    0.002   -0.328   -0.307
##    .tasit2_ssar       0.142    0.090    1.582    0.114    0.142    0.162
##    .tasit2_psar       0.111    0.092    1.209    0.227    0.111    0.125
##    .tasit3_sar        0.290    0.080    3.643    0.000    0.290    0.348
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.775    0.126    6.138    0.000    0.775    0.776
##    .rmet_total        0.315    0.104    3.031    0.002    0.315    0.370
##    .mean_ea           0.855    0.461    1.853    0.064    0.855    0.988
##    .tasit3_lies       0.983    0.154    6.399    0.000    0.983    0.861
##    .tasit2_ssar       0.327    0.085    3.856    0.000    0.327    0.424
##    .tasit2_psar       0.304    0.098    3.115    0.002    0.304    0.386
##    .tasit3_sar        0.250    0.053    4.678    0.000    0.250    0.360
##     simulation        0.223    0.070    3.176    0.001    1.000    1.000
##     mentalizing       0.444    0.135    3.281    0.001    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.224
##     rmet_total        0.630
##     mean_ea           0.012
##     tasit3_lies       0.139
##     tasit2_ssar       0.576
##     tasit2_psar       0.614
##     tasit3_sar        0.640
## 
## 
## Group 2 [Control]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.370    0.421
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.573    0.699
##     mean_ea           0.720    0.637    1.130    0.258    0.266    0.227
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.312    0.361
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.358    0.699
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.374    0.598
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.359    0.484
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.079    0.026    3.076    0.002    0.597    0.597
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.255    0.060    4.221    0.000    0.255    0.290
##    .rmet_total        0.333    0.057    5.842    0.000    0.333    0.407
##    .mean_ea           0.681    0.197    3.466    0.001    0.681    0.582
##    .tasit3_lies       0.373    0.060    6.227    0.000    0.373    0.433
##    .tasit2_ssar       0.468    0.033   13.971    0.000    0.468    0.912
##    .tasit2_psar       0.424    0.045    9.443    0.000    0.424    0.677
##    .tasit3_sar        0.419    0.053    7.875    0.000    0.419    0.564
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.634    0.073    8.671    0.000    0.634    0.823
##    .rmet_total        0.343    0.069    4.970    0.000    0.343    0.511
##    .mean_ea           1.297    0.299    4.340    0.000    1.297    0.948
##    .tasit3_lies       0.646    0.103    6.270    0.000    0.646    0.869
##    .tasit2_ssar       0.134    0.021    6.510    0.000    0.134    0.511
##    .tasit2_psar       0.251    0.049    5.141    0.000    0.251    0.642
##    .tasit3_sar        0.422    0.087    4.841    0.000    0.422    0.766
##     simulation        0.137    0.039    3.522    0.000    1.000    1.000
##     mentalizing       0.128    0.035    3.618    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.177
##     rmet_total        0.489
##     mean_ea           0.052
##     tasit3_lies       0.131
##     tasit2_ssar       0.489
##     tasit2_psar       0.358
##     tasit3_sar        0.234
## 
## 
## Group 3 [SSD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.608    0.579
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.943    0.881
##     mean_ea           0.358    0.138    2.583    0.010    0.218    0.269
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.513    0.521
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.892    0.794
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.932    0.794
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.894    0.846
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.373    0.063    5.916    0.000    0.687    0.687
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.199    0.065   -3.048    0.002   -0.199   -0.189
##    .rmet_total       -0.338    0.065   -5.202    0.000   -0.338   -0.315
##    .mean_ea          -0.198    0.085   -2.335    0.020   -0.198   -0.244
##    .tasit3_lies      -0.170    0.060   -2.839    0.005   -0.170   -0.172
##    .tasit2_ssar      -0.445    0.070   -6.326    0.000   -0.445   -0.396
##    .tasit2_psar      -0.429    0.070   -6.138    0.000   -0.429   -0.365
##    .tasit3_sar       -0.462    0.064   -7.189    0.000   -0.462   -0.438
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.736    0.097    7.611    0.000    0.736    0.665
##    .rmet_total        0.256    0.076    3.358    0.001    0.256    0.223
##    .mean_ea           0.609    0.125    4.870    0.000    0.609    0.928
##    .tasit3_lies       0.706    0.059   12.047    0.000    0.706    0.728
##    .tasit2_ssar       0.468    0.058    8.103    0.000    0.468    0.370
##    .tasit2_psar       0.510    0.062    8.197    0.000    0.510    0.370
##    .tasit3_sar        0.317    0.047    6.733    0.000    0.317    0.284
##     simulation        0.370    0.086    4.316    0.000    1.000    1.000
##     mentalizing       0.796    0.111    7.176    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.335
##     rmet_total        0.777
##     mean_ea           0.072
##     tasit3_lies       0.272
##     tasit2_ssar       0.630
##     tasit2_psar       0.630
##     tasit3_sar        0.716
## 
## Modification Indices:
## 
##            lhs op         rhs block group level     mi    epc sepc.lv sepc.all
## 1   simulation =~  er40_total     1     1     1  0.101 -0.086  -0.041   -0.041
## 2  mentalizing =~ tasit2_ssar     1     1     1  0.118  0.046   0.031    0.035
## 3   simulation =~  er40_total     2     2     1  0.517 -0.198  -0.073   -0.083
## 4  mentalizing =~ tasit2_ssar     2     2     1 16.216 -0.729  -0.261   -0.510
## 5   simulation =~  er40_total     3     3     1  0.645  0.171   0.104    0.099
## 6  mentalizing =~ tasit2_ssar     3     3     1  5.362  0.273   0.243    0.216
## 7   simulation =~ tasit2_ssar     1     1     1  0.056 -0.044  -0.021   -0.023
## 8   simulation =~ tasit2_psar     1     1     1  1.673  0.240   0.114    0.128
## 9   simulation =~  tasit3_sar     1     1     1  1.078 -0.180  -0.085   -0.102
## 10 mentalizing =~  er40_total     1     1     1  0.010  0.017   0.012    0.012
## 11 mentalizing =~  rmet_total     1     1     1  0.303  0.123   0.082    0.089
## 12 mentalizing =~     mean_ea     1     1     1  1.893 -1.439  -0.959   -1.031
## 13 mentalizing =~ tasit3_lies     1     1     1  1.002 -0.179  -0.120   -0.112
## 14  er40_total ~~  rmet_total     1     1     1  1.146 -0.111  -0.111   -0.226
## 15  er40_total ~~     mean_ea     1     1     1  3.540  0.388   0.388    0.477
## 16  er40_total ~~ tasit3_lies     1     1     1  0.333 -0.054  -0.054   -0.062
## 17  er40_total ~~ tasit2_ssar     1     1     1  0.059 -0.015  -0.015   -0.029
## 18  er40_total ~~ tasit2_psar     1     1     1  0.431 -0.039  -0.039   -0.081
## 19  er40_total ~~  tasit3_sar     1     1     1  2.890  0.095   0.095    0.216
## 20  rmet_total ~~     mean_ea     1     1     1  0.028 -0.029  -0.029   -0.056
## 21  rmet_total ~~ tasit3_lies     1     1     1  2.585  0.142   0.142    0.256
## 22  rmet_total ~~ tasit2_ssar     1     1     1  0.933 -0.049  -0.049   -0.151
## 23  rmet_total ~~ tasit2_psar     1     1     1  0.357  0.030   0.030    0.098
## 24  rmet_total ~~  tasit3_sar     1     1     1  0.194  0.021   0.021    0.074
## 25     mean_ea ~~ tasit3_lies     1     1     1  1.299  0.260   0.260    0.283
## 26     mean_ea ~~ tasit2_ssar     1     1     1  0.374  0.091   0.091    0.173
## 27     mean_ea ~~ tasit2_psar     1     1     1  1.246 -0.160  -0.160   -0.314
## 28     mean_ea ~~  tasit3_sar     1     1     1  0.634 -0.106  -0.106   -0.229
## 29 tasit3_lies ~~ tasit2_ssar     1     1     1  0.380 -0.041  -0.041   -0.072
## 30 tasit3_lies ~~ tasit2_psar     1     1     1  0.832  0.059   0.059    0.108
## 31 tasit3_lies ~~  tasit3_sar     1     1     1  3.317 -0.110  -0.110   -0.221
## 32 tasit2_ssar ~~ tasit2_psar     1     1     1  3.838  0.100   0.100    0.317
## 33 tasit2_ssar ~~  tasit3_sar     1     1     1  0.193 -0.021  -0.021   -0.075
## 34 tasit2_psar ~~  tasit3_sar     1     1     1  2.290 -0.077  -0.077   -0.279
## 35  simulation =~ tasit2_ssar     2     2     1 11.923 -0.467  -0.173   -0.337
## 36  simulation =~ tasit2_psar     2     2     1  3.325  0.277   0.102    0.164
## 37  simulation =~  tasit3_sar     2     2     1  5.191  0.401   0.148    0.199
## 38 mentalizing =~  er40_total     2     2     1  1.942 -0.306  -0.110   -0.125
## 39 mentalizing =~  rmet_total     2     2     1  2.038  0.403   0.144    0.176
## 40 mentalizing =~     mean_ea     2     2     1  0.002 -0.041  -0.015   -0.013
## 41 mentalizing =~ tasit3_lies     2     2     1  0.139 -0.080  -0.029   -0.033
## 42  er40_total ~~  rmet_total     2     2     1  0.545 -0.048  -0.048   -0.102
## 43  er40_total ~~     mean_ea     2     2     1  0.859 -0.150  -0.150   -0.165
## 44  er40_total ~~ tasit3_lies     2     2     1  4.583  0.106   0.106    0.165
## 45  er40_total ~~ tasit2_ssar     2     2     1  1.637 -0.034  -0.034   -0.116
## 46  er40_total ~~ tasit2_psar     2     2     1  2.983 -0.056  -0.056   -0.141
## 47  er40_total ~~  tasit3_sar     2     2     1  3.249  0.072   0.072    0.139
## 48  rmet_total ~~     mean_ea     2     2     1  1.302  0.197   0.197    0.295
## 49  rmet_total ~~ tasit3_lies     2     2     1  0.643 -0.044  -0.044   -0.093
## 50  rmet_total ~~ tasit2_ssar     2     2     1  1.807 -0.035  -0.035   -0.162
## 51  rmet_total ~~ tasit2_psar     2     2     1  4.264  0.063   0.063    0.214
## 52  rmet_total ~~  tasit3_sar     2     2     1  1.361  0.042   0.042    0.111
## 53     mean_ea ~~ tasit3_lies     2     2     1  0.632 -0.125  -0.125   -0.137
## 54     mean_ea ~~ tasit2_ssar     2     2     1  0.066  0.022   0.022    0.052
## 55     mean_ea ~~ tasit2_psar     2     2     1  0.163 -0.042  -0.042   -0.074
## 56     mean_ea ~~  tasit3_sar     2     2     1  0.003  0.008   0.008    0.010
## 57 tasit3_lies ~~ tasit2_ssar     2     2     1  0.059 -0.006  -0.006   -0.021
## 58 tasit3_lies ~~ tasit2_psar     2     2     1  0.042  0.007   0.007    0.016
## 59 tasit3_lies ~~  tasit3_sar     2     2     1  0.716 -0.033  -0.033   -0.064
## 60 tasit2_ssar ~~ tasit2_psar     2     2     1  0.556 -0.019  -0.019   -0.104
## 61 tasit2_ssar ~~  tasit3_sar     2     2     1  2.261 -0.038  -0.038   -0.158
## 62 tasit2_psar ~~  tasit3_sar     2     2     1  6.079  0.070   0.070    0.216
## 63  simulation =~ tasit2_ssar     3     3     1  0.813  0.110   0.067    0.060
## 64  simulation =~ tasit2_psar     3     3     1  0.153  0.050   0.030    0.026
## 65  simulation =~  tasit3_sar     3     3     1  1.495 -0.141  -0.086   -0.081
## 66 mentalizing =~  er40_total     3     3     1  0.028  0.016   0.015    0.014
## 67 mentalizing =~  rmet_total     3     3     1  0.008 -0.012  -0.011   -0.010
## 68 mentalizing =~     mean_ea     3     3     1  0.008  0.013   0.012    0.015
## 69 mentalizing =~ tasit3_lies     3     3     1  0.009 -0.009  -0.008   -0.008
## 70  er40_total ~~  rmet_total     3     3     1  0.541 -0.059  -0.059   -0.136
## 71  er40_total ~~     mean_ea     3     3     1  1.638  0.096   0.096    0.144
## 72  er40_total ~~ tasit3_lies     3     3     1  2.107  0.076   0.076    0.106
## 73  er40_total ~~ tasit2_ssar     3     3     1  1.913  0.061   0.061    0.104
## 74  er40_total ~~ tasit2_psar     3     3     1  0.200 -0.021  -0.021   -0.034
## 75  er40_total ~~  tasit3_sar     3     3     1  1.082 -0.041  -0.041   -0.086
## 76  rmet_total ~~     mean_ea     3     3     1  0.005 -0.005  -0.005   -0.013
## 77  rmet_total ~~ tasit3_lies     3     3     1  0.195 -0.029  -0.029   -0.069
## 78  rmet_total ~~ tasit2_ssar     3     3     1  0.460 -0.027  -0.027   -0.079
## 79  rmet_total ~~ tasit2_psar     3     3     1  0.045  0.009   0.009    0.025
## 80  rmet_total ~~  tasit3_sar     3     3     1  0.438  0.025   0.025    0.086
## 81     mean_ea ~~ tasit3_lies     3     3     1  1.989 -0.099  -0.099   -0.151
## 82     mean_ea ~~ tasit2_ssar     3     3     1  3.239 -0.111  -0.111   -0.209
## 83     mean_ea ~~ tasit2_psar     3     3     1  3.280  0.119   0.119    0.214
## 84     mean_ea ~~  tasit3_sar     3     3     1  0.009  0.005   0.005    0.012
## 85 tasit3_lies ~~ tasit2_ssar     3     3     1  0.039 -0.008  -0.008   -0.014
## 86 tasit3_lies ~~ tasit2_psar     3     3     1  9.240  0.134   0.134    0.223
## 87 tasit3_lies ~~  tasit3_sar     3     3     1  7.565 -0.103  -0.103   -0.218
## 88 tasit2_ssar ~~ tasit2_psar     3     3     1  2.978 -0.101  -0.101   -0.206
## 89 tasit2_ssar ~~  tasit3_sar     3     3     1 11.575  0.193   0.193    0.501
## 90 tasit2_psar ~~  tasit3_sar     3     3     1  2.733 -0.098  -0.098   -0.244
##    sepc.nox
## 1    -0.041
## 2     0.035
## 3    -0.083
## 4    -0.510
## 5     0.099
## 6     0.216
## 7    -0.023
## 8     0.128
## 9    -0.102
## 10    0.012
## 11    0.089
## 12   -1.031
## 13   -0.112
## 14   -0.226
## 15    0.477
## 16   -0.062
## 17   -0.029
## 18   -0.081
## 19    0.216
## 20   -0.056
## 21    0.256
## 22   -0.151
## 23    0.098
## 24    0.074
## 25    0.283
## 26    0.173
## 27   -0.314
## 28   -0.229
## 29   -0.072
## 30    0.108
## 31   -0.221
## 32    0.317
## 33   -0.075
## 34   -0.279
## 35   -0.337
## 36    0.164
## 37    0.199
## 38   -0.125
## 39    0.176
## 40   -0.013
## 41   -0.033
## 42   -0.102
## 43   -0.165
## 44    0.165
## 45   -0.116
## 46   -0.141
## 47    0.139
## 48    0.295
## 49   -0.093
## 50   -0.162
## 51    0.214
## 52    0.111
## 53   -0.137
## 54    0.052
## 55   -0.074
## 56    0.010
## 57   -0.021
## 58    0.016
## 59   -0.064
## 60   -0.104
## 61   -0.158
## 62    0.216
## 63    0.060
## 64    0.026
## 65   -0.081
## 66    0.014
## 67   -0.010
## 68    0.015
## 69   -0.008
## 70   -0.136
## 71    0.144
## 72    0.106
## 73    0.104
## 74   -0.034
## 75   -0.086
## 76   -0.013
## 77   -0.069
## 78   -0.079
## 79    0.025
## 80    0.086
## 81   -0.151
## 82   -0.209
## 83    0.214
## 84    0.012
## 85   -0.014
## 86    0.223
## 87   -0.218
## 88   -0.206
## 89    0.501
## 90   -0.244
        anova(CFA_scog_model1_grp_fit,CFA_sc_model1_grp_fit2_part) # sig 
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## 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
## CFA_scog_model1_grp_fit     39 8746.2 9034.8 68.870                   
## CFA_sc_model1_grp_fit2_part 47 8750.0 9003.6 88.629     16.963       8
##                             Pr(>Chisq)  
## CFA_scog_model1_grp_fit                 
## CFA_sc_model1_grp_fit2_part     0.0305 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
      # metric - partial isolating mean ea and tasit2_ssar (according to mod indices from above)
      
        CFA_sc_model1_grp_fit2_part2 <- cfa(model= CFA_scog_model1,data = spasd_spins_yj_z_df,group = "group",
                                            group.equal=c("loadings"),estimator = "MLR", missing = "ml",
                                            group.partial = c("simulation=~mean_ea","mentalizing=~tasit2_ssar"))
        
        summary(CFA_sc_model1_grp_fit2_part2, fit.measures = TRUE, modindices = TRUE, standardized = TRUE, rsquare = TRUE)
## lavaan 0.6.16 ended normally after 84 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
##   Number of equality constraints                     8
## 
##   Number of observations per group:                   
##     ASD                                            100
##     Control                                        209
##     SSD                                            276
##   Number of missing patterns per group:               
##     ASD                                              4
##     Control                                          6
##     SSD                                             20
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                                88.629      87.935
##   Degrees of freedom                                47          47
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.008
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     ASD                                         24.951      24.756
##     Control                                     30.590      30.350
##     SSD                                         33.088      32.829
## 
## Model Test Baseline Model:
## 
##   Test statistic                               973.724     901.247
##   Degrees of freedom                                63          63
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.080
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.954       0.951
##   Tucker-Lewis Index (TLI)                       0.939       0.935
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.942
##   Robust Tucker-Lewis Index (TLI)                            0.922
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4317.003   -4317.003
##   Scaling correction factor                                  1.101
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -4272.688   -4272.688
##   Scaling correction factor                                  1.143
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                                8750.006    8750.006
##   Bayesian (BIC)                              9003.559    9003.559
##   Sample-size adjusted Bayesian (SABIC)       8819.430    8819.430
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.067       0.067
##   90 Percent confidence interval - lower         0.045       0.045
##   90 Percent confidence interval - upper         0.089       0.088
##   P-value H_0: RMSEA <= 0.050                    0.091       0.098
##   P-value H_0: RMSEA >= 0.080                    0.175       0.163
##                                                                   
##   Robust RMSEA                                               0.080
##   90 Percent confidence interval - lower                     0.016
##   90 Percent confidence interval - upper                     0.124
##   P-value H_0: Robust RMSEA <= 0.050                         0.160
##   P-value H_0: Robust RMSEA >= 0.080                         0.523
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.072       0.072
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [ASD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.472    0.473
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.732    0.794
##     mean_ea          -0.220    0.416   -0.528    0.597   -0.104   -0.111
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.398    0.373
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.666    0.759
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.696    0.784
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.668    0.800
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.264    0.088    2.995    0.003    0.839    0.839
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.067    0.101   -0.668    0.504   -0.067   -0.067
##    .rmet_total        0.149    0.093    1.597    0.110    0.149    0.161
##    .mean_ea           0.075    0.229    0.325    0.745    0.075    0.080
##    .tasit3_lies      -0.328    0.105   -3.115    0.002   -0.328   -0.307
##    .tasit2_ssar       0.142    0.090    1.582    0.114    0.142    0.162
##    .tasit2_psar       0.111    0.092    1.209    0.227    0.111    0.125
##    .tasit3_sar        0.290    0.080    3.643    0.000    0.290    0.348
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.775    0.126    6.138    0.000    0.775    0.776
##    .rmet_total        0.315    0.104    3.031    0.002    0.315    0.370
##    .mean_ea           0.855    0.461    1.853    0.064    0.855    0.988
##    .tasit3_lies       0.983    0.154    6.399    0.000    0.983    0.861
##    .tasit2_ssar       0.327    0.085    3.856    0.000    0.327    0.424
##    .tasit2_psar       0.304    0.098    3.115    0.002    0.304    0.386
##    .tasit3_sar        0.250    0.053    4.678    0.000    0.250    0.360
##     simulation        0.223    0.070    3.176    0.001    1.000    1.000
##     mentalizing       0.444    0.135    3.281    0.001    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.224
##     rmet_total        0.630
##     mean_ea           0.012
##     tasit3_lies       0.139
##     tasit2_ssar       0.576
##     tasit2_psar       0.614
##     tasit3_sar        0.640
## 
## 
## Group 2 [Control]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.370    0.421
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.573    0.699
##     mean_ea           0.720    0.637    1.130    0.258    0.266    0.227
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.312    0.361
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.358    0.699
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.374    0.598
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.359    0.484
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.079    0.026    3.076    0.002    0.597    0.597
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.255    0.060    4.221    0.000    0.255    0.290
##    .rmet_total        0.333    0.057    5.842    0.000    0.333    0.407
##    .mean_ea           0.681    0.197    3.466    0.001    0.681    0.582
##    .tasit3_lies       0.373    0.060    6.227    0.000    0.373    0.433
##    .tasit2_ssar       0.468    0.033   13.971    0.000    0.468    0.912
##    .tasit2_psar       0.424    0.045    9.443    0.000    0.424    0.677
##    .tasit3_sar        0.419    0.053    7.875    0.000    0.419    0.564
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.634    0.073    8.671    0.000    0.634    0.823
##    .rmet_total        0.343    0.069    4.970    0.000    0.343    0.511
##    .mean_ea           1.297    0.299    4.340    0.000    1.297    0.948
##    .tasit3_lies       0.646    0.103    6.270    0.000    0.646    0.869
##    .tasit2_ssar       0.134    0.021    6.510    0.000    0.134    0.511
##    .tasit2_psar       0.251    0.049    5.141    0.000    0.251    0.642
##    .tasit3_sar        0.422    0.087    4.841    0.000    0.422    0.766
##     simulation        0.137    0.039    3.522    0.000    1.000    1.000
##     mentalizing       0.128    0.035    3.618    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.177
##     rmet_total        0.489
##     mean_ea           0.052
##     tasit3_lies       0.131
##     tasit2_ssar       0.489
##     tasit2_psar       0.358
##     tasit3_sar        0.234
## 
## 
## Group 3 [SSD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.608    0.579
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.943    0.881
##     mean_ea           0.358    0.138    2.583    0.010    0.218    0.269
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.513    0.521
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.892    0.794
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.932    0.794
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.894    0.846
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.373    0.063    5.916    0.000    0.687    0.687
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.199    0.065   -3.048    0.002   -0.199   -0.189
##    .rmet_total       -0.338    0.065   -5.202    0.000   -0.338   -0.315
##    .mean_ea          -0.198    0.085   -2.335    0.020   -0.198   -0.244
##    .tasit3_lies      -0.170    0.060   -2.839    0.005   -0.170   -0.172
##    .tasit2_ssar      -0.445    0.070   -6.326    0.000   -0.445   -0.396
##    .tasit2_psar      -0.429    0.070   -6.138    0.000   -0.429   -0.365
##    .tasit3_sar       -0.462    0.064   -7.189    0.000   -0.462   -0.438
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.736    0.097    7.611    0.000    0.736    0.665
##    .rmet_total        0.256    0.076    3.358    0.001    0.256    0.223
##    .mean_ea           0.609    0.125    4.870    0.000    0.609    0.928
##    .tasit3_lies       0.706    0.059   12.047    0.000    0.706    0.728
##    .tasit2_ssar       0.468    0.058    8.103    0.000    0.468    0.370
##    .tasit2_psar       0.510    0.062    8.197    0.000    0.510    0.370
##    .tasit3_sar        0.317    0.047    6.733    0.000    0.317    0.284
##     simulation        0.370    0.086    4.316    0.000    1.000    1.000
##     mentalizing       0.796    0.111    7.176    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.335
##     rmet_total        0.777
##     mean_ea           0.072
##     tasit3_lies       0.272
##     tasit2_ssar       0.630
##     tasit2_psar       0.630
##     tasit3_sar        0.716
## 
## Modification Indices:
## 
##            lhs op         rhs block group level     mi    epc sepc.lv sepc.all
## 1   simulation =~  er40_total     1     1     1  0.101 -0.086  -0.041   -0.041
## 2  mentalizing =~ tasit2_ssar     1     1     1  0.118  0.046   0.031    0.035
## 3   simulation =~  er40_total     2     2     1  0.517 -0.198  -0.073   -0.083
## 4  mentalizing =~ tasit2_ssar     2     2     1 16.216 -0.729  -0.261   -0.510
## 5   simulation =~  er40_total     3     3     1  0.645  0.171   0.104    0.099
## 6  mentalizing =~ tasit2_ssar     3     3     1  5.362  0.273   0.243    0.216
## 7   simulation =~ tasit2_ssar     1     1     1  0.056 -0.044  -0.021   -0.023
## 8   simulation =~ tasit2_psar     1     1     1  1.673  0.240   0.114    0.128
## 9   simulation =~  tasit3_sar     1     1     1  1.078 -0.180  -0.085   -0.102
## 10 mentalizing =~  er40_total     1     1     1  0.010  0.017   0.012    0.012
## 11 mentalizing =~  rmet_total     1     1     1  0.303  0.123   0.082    0.089
## 12 mentalizing =~     mean_ea     1     1     1  1.893 -1.439  -0.959   -1.031
## 13 mentalizing =~ tasit3_lies     1     1     1  1.002 -0.179  -0.120   -0.112
## 14  er40_total ~~  rmet_total     1     1     1  1.146 -0.111  -0.111   -0.226
## 15  er40_total ~~     mean_ea     1     1     1  3.540  0.388   0.388    0.477
## 16  er40_total ~~ tasit3_lies     1     1     1  0.333 -0.054  -0.054   -0.062
## 17  er40_total ~~ tasit2_ssar     1     1     1  0.059 -0.015  -0.015   -0.029
## 18  er40_total ~~ tasit2_psar     1     1     1  0.431 -0.039  -0.039   -0.081
## 19  er40_total ~~  tasit3_sar     1     1     1  2.890  0.095   0.095    0.216
## 20  rmet_total ~~     mean_ea     1     1     1  0.028 -0.029  -0.029   -0.056
## 21  rmet_total ~~ tasit3_lies     1     1     1  2.585  0.142   0.142    0.256
## 22  rmet_total ~~ tasit2_ssar     1     1     1  0.933 -0.049  -0.049   -0.151
## 23  rmet_total ~~ tasit2_psar     1     1     1  0.357  0.030   0.030    0.098
## 24  rmet_total ~~  tasit3_sar     1     1     1  0.194  0.021   0.021    0.074
## 25     mean_ea ~~ tasit3_lies     1     1     1  1.299  0.260   0.260    0.283
## 26     mean_ea ~~ tasit2_ssar     1     1     1  0.374  0.091   0.091    0.173
## 27     mean_ea ~~ tasit2_psar     1     1     1  1.246 -0.160  -0.160   -0.314
## 28     mean_ea ~~  tasit3_sar     1     1     1  0.634 -0.106  -0.106   -0.229
## 29 tasit3_lies ~~ tasit2_ssar     1     1     1  0.380 -0.041  -0.041   -0.072
## 30 tasit3_lies ~~ tasit2_psar     1     1     1  0.832  0.059   0.059    0.108
## 31 tasit3_lies ~~  tasit3_sar     1     1     1  3.317 -0.110  -0.110   -0.221
## 32 tasit2_ssar ~~ tasit2_psar     1     1     1  3.838  0.100   0.100    0.317
## 33 tasit2_ssar ~~  tasit3_sar     1     1     1  0.193 -0.021  -0.021   -0.075
## 34 tasit2_psar ~~  tasit3_sar     1     1     1  2.290 -0.077  -0.077   -0.279
## 35  simulation =~ tasit2_ssar     2     2     1 11.923 -0.467  -0.173   -0.337
## 36  simulation =~ tasit2_psar     2     2     1  3.325  0.277   0.102    0.164
## 37  simulation =~  tasit3_sar     2     2     1  5.191  0.401   0.148    0.199
## 38 mentalizing =~  er40_total     2     2     1  1.942 -0.306  -0.110   -0.125
## 39 mentalizing =~  rmet_total     2     2     1  2.038  0.403   0.144    0.176
## 40 mentalizing =~     mean_ea     2     2     1  0.002 -0.041  -0.015   -0.013
## 41 mentalizing =~ tasit3_lies     2     2     1  0.139 -0.080  -0.029   -0.033
## 42  er40_total ~~  rmet_total     2     2     1  0.545 -0.048  -0.048   -0.102
## 43  er40_total ~~     mean_ea     2     2     1  0.859 -0.150  -0.150   -0.165
## 44  er40_total ~~ tasit3_lies     2     2     1  4.583  0.106   0.106    0.165
## 45  er40_total ~~ tasit2_ssar     2     2     1  1.637 -0.034  -0.034   -0.116
## 46  er40_total ~~ tasit2_psar     2     2     1  2.983 -0.056  -0.056   -0.141
## 47  er40_total ~~  tasit3_sar     2     2     1  3.249  0.072   0.072    0.139
## 48  rmet_total ~~     mean_ea     2     2     1  1.302  0.197   0.197    0.295
## 49  rmet_total ~~ tasit3_lies     2     2     1  0.643 -0.044  -0.044   -0.093
## 50  rmet_total ~~ tasit2_ssar     2     2     1  1.807 -0.035  -0.035   -0.162
## 51  rmet_total ~~ tasit2_psar     2     2     1  4.264  0.063   0.063    0.214
## 52  rmet_total ~~  tasit3_sar     2     2     1  1.361  0.042   0.042    0.111
## 53     mean_ea ~~ tasit3_lies     2     2     1  0.632 -0.125  -0.125   -0.137
## 54     mean_ea ~~ tasit2_ssar     2     2     1  0.066  0.022   0.022    0.052
## 55     mean_ea ~~ tasit2_psar     2     2     1  0.163 -0.042  -0.042   -0.074
## 56     mean_ea ~~  tasit3_sar     2     2     1  0.003  0.008   0.008    0.010
## 57 tasit3_lies ~~ tasit2_ssar     2     2     1  0.059 -0.006  -0.006   -0.021
## 58 tasit3_lies ~~ tasit2_psar     2     2     1  0.042  0.007   0.007    0.016
## 59 tasit3_lies ~~  tasit3_sar     2     2     1  0.716 -0.033  -0.033   -0.064
## 60 tasit2_ssar ~~ tasit2_psar     2     2     1  0.556 -0.019  -0.019   -0.104
## 61 tasit2_ssar ~~  tasit3_sar     2     2     1  2.261 -0.038  -0.038   -0.158
## 62 tasit2_psar ~~  tasit3_sar     2     2     1  6.079  0.070   0.070    0.216
## 63  simulation =~ tasit2_ssar     3     3     1  0.813  0.110   0.067    0.060
## 64  simulation =~ tasit2_psar     3     3     1  0.153  0.050   0.030    0.026
## 65  simulation =~  tasit3_sar     3     3     1  1.495 -0.141  -0.086   -0.081
## 66 mentalizing =~  er40_total     3     3     1  0.028  0.016   0.015    0.014
## 67 mentalizing =~  rmet_total     3     3     1  0.008 -0.012  -0.011   -0.010
## 68 mentalizing =~     mean_ea     3     3     1  0.008  0.013   0.012    0.015
## 69 mentalizing =~ tasit3_lies     3     3     1  0.009 -0.009  -0.008   -0.008
## 70  er40_total ~~  rmet_total     3     3     1  0.541 -0.059  -0.059   -0.136
## 71  er40_total ~~     mean_ea     3     3     1  1.638  0.096   0.096    0.144
## 72  er40_total ~~ tasit3_lies     3     3     1  2.107  0.076   0.076    0.106
## 73  er40_total ~~ tasit2_ssar     3     3     1  1.913  0.061   0.061    0.104
## 74  er40_total ~~ tasit2_psar     3     3     1  0.200 -0.021  -0.021   -0.034
## 75  er40_total ~~  tasit3_sar     3     3     1  1.082 -0.041  -0.041   -0.086
## 76  rmet_total ~~     mean_ea     3     3     1  0.005 -0.005  -0.005   -0.013
## 77  rmet_total ~~ tasit3_lies     3     3     1  0.195 -0.029  -0.029   -0.069
## 78  rmet_total ~~ tasit2_ssar     3     3     1  0.460 -0.027  -0.027   -0.079
## 79  rmet_total ~~ tasit2_psar     3     3     1  0.045  0.009   0.009    0.025
## 80  rmet_total ~~  tasit3_sar     3     3     1  0.438  0.025   0.025    0.086
## 81     mean_ea ~~ tasit3_lies     3     3     1  1.989 -0.099  -0.099   -0.151
## 82     mean_ea ~~ tasit2_ssar     3     3     1  3.239 -0.111  -0.111   -0.209
## 83     mean_ea ~~ tasit2_psar     3     3     1  3.280  0.119   0.119    0.214
## 84     mean_ea ~~  tasit3_sar     3     3     1  0.009  0.005   0.005    0.012
## 85 tasit3_lies ~~ tasit2_ssar     3     3     1  0.039 -0.008  -0.008   -0.014
## 86 tasit3_lies ~~ tasit2_psar     3     3     1  9.240  0.134   0.134    0.223
## 87 tasit3_lies ~~  tasit3_sar     3     3     1  7.565 -0.103  -0.103   -0.218
## 88 tasit2_ssar ~~ tasit2_psar     3     3     1  2.978 -0.101  -0.101   -0.206
## 89 tasit2_ssar ~~  tasit3_sar     3     3     1 11.575  0.193   0.193    0.501
## 90 tasit2_psar ~~  tasit3_sar     3     3     1  2.733 -0.098  -0.098   -0.244
##    sepc.nox
## 1    -0.041
## 2     0.035
## 3    -0.083
## 4    -0.510
## 5     0.099
## 6     0.216
## 7    -0.023
## 8     0.128
## 9    -0.102
## 10    0.012
## 11    0.089
## 12   -1.031
## 13   -0.112
## 14   -0.226
## 15    0.477
## 16   -0.062
## 17   -0.029
## 18   -0.081
## 19    0.216
## 20   -0.056
## 21    0.256
## 22   -0.151
## 23    0.098
## 24    0.074
## 25    0.283
## 26    0.173
## 27   -0.314
## 28   -0.229
## 29   -0.072
## 30    0.108
## 31   -0.221
## 32    0.317
## 33   -0.075
## 34   -0.279
## 35   -0.337
## 36    0.164
## 37    0.199
## 38   -0.125
## 39    0.176
## 40   -0.013
## 41   -0.033
## 42   -0.102
## 43   -0.165
## 44    0.165
## 45   -0.116
## 46   -0.141
## 47    0.139
## 48    0.295
## 49   -0.093
## 50   -0.162
## 51    0.214
## 52    0.111
## 53   -0.137
## 54    0.052
## 55   -0.074
## 56    0.010
## 57   -0.021
## 58    0.016
## 59   -0.064
## 60   -0.104
## 61   -0.158
## 62    0.216
## 63    0.060
## 64    0.026
## 65   -0.081
## 66    0.014
## 67   -0.010
## 68    0.015
## 69   -0.008
## 70   -0.136
## 71    0.144
## 72    0.106
## 73    0.104
## 74   -0.034
## 75   -0.086
## 76   -0.013
## 77   -0.069
## 78   -0.079
## 79    0.025
## 80    0.086
## 81   -0.151
## 82   -0.209
## 83    0.214
## 84    0.012
## 85   -0.014
## 86    0.223
## 87   -0.218
## 88   -0.206
## 89    0.501
## 90   -0.244
        anova(CFA_scog_model1_grp_fit,CFA_sc_model1_grp_fit2_part2)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## 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
## CFA_scog_model1_grp_fit      39 8746.2 9034.8 68.870                   
## CFA_sc_model1_grp_fit2_part2 47 8750.0 9003.6 88.629     16.963       8
##                              Pr(>Chisq)  
## CFA_scog_model1_grp_fit                  
## CFA_sc_model1_grp_fit2_part2     0.0305 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
      # metric - partial isolating mean ea, tasit2_ssar, tasit3_psar (according to mod indices from above)
      
      
        CFA_sc_model1_grp_fit2_part3 <- cfa(model= CFA_scog_model1,data = spasd_spins_yj_z_df, group ="group",
                                            group.equal=c("loadings"),estimator = "MLR", missing = "ml",
                                            group.partial=
                                          c("simulation=~mean_ea","mentalizing=~tasit2_ssar","mentalizing=~tasit3_psar"))
        
        
        summary(CFA_sc_model1_grp_fit2_part3, fit.measures = TRUE, modindices = TRUE, standardized = TRUE, rsquare = TRUE)
## lavaan 0.6.16 ended normally after 84 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
##   Number of equality constraints                     8
## 
##   Number of observations per group:                   
##     ASD                                            100
##     Control                                        209
##     SSD                                            276
##   Number of missing patterns per group:               
##     ASD                                              4
##     Control                                          6
##     SSD                                             20
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                                88.629      87.935
##   Degrees of freedom                                47          47
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.008
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     ASD                                         24.951      24.756
##     Control                                     30.590      30.350
##     SSD                                         33.088      32.829
## 
## Model Test Baseline Model:
## 
##   Test statistic                               973.724     901.247
##   Degrees of freedom                                63          63
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.080
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.954       0.951
##   Tucker-Lewis Index (TLI)                       0.939       0.935
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.942
##   Robust Tucker-Lewis Index (TLI)                            0.922
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4317.003   -4317.003
##   Scaling correction factor                                  1.101
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -4272.688   -4272.688
##   Scaling correction factor                                  1.143
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                                8750.006    8750.006
##   Bayesian (BIC)                              9003.559    9003.559
##   Sample-size adjusted Bayesian (SABIC)       8819.430    8819.430
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.067       0.067
##   90 Percent confidence interval - lower         0.045       0.045
##   90 Percent confidence interval - upper         0.089       0.088
##   P-value H_0: RMSEA <= 0.050                    0.091       0.098
##   P-value H_0: RMSEA >= 0.080                    0.175       0.163
##                                                                   
##   Robust RMSEA                                               0.080
##   90 Percent confidence interval - lower                     0.016
##   90 Percent confidence interval - upper                     0.124
##   P-value H_0: Robust RMSEA <= 0.050                         0.160
##   P-value H_0: Robust RMSEA >= 0.080                         0.523
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.072       0.072
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [ASD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.472    0.473
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.732    0.794
##     mean_ea          -0.220    0.416   -0.528    0.597   -0.104   -0.111
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.398    0.373
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.666    0.759
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.696    0.784
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.668    0.800
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.264    0.088    2.995    0.003    0.839    0.839
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.067    0.101   -0.668    0.504   -0.067   -0.067
##    .rmet_total        0.149    0.093    1.597    0.110    0.149    0.161
##    .mean_ea           0.075    0.229    0.325    0.745    0.075    0.080
##    .tasit3_lies      -0.328    0.105   -3.115    0.002   -0.328   -0.307
##    .tasit2_ssar       0.142    0.090    1.582    0.114    0.142    0.162
##    .tasit2_psar       0.111    0.092    1.209    0.227    0.111    0.125
##    .tasit3_sar        0.290    0.080    3.643    0.000    0.290    0.348
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.775    0.126    6.138    0.000    0.775    0.776
##    .rmet_total        0.315    0.104    3.031    0.002    0.315    0.370
##    .mean_ea           0.855    0.461    1.853    0.064    0.855    0.988
##    .tasit3_lies       0.983    0.154    6.399    0.000    0.983    0.861
##    .tasit2_ssar       0.327    0.085    3.856    0.000    0.327    0.424
##    .tasit2_psar       0.304    0.098    3.115    0.002    0.304    0.386
##    .tasit3_sar        0.250    0.053    4.678    0.000    0.250    0.360
##     simulation        0.223    0.070    3.176    0.001    1.000    1.000
##     mentalizing       0.444    0.135    3.281    0.001    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.224
##     rmet_total        0.630
##     mean_ea           0.012
##     tasit3_lies       0.139
##     tasit2_ssar       0.576
##     tasit2_psar       0.614
##     tasit3_sar        0.640
## 
## 
## Group 2 [Control]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.370    0.421
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.573    0.699
##     mean_ea           0.720    0.637    1.130    0.258    0.266    0.227
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.312    0.361
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.358    0.699
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.374    0.598
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.359    0.484
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.079    0.026    3.076    0.002    0.597    0.597
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.255    0.060    4.221    0.000    0.255    0.290
##    .rmet_total        0.333    0.057    5.842    0.000    0.333    0.407
##    .mean_ea           0.681    0.197    3.466    0.001    0.681    0.582
##    .tasit3_lies       0.373    0.060    6.227    0.000    0.373    0.433
##    .tasit2_ssar       0.468    0.033   13.971    0.000    0.468    0.912
##    .tasit2_psar       0.424    0.045    9.443    0.000    0.424    0.677
##    .tasit3_sar        0.419    0.053    7.875    0.000    0.419    0.564
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.634    0.073    8.671    0.000    0.634    0.823
##    .rmet_total        0.343    0.069    4.970    0.000    0.343    0.511
##    .mean_ea           1.297    0.299    4.340    0.000    1.297    0.948
##    .tasit3_lies       0.646    0.103    6.270    0.000    0.646    0.869
##    .tasit2_ssar       0.134    0.021    6.510    0.000    0.134    0.511
##    .tasit2_psar       0.251    0.049    5.141    0.000    0.251    0.642
##    .tasit3_sar        0.422    0.087    4.841    0.000    0.422    0.766
##     simulation        0.137    0.039    3.522    0.000    1.000    1.000
##     mentalizing       0.128    0.035    3.618    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.177
##     rmet_total        0.489
##     mean_ea           0.052
##     tasit3_lies       0.131
##     tasit2_ssar       0.489
##     tasit2_psar       0.358
##     tasit3_sar        0.234
## 
## 
## Group 3 [SSD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.608    0.579
##     rmt_ttl (.p2.)    1.551    0.196    7.915    0.000    0.943    0.881
##     mean_ea           0.358    0.138    2.583    0.010    0.218    0.269
##     tst3_ls (.p4.)    0.843    0.102    8.233    0.000    0.513    0.521
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.892    0.794
##     tst2_ps (.p6.)    1.045    0.076   13.721    0.000    0.932    0.794
##     tst3_sr (.p7.)    1.002    0.067   14.854    0.000    0.894    0.846
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.373    0.063    5.916    0.000    0.687    0.687
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.199    0.065   -3.048    0.002   -0.199   -0.189
##    .rmet_total       -0.338    0.065   -5.202    0.000   -0.338   -0.315
##    .mean_ea          -0.198    0.085   -2.335    0.020   -0.198   -0.244
##    .tasit3_lies      -0.170    0.060   -2.839    0.005   -0.170   -0.172
##    .tasit2_ssar      -0.445    0.070   -6.326    0.000   -0.445   -0.396
##    .tasit2_psar      -0.429    0.070   -6.138    0.000   -0.429   -0.365
##    .tasit3_sar       -0.462    0.064   -7.189    0.000   -0.462   -0.438
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.736    0.097    7.611    0.000    0.736    0.665
##    .rmet_total        0.256    0.076    3.358    0.001    0.256    0.223
##    .mean_ea           0.609    0.125    4.870    0.000    0.609    0.928
##    .tasit3_lies       0.706    0.059   12.047    0.000    0.706    0.728
##    .tasit2_ssar       0.468    0.058    8.103    0.000    0.468    0.370
##    .tasit2_psar       0.510    0.062    8.197    0.000    0.510    0.370
##    .tasit3_sar        0.317    0.047    6.733    0.000    0.317    0.284
##     simulation        0.370    0.086    4.316    0.000    1.000    1.000
##     mentalizing       0.796    0.111    7.176    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.335
##     rmet_total        0.777
##     mean_ea           0.072
##     tasit3_lies       0.272
##     tasit2_ssar       0.630
##     tasit2_psar       0.630
##     tasit3_sar        0.716
## 
## Modification Indices:
## 
##            lhs op         rhs block group level     mi    epc sepc.lv sepc.all
## 1   simulation =~  er40_total     1     1     1  0.101 -0.086  -0.041   -0.041
## 2  mentalizing =~ tasit2_ssar     1     1     1  0.118  0.046   0.031    0.035
## 3   simulation =~  er40_total     2     2     1  0.517 -0.198  -0.073   -0.083
## 4  mentalizing =~ tasit2_ssar     2     2     1 16.216 -0.729  -0.261   -0.510
## 5   simulation =~  er40_total     3     3     1  0.645  0.171   0.104    0.099
## 6  mentalizing =~ tasit2_ssar     3     3     1  5.362  0.273   0.243    0.216
## 7   simulation =~ tasit2_ssar     1     1     1  0.056 -0.044  -0.021   -0.023
## 8   simulation =~ tasit2_psar     1     1     1  1.673  0.240   0.114    0.128
## 9   simulation =~  tasit3_sar     1     1     1  1.078 -0.180  -0.085   -0.102
## 10 mentalizing =~  er40_total     1     1     1  0.010  0.017   0.012    0.012
## 11 mentalizing =~  rmet_total     1     1     1  0.303  0.123   0.082    0.089
## 12 mentalizing =~     mean_ea     1     1     1  1.893 -1.439  -0.959   -1.031
## 13 mentalizing =~ tasit3_lies     1     1     1  1.002 -0.179  -0.120   -0.112
## 14  er40_total ~~  rmet_total     1     1     1  1.146 -0.111  -0.111   -0.226
## 15  er40_total ~~     mean_ea     1     1     1  3.540  0.388   0.388    0.477
## 16  er40_total ~~ tasit3_lies     1     1     1  0.333 -0.054  -0.054   -0.062
## 17  er40_total ~~ tasit2_ssar     1     1     1  0.059 -0.015  -0.015   -0.029
## 18  er40_total ~~ tasit2_psar     1     1     1  0.431 -0.039  -0.039   -0.081
## 19  er40_total ~~  tasit3_sar     1     1     1  2.890  0.095   0.095    0.216
## 20  rmet_total ~~     mean_ea     1     1     1  0.028 -0.029  -0.029   -0.056
## 21  rmet_total ~~ tasit3_lies     1     1     1  2.585  0.142   0.142    0.256
## 22  rmet_total ~~ tasit2_ssar     1     1     1  0.933 -0.049  -0.049   -0.151
## 23  rmet_total ~~ tasit2_psar     1     1     1  0.357  0.030   0.030    0.098
## 24  rmet_total ~~  tasit3_sar     1     1     1  0.194  0.021   0.021    0.074
## 25     mean_ea ~~ tasit3_lies     1     1     1  1.299  0.260   0.260    0.283
## 26     mean_ea ~~ tasit2_ssar     1     1     1  0.374  0.091   0.091    0.173
## 27     mean_ea ~~ tasit2_psar     1     1     1  1.246 -0.160  -0.160   -0.314
## 28     mean_ea ~~  tasit3_sar     1     1     1  0.634 -0.106  -0.106   -0.229
## 29 tasit3_lies ~~ tasit2_ssar     1     1     1  0.380 -0.041  -0.041   -0.072
## 30 tasit3_lies ~~ tasit2_psar     1     1     1  0.832  0.059   0.059    0.108
## 31 tasit3_lies ~~  tasit3_sar     1     1     1  3.317 -0.110  -0.110   -0.221
## 32 tasit2_ssar ~~ tasit2_psar     1     1     1  3.838  0.100   0.100    0.317
## 33 tasit2_ssar ~~  tasit3_sar     1     1     1  0.193 -0.021  -0.021   -0.075
## 34 tasit2_psar ~~  tasit3_sar     1     1     1  2.290 -0.077  -0.077   -0.279
## 35  simulation =~ tasit2_ssar     2     2     1 11.923 -0.467  -0.173   -0.337
## 36  simulation =~ tasit2_psar     2     2     1  3.325  0.277   0.102    0.164
## 37  simulation =~  tasit3_sar     2     2     1  5.191  0.401   0.148    0.199
## 38 mentalizing =~  er40_total     2     2     1  1.942 -0.306  -0.110   -0.125
## 39 mentalizing =~  rmet_total     2     2     1  2.038  0.403   0.144    0.176
## 40 mentalizing =~     mean_ea     2     2     1  0.002 -0.041  -0.015   -0.013
## 41 mentalizing =~ tasit3_lies     2     2     1  0.139 -0.080  -0.029   -0.033
## 42  er40_total ~~  rmet_total     2     2     1  0.545 -0.048  -0.048   -0.102
## 43  er40_total ~~     mean_ea     2     2     1  0.859 -0.150  -0.150   -0.165
## 44  er40_total ~~ tasit3_lies     2     2     1  4.583  0.106   0.106    0.165
## 45  er40_total ~~ tasit2_ssar     2     2     1  1.637 -0.034  -0.034   -0.116
## 46  er40_total ~~ tasit2_psar     2     2     1  2.983 -0.056  -0.056   -0.141
## 47  er40_total ~~  tasit3_sar     2     2     1  3.249  0.072   0.072    0.139
## 48  rmet_total ~~     mean_ea     2     2     1  1.302  0.197   0.197    0.295
## 49  rmet_total ~~ tasit3_lies     2     2     1  0.643 -0.044  -0.044   -0.093
## 50  rmet_total ~~ tasit2_ssar     2     2     1  1.807 -0.035  -0.035   -0.162
## 51  rmet_total ~~ tasit2_psar     2     2     1  4.264  0.063   0.063    0.214
## 52  rmet_total ~~  tasit3_sar     2     2     1  1.361  0.042   0.042    0.111
## 53     mean_ea ~~ tasit3_lies     2     2     1  0.632 -0.125  -0.125   -0.137
## 54     mean_ea ~~ tasit2_ssar     2     2     1  0.066  0.022   0.022    0.052
## 55     mean_ea ~~ tasit2_psar     2     2     1  0.163 -0.042  -0.042   -0.074
## 56     mean_ea ~~  tasit3_sar     2     2     1  0.003  0.008   0.008    0.010
## 57 tasit3_lies ~~ tasit2_ssar     2     2     1  0.059 -0.006  -0.006   -0.021
## 58 tasit3_lies ~~ tasit2_psar     2     2     1  0.042  0.007   0.007    0.016
## 59 tasit3_lies ~~  tasit3_sar     2     2     1  0.716 -0.033  -0.033   -0.064
## 60 tasit2_ssar ~~ tasit2_psar     2     2     1  0.556 -0.019  -0.019   -0.104
## 61 tasit2_ssar ~~  tasit3_sar     2     2     1  2.261 -0.038  -0.038   -0.158
## 62 tasit2_psar ~~  tasit3_sar     2     2     1  6.079  0.070   0.070    0.216
## 63  simulation =~ tasit2_ssar     3     3     1  0.813  0.110   0.067    0.060
## 64  simulation =~ tasit2_psar     3     3     1  0.153  0.050   0.030    0.026
## 65  simulation =~  tasit3_sar     3     3     1  1.495 -0.141  -0.086   -0.081
## 66 mentalizing =~  er40_total     3     3     1  0.028  0.016   0.015    0.014
## 67 mentalizing =~  rmet_total     3     3     1  0.008 -0.012  -0.011   -0.010
## 68 mentalizing =~     mean_ea     3     3     1  0.008  0.013   0.012    0.015
## 69 mentalizing =~ tasit3_lies     3     3     1  0.009 -0.009  -0.008   -0.008
## 70  er40_total ~~  rmet_total     3     3     1  0.541 -0.059  -0.059   -0.136
## 71  er40_total ~~     mean_ea     3     3     1  1.638  0.096   0.096    0.144
## 72  er40_total ~~ tasit3_lies     3     3     1  2.107  0.076   0.076    0.106
## 73  er40_total ~~ tasit2_ssar     3     3     1  1.913  0.061   0.061    0.104
## 74  er40_total ~~ tasit2_psar     3     3     1  0.200 -0.021  -0.021   -0.034
## 75  er40_total ~~  tasit3_sar     3     3     1  1.082 -0.041  -0.041   -0.086
## 76  rmet_total ~~     mean_ea     3     3     1  0.005 -0.005  -0.005   -0.013
## 77  rmet_total ~~ tasit3_lies     3     3     1  0.195 -0.029  -0.029   -0.069
## 78  rmet_total ~~ tasit2_ssar     3     3     1  0.460 -0.027  -0.027   -0.079
## 79  rmet_total ~~ tasit2_psar     3     3     1  0.045  0.009   0.009    0.025
## 80  rmet_total ~~  tasit3_sar     3     3     1  0.438  0.025   0.025    0.086
## 81     mean_ea ~~ tasit3_lies     3     3     1  1.989 -0.099  -0.099   -0.151
## 82     mean_ea ~~ tasit2_ssar     3     3     1  3.239 -0.111  -0.111   -0.209
## 83     mean_ea ~~ tasit2_psar     3     3     1  3.280  0.119   0.119    0.214
## 84     mean_ea ~~  tasit3_sar     3     3     1  0.009  0.005   0.005    0.012
## 85 tasit3_lies ~~ tasit2_ssar     3     3     1  0.039 -0.008  -0.008   -0.014
## 86 tasit3_lies ~~ tasit2_psar     3     3     1  9.240  0.134   0.134    0.223
## 87 tasit3_lies ~~  tasit3_sar     3     3     1  7.565 -0.103  -0.103   -0.218
## 88 tasit2_ssar ~~ tasit2_psar     3     3     1  2.978 -0.101  -0.101   -0.206
## 89 tasit2_ssar ~~  tasit3_sar     3     3     1 11.575  0.193   0.193    0.501
## 90 tasit2_psar ~~  tasit3_sar     3     3     1  2.733 -0.098  -0.098   -0.244
##    sepc.nox
## 1    -0.041
## 2     0.035
## 3    -0.083
## 4    -0.510
## 5     0.099
## 6     0.216
## 7    -0.023
## 8     0.128
## 9    -0.102
## 10    0.012
## 11    0.089
## 12   -1.031
## 13   -0.112
## 14   -0.226
## 15    0.477
## 16   -0.062
## 17   -0.029
## 18   -0.081
## 19    0.216
## 20   -0.056
## 21    0.256
## 22   -0.151
## 23    0.098
## 24    0.074
## 25    0.283
## 26    0.173
## 27   -0.314
## 28   -0.229
## 29   -0.072
## 30    0.108
## 31   -0.221
## 32    0.317
## 33   -0.075
## 34   -0.279
## 35   -0.337
## 36    0.164
## 37    0.199
## 38   -0.125
## 39    0.176
## 40   -0.013
## 41   -0.033
## 42   -0.102
## 43   -0.165
## 44    0.165
## 45   -0.116
## 46   -0.141
## 47    0.139
## 48    0.295
## 49   -0.093
## 50   -0.162
## 51    0.214
## 52    0.111
## 53   -0.137
## 54    0.052
## 55   -0.074
## 56    0.010
## 57   -0.021
## 58    0.016
## 59   -0.064
## 60   -0.104
## 61   -0.158
## 62    0.216
## 63    0.060
## 64    0.026
## 65   -0.081
## 66    0.014
## 67   -0.010
## 68    0.015
## 69   -0.008
## 70   -0.136
## 71    0.144
## 72    0.106
## 73    0.104
## 74   -0.034
## 75   -0.086
## 76   -0.013
## 77   -0.069
## 78   -0.079
## 79    0.025
## 80    0.086
## 81   -0.151
## 82   -0.209
## 83    0.214
## 84    0.012
## 85   -0.014
## 86    0.223
## 87   -0.218
## 88   -0.206
## 89    0.501
## 90   -0.244
        anova(CFA_scog_model1_grp_fit,CFA_sc_model1_grp_fit2_part3)
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## 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
## CFA_scog_model1_grp_fit      39 8746.2 9034.8 68.870                   
## CFA_sc_model1_grp_fit2_part3 47 8750.0 9003.6 88.629     16.963       8
##                              Pr(>Chisq)  
## CFA_scog_model1_grp_fit                  
## CFA_sc_model1_grp_fit2_part3     0.0305 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
      #! metric - partial isolating mean ea and tasit2_psar (according to mod indices from above)
      
        CFA_sc_model1_grp_fit2_part2a <- cfa(model= CFA_scog_model1,data = spasd_spins_yj_z_df, group = "group",
                                             group.equal=c("loadings"),estimator = "MLR", missing = "ml",
                                             group.partial = c("simulation=~mean_ea","mentalizing=~tasit2_psar"))
        
        summary(CFA_sc_model1_grp_fit2_part2a, fit.measures = TRUE, modindices = TRUE, standardized = TRUE, rsquare =
                  TRUE)
## lavaan 0.6.16 ended normally after 92 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        66
##   Number of equality constraints                     6
## 
##   Number of observations per group:                   
##     ASD                                            100
##     Control                                        209
##     SSD                                            276
##   Number of missing patterns per group:               
##     ASD                                              4
##     Control                                          6
##     SSD                                             20
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                                80.391      79.328
##   Degrees of freedom                                45          45
##   P-value (Chi-square)                           0.001       0.001
##   Scaling correction factor                                  1.013
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     ASD                                         23.345      23.036
##     Control                                     26.434      26.085
##     SSD                                         30.612      30.207
## 
## Model Test Baseline Model:
## 
##   Test statistic                               973.724     901.247
##   Degrees of freedom                                63          63
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.080
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.961       0.959
##   Tucker-Lewis Index (TLI)                       0.946       0.943
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.950
##   Robust Tucker-Lewis Index (TLI)                            0.929
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4312.884   -4312.884
##   Scaling correction factor                                  1.128
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -4272.688   -4272.688
##   Scaling correction factor                                  1.143
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                                8745.767    8745.767
##   Bayesian (BIC)                              9008.064    9008.064
##   Sample-size adjusted Bayesian (SABIC)       8817.586    8817.586
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.064       0.063
##   90 Percent confidence interval - lower         0.040       0.039
##   90 Percent confidence interval - upper         0.086       0.085
##   P-value H_0: RMSEA <= 0.050                    0.156       0.172
##   P-value H_0: RMSEA >= 0.080                    0.116       0.101
##                                                                   
##   Robust RMSEA                                               0.076
##   90 Percent confidence interval - lower                     0.000
##   90 Percent confidence interval - upper                     0.123
##   P-value H_0: Robust RMSEA <= 0.050                         0.207
##   P-value H_0: Robust RMSEA >= 0.080                         0.474
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.071       0.071
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [ASD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.468    0.469
##     rmt_ttl (.p2.)    1.571    0.202    7.783    0.000    0.736    0.797
##     mean_ea          -0.227    0.416   -0.547    0.584   -0.107   -0.115
##     tst3_ls (.p4.)    0.847    0.103    8.215    0.000    0.397    0.372
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.642    0.744
##     tst2_ps           1.184    0.149    7.953    0.000    0.760    0.825
##     tst3_sr (.p7.)    0.987    0.062   15.878    0.000    0.634    0.776
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.251    0.087    2.888    0.004    0.836    0.836
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.067    0.101   -0.667    0.505   -0.067   -0.067
##    .rmet_total        0.149    0.093    1.597    0.110    0.149    0.161
##    .mean_ea           0.073    0.230    0.319    0.750    0.073    0.079
##    .tasit3_lies      -0.328    0.105   -3.115    0.002   -0.328   -0.308
##    .tasit2_ssar       0.142    0.090    1.588    0.112    0.142    0.165
##    .tasit2_psar       0.111    0.092    1.209    0.227    0.111    0.121
##    .tasit3_sar        0.290    0.080    3.642    0.000    0.290    0.355
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.779    0.127    6.152    0.000    0.779    0.780
##    .rmet_total        0.311    0.105    2.956    0.003    0.311    0.365
##    .mean_ea           0.854    0.461    1.852    0.064    0.854    0.987
##    .tasit3_lies       0.979    0.153    6.395    0.000    0.979    0.861
##    .tasit2_ssar       0.333    0.084    3.982    0.000    0.333    0.447
##    .tasit2_psar       0.270    0.098    2.762    0.006    0.270    0.319
##    .tasit3_sar        0.265    0.053    4.967    0.000    0.265    0.398
##     simulation        0.219    0.069    3.158    0.002    1.000    1.000
##     mentalizing       0.412    0.134    3.082    0.002    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.220
##     rmet_total        0.635
##     mean_ea           0.013
##     tasit3_lies       0.139
##     tasit2_ssar       0.553
##     tasit2_psar       0.681
##     tasit3_sar        0.602
## 
## 
## Group 2 [Control]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.368    0.418
##     rmt_ttl (.p2.)    1.571    0.202    7.783    0.000    0.578    0.706
##     mean_ea           0.708    0.618    1.147    0.252    0.261    0.223
##     tst3_ls (.p4.)    0.847    0.103    8.215    0.000    0.312    0.361
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.319    0.634
##     tst2_ps           1.478    0.255    5.788    0.000    0.472    0.727
##     tst3_sr (.p7.)    0.987    0.062   15.878    0.000    0.315    0.431
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.070    0.025    2.862    0.004    0.598    0.598
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.255    0.060    4.222    0.000    0.255    0.290
##    .rmet_total        0.333    0.057    5.838    0.000    0.333    0.407
##    .mean_ea           0.682    0.197    3.469    0.001    0.682    0.583
##    .tasit3_lies       0.373    0.060    6.224    0.000    0.373    0.433
##    .tasit2_ssar       0.468    0.033   13.971    0.000    0.468    0.928
##    .tasit2_psar       0.424    0.045    9.443    0.000    0.424    0.653
##    .tasit3_sar        0.419    0.053    7.875    0.000    0.419    0.573
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.639    0.074    8.653    0.000    0.639    0.825
##    .rmet_total        0.336    0.069    4.855    0.000    0.336    0.501
##    .mean_ea           1.300    0.296    4.388    0.000    1.300    0.950
##    .tasit3_lies       0.647    0.103    6.265    0.000    0.647    0.869
##    .tasit2_ssar       0.152    0.022    7.007    0.000    0.152    0.598
##    .tasit2_psar       0.198    0.054    3.707    0.000    0.198    0.472
##    .tasit3_sar        0.436    0.088    4.984    0.000    0.436    0.815
##     simulation        0.135    0.038    3.521    0.000    1.000    1.000
##     mentalizing       0.102    0.036    2.828    0.005    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.175
##     rmet_total        0.499
##     mean_ea           0.050
##     tasit3_lies       0.131
##     tasit2_ssar       0.402
##     tasit2_psar       0.528
##     tasit3_sar        0.185
## 
## 
## Group 3 [SSD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.603    0.575
##     rmt_ttl (.p2.)    1.571    0.202    7.783    0.000    0.948    0.885
##     mean_ea           0.358    0.140    2.559    0.010    0.216    0.267
##     tst3_ls (.p4.)    0.847    0.103    8.215    0.000    0.511    0.519
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.928    0.811
##     tst2_ps           0.929    0.079   11.772    0.000    0.862    0.761
##     tst3_sr (.p7.)    0.987    0.062   15.878    0.000    0.916    0.858
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.380    0.064    5.944    0.000    0.679    0.679
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total       -0.199    0.065   -3.047    0.002   -0.199   -0.189
##    .rmet_total       -0.338    0.065   -5.203    0.000   -0.338   -0.315
##    .mean_ea          -0.198    0.085   -2.342    0.019   -0.198   -0.245
##    .tasit3_lies      -0.170    0.060   -2.838    0.005   -0.170   -0.172
##    .tasit2_ssar      -0.446    0.070   -6.336    0.000   -0.446   -0.390
##    .tasit2_psar      -0.424    0.070   -6.088    0.000   -0.424   -0.375
##    .tasit3_sar       -0.463    0.064   -7.192    0.000   -0.463   -0.434
##     simulation        0.000                               0.000    0.000
##     mentalizing       0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.738    0.097    7.601    0.000    0.738    0.670
##    .rmet_total        0.248    0.077    3.220    0.001    0.248    0.217
##    .mean_ea           0.610    0.125    4.872    0.000    0.610    0.929
##    .tasit3_lies       0.708    0.059   12.087    0.000    0.708    0.730
##    .tasit2_ssar       0.448    0.057    7.884    0.000    0.448    0.342
##    .tasit2_psar       0.539    0.064    8.464    0.000    0.539    0.420
##    .tasit3_sar        0.301    0.047    6.427    0.000    0.301    0.264
##     simulation        0.364    0.086    4.255    0.000    1.000    1.000
##     mentalizing       0.861    0.112    7.697    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.330
##     rmet_total        0.783
##     mean_ea           0.071
##     tasit3_lies       0.270
##     tasit2_ssar       0.658
##     tasit2_psar       0.580
##     tasit3_sar        0.736
## 
## Modification Indices:
## 
##            lhs op         rhs block group level    mi    epc sepc.lv sepc.all
## 1   simulation =~  er40_total     1     1     1 0.110 -0.091  -0.043   -0.043
## 2  mentalizing =~ tasit2_ssar     1     1     1 0.909  0.148   0.095    0.110
## 3   simulation =~  er40_total     2     2     1 0.734 -0.235  -0.086   -0.098
## 4  mentalizing =~ tasit2_ssar     2     2     1 9.255 -0.689  -0.220   -0.436
## 5   simulation =~  er40_total     3     3     1 0.856  0.197   0.119    0.113
## 6  mentalizing =~ tasit2_ssar     3     3     1 1.006  0.138   0.128    0.112
## 7   simulation =~ tasit2_ssar     1     1     1 0.060  0.051   0.024    0.028
## 8   simulation =~ tasit2_psar     1     1     1 0.054  0.134   0.063    0.068
## 9   simulation =~  tasit3_sar     1     1     1 0.116 -0.068  -0.032   -0.039
## 10 mentalizing =~  er40_total     1     1     1 0.005  0.012   0.008    0.008
## 11 mentalizing =~  rmet_total     1     1     1 0.256  0.118   0.076    0.082
## 12 mentalizing =~     mean_ea     1     1     1 1.957 -1.484  -0.953   -1.024
## 13 mentalizing =~ tasit3_lies     1     1     1 0.806 -0.166  -0.107   -0.100
## 14  er40_total ~~  rmet_total     1     1     1 0.956 -0.101  -0.101   -0.206
## 15  er40_total ~~     mean_ea     1     1     1 3.540  0.388   0.388    0.476
## 16  er40_total ~~ tasit3_lies     1     1     1 0.332 -0.054  -0.054   -0.062
## 17  er40_total ~~ tasit2_ssar     1     1     1 0.017 -0.008  -0.008   -0.015
## 18  er40_total ~~ tasit2_psar     1     1     1 0.592 -0.047  -0.047   -0.102
## 19  er40_total ~~  tasit3_sar     1     1     1 3.153  0.099   0.099    0.217
## 20  rmet_total ~~     mean_ea     1     1     1 0.018 -0.024  -0.024   -0.046
## 21  rmet_total ~~ tasit3_lies     1     1     1 2.300  0.135   0.135    0.244
## 22  rmet_total ~~ tasit2_ssar     1     1     1 0.706 -0.042  -0.042   -0.130
## 23  rmet_total ~~ tasit2_psar     1     1     1 0.029  0.009   0.009    0.032
## 24  rmet_total ~~  tasit3_sar     1     1     1 0.531  0.034   0.034    0.120
## 25     mean_ea ~~ tasit3_lies     1     1     1 1.326  0.262   0.262    0.286
## 26     mean_ea ~~ tasit2_ssar     1     1     1 0.373  0.091   0.091    0.170
## 27     mean_ea ~~ tasit2_psar     1     1     1 1.256 -0.160  -0.160   -0.333
## 28     mean_ea ~~  tasit3_sar     1     1     1 0.540 -0.097  -0.097   -0.204
## 29 tasit3_lies ~~ tasit2_ssar     1     1     1 0.508 -0.047  -0.047   -0.082
## 30 tasit3_lies ~~ tasit2_psar     1     1     1 0.873  0.061   0.061    0.118
## 31 tasit3_lies ~~  tasit3_sar     1     1     1 3.271 -0.108  -0.108   -0.212
## 32 tasit2_ssar ~~ tasit2_psar     1     1     1 2.483  0.086   0.086    0.287
## 33 tasit2_ssar ~~  tasit3_sar     1     1     1 0.054  0.012   0.012    0.041
## 34 tasit2_psar ~~  tasit3_sar     1     1     1 3.201 -0.097  -0.097   -0.363
## 35  simulation =~ tasit2_ssar     2     2     1 6.152 -0.390  -0.144   -0.285
## 36  simulation =~ tasit2_psar     2     2     1 0.009 -0.030  -0.011   -0.017
## 37  simulation =~  tasit3_sar     2     2     1 9.196  0.561   0.206    0.282
## 38 mentalizing =~  er40_total     2     2     1 2.631 -0.394  -0.126   -0.143
## 39 mentalizing =~  rmet_total     2     2     1 2.548  0.501   0.160    0.196
## 40 mentalizing =~     mean_ea     2     2     1 0.018 -0.147  -0.047   -0.040
## 41 mentalizing =~ tasit3_lies     2     2     1 0.114 -0.080  -0.025   -0.029
## 42  er40_total ~~  rmet_total     2     2     1 0.449 -0.043  -0.043   -0.093
## 43  er40_total ~~     mean_ea     2     2     1 0.832 -0.148  -0.148   -0.162
## 44  er40_total ~~ tasit3_lies     2     2     1 4.738  0.107   0.107    0.167
## 45  er40_total ~~ tasit2_ssar     2     2     1 0.692 -0.022  -0.022   -0.070
## 46  er40_total ~~ tasit2_psar     2     2     1 4.123 -0.068  -0.068   -0.190
## 47  er40_total ~~  tasit3_sar     2     2     1 3.269  0.072   0.072    0.137
## 48  rmet_total ~~     mean_ea     2     2     1 1.403  0.203   0.203    0.307
## 49  rmet_total ~~ tasit3_lies     2     2     1 0.803 -0.049  -0.049   -0.106
## 50  rmet_total ~~ tasit2_ssar     2     2     1 0.490 -0.018  -0.018   -0.081
## 51  rmet_total ~~ tasit2_psar     2     2     1 1.920  0.049   0.049    0.192
## 52  rmet_total ~~  tasit3_sar     2     2     1 1.425  0.043   0.043    0.112
## 53     mean_ea ~~ tasit3_lies     2     2     1 0.618 -0.124  -0.124   -0.135
## 54     mean_ea ~~ tasit2_ssar     2     2     1 0.108  0.027   0.027    0.061
## 55     mean_ea ~~ tasit2_psar     2     2     1 0.215 -0.048  -0.048   -0.095
## 56     mean_ea ~~  tasit3_sar     2     2     1 0.008  0.011   0.011    0.015
## 57 tasit3_lies ~~ tasit2_ssar     2     2     1 0.010 -0.003  -0.003   -0.008
## 58 tasit3_lies ~~ tasit2_psar     2     2     1 0.000  0.000   0.000    0.000
## 59 tasit3_lies ~~  tasit3_sar     2     2     1 0.663 -0.032  -0.032   -0.061
## 60 tasit2_ssar ~~ tasit2_psar     2     2     1 2.641 -0.051  -0.051   -0.292
## 61 tasit2_ssar ~~  tasit3_sar     2     2     1 0.009 -0.003  -0.003   -0.010
## 62 tasit2_psar ~~  tasit3_sar     2     2     1 2.876  0.052   0.052    0.177
## 63  simulation =~ tasit2_ssar     3     3     1 0.008  0.011   0.007    0.006
## 64  simulation =~ tasit2_psar     3     3     1 5.919  0.374   0.226    0.199
## 65  simulation =~  tasit3_sar     3     3     1 3.723 -0.239  -0.144   -0.135
## 66 mentalizing =~  er40_total     3     3     1 0.095  0.029   0.027    0.025
## 67 mentalizing =~  rmet_total     3     3     1 0.016 -0.016  -0.015   -0.014
## 68 mentalizing =~     mean_ea     3     3     1 0.000  0.002   0.002    0.003
## 69 mentalizing =~ tasit3_lies     3     3     1 0.035 -0.016  -0.015   -0.015
## 70  er40_total ~~  rmet_total     3     3     1 0.665 -0.066  -0.066   -0.154
## 71  er40_total ~~     mean_ea     3     3     1 1.660  0.097   0.097    0.145
## 72  er40_total ~~ tasit3_lies     3     3     1 2.282  0.079   0.079    0.110
## 73  er40_total ~~ tasit2_ssar     3     3     1 1.919  0.061   0.061    0.106
## 74  er40_total ~~ tasit2_psar     3     3     1 0.103 -0.015  -0.015   -0.024
## 75  er40_total ~~  tasit3_sar     3     3     1 1.231 -0.044  -0.044   -0.093
## 76  rmet_total ~~     mean_ea     3     3     1 0.001 -0.002  -0.002   -0.006
## 77  rmet_total ~~ tasit3_lies     3     3     1 0.184 -0.029  -0.029   -0.069
## 78  rmet_total ~~ tasit2_ssar     3     3     1 0.713 -0.034  -0.034   -0.102
## 79  rmet_total ~~ tasit2_psar     3     3     1 0.260  0.021   0.021    0.058
## 80  rmet_total ~~  tasit3_sar     3     3     1 0.333  0.022   0.022    0.079
## 81     mean_ea ~~ tasit3_lies     3     3     1 1.919 -0.097  -0.097   -0.148
## 82     mean_ea ~~ tasit2_ssar     3     3     1 3.156 -0.110  -0.110   -0.209
## 83     mean_ea ~~ tasit2_psar     3     3     1 3.079  0.115   0.115    0.201
## 84     mean_ea ~~  tasit3_sar     3     3     1 0.057  0.013   0.013    0.031
## 85 tasit3_lies ~~ tasit2_ssar     3     3     1 0.004 -0.003  -0.003   -0.004
## 86 tasit3_lies ~~ tasit2_psar     3     3     1 9.264  0.134   0.134    0.216
## 87 tasit3_lies ~~  tasit3_sar     3     3     1 7.189 -0.101  -0.101   -0.218
## 88 tasit2_ssar ~~ tasit2_psar     3     3     1 1.410 -0.069  -0.069   -0.141
## 89 tasit2_ssar ~~  tasit3_sar     3     3     1 5.919  0.176   0.176    0.480
## 90 tasit2_psar ~~  tasit3_sar     3     3     1 0.824 -0.053  -0.053   -0.132
##    sepc.nox
## 1    -0.043
## 2     0.110
## 3    -0.098
## 4    -0.436
## 5     0.113
## 6     0.112
## 7     0.028
## 8     0.068
## 9    -0.039
## 10    0.008
## 11    0.082
## 12   -1.024
## 13   -0.100
## 14   -0.206
## 15    0.476
## 16   -0.062
## 17   -0.015
## 18   -0.102
## 19    0.217
## 20   -0.046
## 21    0.244
## 22   -0.130
## 23    0.032
## 24    0.120
## 25    0.286
## 26    0.170
## 27   -0.333
## 28   -0.204
## 29   -0.082
## 30    0.118
## 31   -0.212
## 32    0.287
## 33    0.041
## 34   -0.363
## 35   -0.285
## 36   -0.017
## 37    0.282
## 38   -0.143
## 39    0.196
## 40   -0.040
## 41   -0.029
## 42   -0.093
## 43   -0.162
## 44    0.167
## 45   -0.070
## 46   -0.190
## 47    0.137
## 48    0.307
## 49   -0.106
## 50   -0.081
## 51    0.192
## 52    0.112
## 53   -0.135
## 54    0.061
## 55   -0.095
## 56    0.015
## 57   -0.008
## 58    0.000
## 59   -0.061
## 60   -0.292
## 61   -0.010
## 62    0.177
## 63    0.006
## 64    0.199
## 65   -0.135
## 66    0.025
## 67   -0.014
## 68    0.003
## 69   -0.015
## 70   -0.154
## 71    0.145
## 72    0.110
## 73    0.106
## 74   -0.024
## 75   -0.093
## 76   -0.006
## 77   -0.069
## 78   -0.102
## 79    0.058
## 80    0.079
## 81   -0.148
## 82   -0.209
## 83    0.201
## 84    0.031
## 85   -0.004
## 86    0.216
## 87   -0.218
## 88   -0.141
## 89    0.480
## 90   -0.132
        # compare configural & metric models 
        
        anova(CFA_scog_model1_grp_fit,CFA_sc_model1_grp_fit2_part2a) # non sig diff in models
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## 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
## CFA_scog_model1_grp_fit       39 8746.2 9034.8 68.870                   
## CFA_sc_model1_grp_fit2_part2a 45 8745.8 9008.1 80.391     9.1555       6
##                               Pr(>Chisq)
## CFA_scog_model1_grp_fit                 
## CFA_sc_model1_grp_fit2_part2a      0.165
  # scalar invariance - are item intercepts equal across groups
      
      # scalar invariance - partial isolating mean ea & tasit2_psar
        
        CFA_sc_model1_grp_fit3_part3a <- cfa(model=CFA_scog_model1,data = spasd_spins_yj_z_df,group = "group",
                                             group.equal=c("loadings","intercepts"), estimator = "MLR", missing = "ml",
                                             group.partial = c("simulation=~mean_ea","mentalizing=~tasit2_psar"))
        
        summary(CFA_sc_model1_grp_fit3_part3a, fit.measures = TRUE, modindices = TRUE, standardized = TRUE, rsquare =
                  TRUE)
## lavaan 0.6.16 ended normally after 98 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        70
##   Number of equality constraints                    20
## 
##   Number of observations per group:                   
##     ASD                                            100
##     Control                                        209
##     SSD                                            276
##   Number of missing patterns per group:               
##     ASD                                              4
##     Control                                          6
##     SSD                                             20
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               118.659     120.493
##   Degrees of freedom                                55          55
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.985
##     Yuan-Bentler correction (Mplus variant)                       
##   Test statistic for each group:
##     ASD                                         46.701      47.423
##     Control                                     38.381      38.975
##     SSD                                         33.576      34.095
## 
## Model Test Baseline Model:
## 
##   Test statistic                               973.724     901.247
##   Degrees of freedom                                63          63
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.080
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.930       0.922
##   Tucker-Lewis Index (TLI)                       0.920       0.911
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.902
##   Robust Tucker-Lewis Index (TLI)                            0.888
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4332.018   -4332.018
##   Scaling correction factor                                  0.941
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)      -4272.688   -4272.688
##   Scaling correction factor                                  1.143
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                                8764.035    8764.035
##   Bayesian (BIC)                              8982.616    8982.616
##   Sample-size adjusted Bayesian (SABIC)       8823.884    8823.884
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.077       0.078
##   90 Percent confidence interval - lower         0.058       0.059
##   90 Percent confidence interval - upper         0.096       0.097
##   P-value H_0: RMSEA <= 0.050                    0.012       0.009
##   P-value H_0: RMSEA >= 0.080                    0.417       0.455
##                                                                   
##   Robust RMSEA                                               0.096
##   90 Percent confidence interval - lower                     0.055
##   90 Percent confidence interval - upper                     0.132
##   P-value H_0: Robust RMSEA <= 0.050                         0.035
##   P-value H_0: Robust RMSEA >= 0.080                         0.762
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.092       0.092
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## 
## Group 1 [ASD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.455    0.457
##     rmt_ttl (.p2.)    1.496    0.152    9.844    0.000    0.681    0.734
##     mean_ea          -0.281    0.417   -0.674    0.500   -0.128   -0.137
##     tst3_ls (.p4.)    0.897    0.094    9.548    0.000    0.408    0.357
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.636    0.735
##     tst2_ps           1.197    0.150    7.974    0.000    0.762    0.827
##     tst3_sr (.p7.)    0.991    0.053   18.789    0.000    0.631    0.770
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.257    0.087    2.966    0.003    0.887    0.887
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_tt (.18.)    0.010    0.072    0.143    0.886    0.010    0.010
##    .rmt_ttl (.19.)    0.020    0.100    0.199    0.842    0.020    0.021
##    .mean_ea (.20.)   -0.009    0.114   -0.079    0.937   -0.009   -0.010
##    .tst3_ls (.21.)    0.046    0.068    0.666    0.505    0.046    0.040
##    .tst2_ss (.22.)    0.232    0.076    3.063    0.002    0.232    0.268
##    .tst2_ps (.23.)    0.138    0.077    1.795    0.073    0.138    0.150
##    .tst3_sr (.24.)    0.225    0.076    2.955    0.003    0.225    0.275
##     simultn           0.000                               0.000    0.000
##     mntlzng           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.782    0.131    5.970    0.000    0.782    0.791
##    .rmet_total        0.397    0.108    3.671    0.000    0.397    0.462
##    .mean_ea           0.854    0.488    1.750    0.080    0.854    0.981
##    .tasit3_lies       1.142    0.212    5.398    0.000    1.142    0.873
##    .tasit2_ssar       0.345    0.089    3.894    0.000    0.345    0.460
##    .tasit2_psar       0.269    0.100    2.691    0.007    0.269    0.317
##    .tasit3_sar        0.273    0.052    5.229    0.000    0.273    0.407
##     simulation        0.207    0.070    2.959    0.003    1.000    1.000
##     mentalizing       0.405    0.129    3.137    0.002    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.209
##     rmet_total        0.538
##     mean_ea           0.019
##     tasit3_lies       0.127
##     tasit2_ssar       0.540
##     tasit2_psar       0.683
##     tasit3_sar        0.593
## 
## 
## Group 2 [Control]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.357    0.409
##     rmt_ttl (.p2.)    1.496    0.152    9.844    0.000    0.534    0.656
##     mean_ea           1.540    0.821    1.876    0.061    0.550    0.422
##     tst3_ls (.p4.)    0.897    0.094    9.548    0.000    0.320    0.368
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.331    0.653
##     tst2_ps           1.353    0.190    7.120    0.000    0.448    0.696
##     tst3_sr (.p7.)    0.991    0.053   18.789    0.000    0.328    0.447
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.073    0.024    2.977    0.003    0.613    0.613
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_tt (.18.)    0.010    0.072    0.143    0.886    0.010    0.012
##    .rmt_ttl (.19.)    0.020    0.100    0.199    0.842    0.020    0.024
##    .mean_ea (.20.)   -0.009    0.114   -0.079    0.937   -0.009   -0.007
##    .tst3_ls (.21.)    0.046    0.068    0.666    0.505    0.046    0.052
##    .tst2_ss (.22.)    0.232    0.076    3.063    0.002    0.232    0.457
##    .tst2_ps (.23.)    0.138    0.077    1.795    0.073    0.138    0.215
##    .tst3_sr (.24.)    0.225    0.076    2.955    0.003    0.225    0.306
##     simultn           0.246    0.084    2.922    0.003    0.688    0.688
##     mntlzng           0.219    0.079    2.771    0.006    0.660    0.660
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.637    0.075    8.504    0.000    0.637    0.833
##    .rmet_total        0.378    0.070    5.417    0.000    0.378    0.570
##    .mean_ea           1.398    0.420    3.328    0.001    1.398    0.822
##    .tasit3_lies       0.656    0.106    6.170    0.000    0.656    0.865
##    .tasit2_ssar       0.147    0.022    6.760    0.000    0.147    0.573
##    .tasit2_psar       0.214    0.055    3.874    0.000    0.214    0.516
##    .tasit3_sar        0.431    0.088    4.922    0.000    0.431    0.800
##     simulation        0.128    0.040    3.176    0.001    1.000    1.000
##     mentalizing       0.110    0.033    3.315    0.001    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.167
##     rmet_total        0.430
##     mean_ea           0.178
##     tasit3_lies       0.135
##     tasit2_ssar       0.427
##     tasit2_psar       0.484
##     tasit3_sar        0.200
## 
## 
## Group 3 [SSD]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation =~                                                         
##     er40_tt           1.000                               0.615    0.585
##     rmt_ttl (.p2.)    1.496    0.152    9.844    0.000    0.919    0.865
##     mean_ea           0.449    0.142    3.154    0.002    0.276    0.333
##     tst3_ls (.p4.)    0.897    0.094    9.548    0.000    0.551    0.551
##   mentalizing =~                                                        
##     tst2_ss           1.000                               0.937    0.815
##     tst2_ps           0.883    0.071   12.467    0.000    0.827    0.743
##     tst3_sr (.p7.)    0.991    0.053   18.789    0.000    0.928    0.863
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   simulation ~~                                                         
##     mentalizing       0.393    0.058    6.729    0.000    0.683    0.683
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_tt (.18.)    0.010    0.072    0.143    0.886    0.010    0.010
##    .rmt_ttl (.19.)    0.020    0.100    0.199    0.842    0.020    0.019
##    .mean_ea (.20.)   -0.009    0.114   -0.079    0.937   -0.009   -0.011
##    .tst3_ls (.21.)    0.046    0.068    0.666    0.505    0.046    0.046
##    .tst2_ss (.22.)    0.232    0.076    3.063    0.002    0.232    0.202
##    .tst2_ps (.23.)    0.138    0.077    1.795    0.073    0.138    0.124
##    .tst3_sr (.24.)    0.225    0.076    2.955    0.003    0.225    0.209
##     simultn          -0.237    0.077   -3.053    0.002   -0.385   -0.385
##     mntlzng          -0.677    0.099   -6.822    0.000   -0.723   -0.723
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .er40_total        0.727    0.091    8.032    0.000    0.727    0.658
##    .rmet_total        0.284    0.071    3.986    0.000    0.284    0.251
##    .mean_ea           0.611    0.126    4.847    0.000    0.611    0.889
##    .tasit3_lies       0.697    0.058   12.115    0.000    0.697    0.696
##    .tasit2_ssar       0.443    0.055    8.106    0.000    0.443    0.336
##    .tasit2_psar       0.555    0.060    9.199    0.000    0.555    0.448
##    .tasit3_sar        0.294    0.045    6.556    0.000    0.294    0.255
##     simulation        0.378    0.075    5.043    0.000    1.000    1.000
##     mentalizing       0.877    0.107    8.192    0.000    1.000    1.000
## 
## R-Square:
##                    Estimate
##     er40_total        0.342
##     rmet_total        0.749
##     mean_ea           0.111
##     tasit3_lies       0.304
##     tasit2_ssar       0.664
##     tasit2_psar       0.552
##     tasit3_sar        0.745
## 
## Modification Indices:
## 
##            lhs op         rhs block group level    mi    epc sepc.lv sepc.all
## 1   simulation =~  er40_total     1     1     1 0.014 -0.032  -0.015   -0.015
## 2  mentalizing =~ tasit2_ssar     1     1     1 0.803  0.136   0.087    0.100
## 3   simulation ~1                 1     1     1 3.310  0.367   0.806    0.806
## 4  mentalizing ~1                 1     1     1 2.177 -0.304  -0.479   -0.479
## 5   simulation =~  er40_total     2     2     1 0.135 -0.088  -0.032   -0.036
## 6  mentalizing =~ tasit2_ssar     2     2     1 4.403 -0.418  -0.138   -0.273
## 7   simulation =~  er40_total     3     3     1 0.161  0.082   0.050    0.048
## 8  mentalizing =~ tasit2_ssar     3     3     1 0.387  0.083   0.078    0.068
## 9   simulation =~ tasit2_ssar     1     1     1 0.194  0.094   0.043    0.050
## 10  simulation =~ tasit2_psar     1     1     1 0.010  0.089   0.040    0.044
## 11  simulation =~  tasit3_sar     1     1     1 0.215 -0.098  -0.044   -0.054
## 12 mentalizing =~  er40_total     1     1     1 0.000  0.001   0.001    0.001
## 13 mentalizing =~  rmet_total     1     1     1 0.468  0.156   0.099    0.107
## 14 mentalizing =~     mean_ea     1     1     1 2.449 -2.511  -1.597   -1.712
## 15 mentalizing =~ tasit3_lies     1     1     1 1.149 -0.214  -0.136   -0.119
## 16  er40_total ~~  rmet_total     1     1     1 0.209 -0.048  -0.048   -0.086
## 17  er40_total ~~     mean_ea     1     1     1 3.498  0.387   0.387    0.473
## 18  er40_total ~~ tasit3_lies     1     1     1 0.021 -0.015  -0.015   -0.016
## 19  er40_total ~~ tasit2_ssar     1     1     1 0.035 -0.012  -0.012   -0.022
## 20  er40_total ~~ tasit2_psar     1     1     1 0.847 -0.057  -0.057   -0.124
## 21  er40_total ~~  tasit3_sar     1     1     1 2.470  0.089   0.089    0.192
## 22  rmet_total ~~     mean_ea     1     1     1 0.023  0.026   0.026    0.045
## 23  rmet_total ~~ tasit3_lies     1     1     1 0.713  0.081   0.081    0.121
## 24  rmet_total ~~ tasit2_ssar     1     1     1 1.223 -0.058  -0.058   -0.156
## 25  rmet_total ~~ tasit2_psar     1     1     1 0.009  0.005   0.005    0.016
## 26  rmet_total ~~  tasit3_sar     1     1     1 1.489  0.060   0.060    0.182
## 27     mean_ea ~~ tasit3_lies     1     1     1 1.049  0.251   0.251    0.254
## 28     mean_ea ~~ tasit2_ssar     1     1     1 0.224  0.072   0.072    0.132
## 29     mean_ea ~~ tasit2_psar     1     1     1 1.716 -0.190  -0.190   -0.396
## 30     mean_ea ~~  tasit3_sar     1     1     1 0.248 -0.067  -0.067   -0.139
## 31 tasit3_lies ~~ tasit2_ssar     1     1     1 0.043 -0.015  -0.015   -0.024
## 32 tasit3_lies ~~ tasit2_psar     1     1     1 0.951  0.069   0.069    0.124
## 33 tasit3_lies ~~  tasit3_sar     1     1     1 4.904 -0.145  -0.145   -0.259
## 34 tasit2_ssar ~~ tasit2_psar     1     1     1 2.866  0.093   0.093    0.305
## 35 tasit2_ssar ~~  tasit3_sar     1     1     1 0.010  0.005   0.005    0.017
## 36 tasit2_psar ~~  tasit3_sar     1     1     1 3.187 -0.097  -0.097   -0.359
## 37  simulation =~ tasit2_ssar     2     2     1 3.213 -0.274  -0.098   -0.193
## 38  simulation =~ tasit2_psar     2     2     1 0.026 -0.054  -0.019   -0.030
## 39  simulation =~  tasit3_sar     2     2     1 4.682  0.375   0.134    0.182
## 40 mentalizing =~  er40_total     2     2     1 1.737 -0.286  -0.095   -0.108
## 41 mentalizing =~  rmet_total     2     2     1 0.016  0.034   0.011    0.014
## 42 mentalizing =~     mean_ea     2     2     1 0.200  0.538   0.178    0.137
## 43 mentalizing =~ tasit3_lies     2     2     1 1.311  0.245   0.081    0.093
## 44  er40_total ~~  rmet_total     2     2     1 0.000 -0.001  -0.001   -0.002
## 45  er40_total ~~     mean_ea     2     2     1 0.489 -0.121  -0.121   -0.128
## 46  er40_total ~~ tasit3_lies     2     2     1 4.575  0.107   0.107    0.165
## 47  er40_total ~~ tasit2_ssar     2     2     1 1.091 -0.027  -0.027   -0.089
## 48  er40_total ~~ tasit2_psar     2     2     1 3.878 -0.065  -0.065   -0.177
## 49  er40_total ~~  tasit3_sar     2     2     1 3.232  0.072   0.072    0.137
## 50  rmet_total ~~     mean_ea     2     2     1 0.278 -0.089  -0.089   -0.123
## 51  rmet_total ~~ tasit3_lies     2     2     1 0.361 -0.032  -0.032   -0.065
## 52  rmet_total ~~ tasit2_ssar     2     2     1 0.769 -0.022  -0.022   -0.094
## 53  rmet_total ~~ tasit2_psar     2     2     1 3.107  0.058   0.058    0.205
## 54  rmet_total ~~  tasit3_sar     2     2     1 1.731  0.047   0.047    0.117
## 55     mean_ea ~~ tasit3_lies     2     2     1 1.405 -0.202  -0.202   -0.211
## 56     mean_ea ~~ tasit2_ssar     2     2     1 0.067  0.023   0.023    0.051
## 57     mean_ea ~~ tasit2_psar     2     2     1 0.835 -0.102  -0.102   -0.187
## 58     mean_ea ~~  tasit3_sar     2     2     1 0.150  0.053   0.053    0.068
## 59 tasit3_lies ~~ tasit2_ssar     2     2     1 0.012 -0.003  -0.003   -0.009
## 60 tasit3_lies ~~ tasit2_psar     2     2     1 0.001 -0.001  -0.001   -0.002
## 61 tasit3_lies ~~  tasit3_sar     2     2     1 0.937 -0.039  -0.039   -0.073
## 62 tasit2_ssar ~~ tasit2_psar     2     2     1 1.956 -0.042  -0.042   -0.234
## 63 tasit2_ssar ~~  tasit3_sar     2     2     1 0.327 -0.015  -0.015   -0.060
## 64 tasit2_psar ~~  tasit3_sar     2     2     1 3.603  0.057   0.057    0.187
## 65  simulation =~ tasit2_ssar     3     3     1 0.001 -0.003  -0.002   -0.002
## 66  simulation =~ tasit2_psar     3     3     1 7.928  0.419   0.258    0.232
## 67  simulation =~  tasit3_sar     3     3     1 4.038 -0.243  -0.149   -0.139
## 68 mentalizing =~  er40_total     3     3     1 0.266 -0.046  -0.043   -0.041
## 69 mentalizing =~  rmet_total     3     3     1 1.354  0.135   0.127    0.119
## 70 mentalizing =~     mean_ea     3     3     1 0.336  0.082   0.076    0.092
## 71 mentalizing =~ tasit3_lies     3     3     1 1.113 -0.091  -0.085   -0.085
## 72  er40_total ~~  rmet_total     3     3     1 0.159 -0.029  -0.029   -0.064
## 73  er40_total ~~     mean_ea     3     3     1 1.404  0.090   0.090    0.135
## 74  er40_total ~~ tasit3_lies     3     3     1 1.434  0.062   0.062    0.087
## 75  er40_total ~~ tasit2_ssar     3     3     1 1.708  0.057   0.057    0.101
## 76  er40_total ~~ tasit2_psar     3     3     1 0.121 -0.016  -0.016   -0.025
## 77  er40_total ~~  tasit3_sar     3     3     1 1.524 -0.049  -0.049   -0.106
## 78  rmet_total ~~     mean_ea     3     3     1 0.000 -0.001  -0.001   -0.003
## 79  rmet_total ~~ tasit3_lies     3     3     1 0.227 -0.031  -0.031   -0.069
## 80  rmet_total ~~ tasit2_ssar     3     3     1 0.495 -0.028  -0.028   -0.079
## 81  rmet_total ~~ tasit2_psar     3     3     1 0.451  0.027   0.027    0.069
## 82  rmet_total ~~  tasit3_sar     3     3     1 0.453  0.025   0.025    0.086
## 83     mean_ea ~~ tasit3_lies     3     3     1 2.709 -0.117  -0.117   -0.179
## 84     mean_ea ~~ tasit2_ssar     3     3     1 2.971 -0.107  -0.107   -0.205
## 85     mean_ea ~~ tasit2_psar     3     3     1 2.940  0.114   0.114    0.195
## 86     mean_ea ~~  tasit3_sar     3     3     1 0.044  0.012   0.012    0.028
## 87 tasit3_lies ~~ tasit2_ssar     3     3     1 0.009 -0.004  -0.004   -0.007
## 88 tasit3_lies ~~ tasit2_psar     3     3     1 8.444  0.128   0.128    0.206
## 89 tasit3_lies ~~  tasit3_sar     3     3     1 7.400 -0.102  -0.102   -0.226
## 90 tasit2_ssar ~~ tasit2_psar     3     3     1 0.605 -0.041  -0.041   -0.083
## 91 tasit2_ssar ~~  tasit3_sar     3     3     1 2.443  0.107   0.107    0.295
## 92 tasit2_psar ~~  tasit3_sar     3     3     1 0.350 -0.031  -0.031   -0.077
##    sepc.nox
## 1    -0.015
## 2     0.100
## 3     0.806
## 4    -0.479
## 5    -0.036
## 6    -0.273
## 7     0.048
## 8     0.068
## 9     0.050
## 10    0.044
## 11   -0.054
## 12    0.001
## 13    0.107
## 14   -1.712
## 15   -0.119
## 16   -0.086
## 17    0.473
## 18   -0.016
## 19   -0.022
## 20   -0.124
## 21    0.192
## 22    0.045
## 23    0.121
## 24   -0.156
## 25    0.016
## 26    0.182
## 27    0.254
## 28    0.132
## 29   -0.396
## 30   -0.139
## 31   -0.024
## 32    0.124
## 33   -0.259
## 34    0.305
## 35    0.017
## 36   -0.359
## 37   -0.193
## 38   -0.030
## 39    0.182
## 40   -0.108
## 41    0.014
## 42    0.137
## 43    0.093
## 44   -0.002
## 45   -0.128
## 46    0.165
## 47   -0.089
## 48   -0.177
## 49    0.137
## 50   -0.123
## 51   -0.065
## 52   -0.094
## 53    0.205
## 54    0.117
## 55   -0.211
## 56    0.051
## 57   -0.187
## 58    0.068
## 59   -0.009
## 60   -0.002
## 61   -0.073
## 62   -0.234
## 63   -0.060
## 64    0.187
## 65   -0.002
## 66    0.232
## 67   -0.139
## 68   -0.041
## 69    0.119
## 70    0.092
## 71   -0.085
## 72   -0.064
## 73    0.135
## 74    0.087
## 75    0.101
## 76   -0.025
## 77   -0.106
## 78   -0.003
## 79   -0.069
## 80   -0.079
## 81    0.069
## 82    0.086
## 83   -0.179
## 84   -0.205
## 85    0.195
## 86    0.028
## 87   -0.007
## 88    0.206
## 89   -0.226
## 90   -0.083
## 91    0.295
## 92   -0.077
      #  compare metric & scalar models 
        
        anova(CFA_sc_model1_grp_fit2_part2a, CFA_sc_model1_grp_fit3_part3a) # sig diff - did not pass scalar invariance
## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## 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
## CFA_sc_model1_grp_fit2_part2a 45 8745.8 9008.1  80.391                   
## CFA_sc_model1_grp_fit3_part3a 55 8764.0 8982.6 118.659     44.705      10
##                               Pr(>Chisq)    
## CFA_sc_model1_grp_fit2_part2a               
## CFA_sc_model1_grp_fit3_part3a  2.458e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
        modindices(CFA_sc_model1_grp_fit3_part3a , sort = TRUE, maximum.number = 10)
##             lhs op         rhs block group level    mi    epc sepc.lv sepc.all
## 178 tasit3_lies ~~ tasit2_psar     3     3     1 8.444  0.128   0.128    0.206
## 156  simulation =~ tasit2_psar     3     3     1 7.928  0.419   0.258    0.232
## 179 tasit3_lies ~~  tasit3_sar     3     3     1 7.400 -0.102  -0.102   -0.226
## 123 tasit3_lies ~~  tasit3_sar     1     1     1 4.904 -0.145  -0.145   -0.259
## 129  simulation =~  tasit3_sar     2     2     1 4.682  0.375   0.134    0.182
## 136  er40_total ~~ tasit3_lies     2     2     1 4.575  0.107   0.107    0.165
## 31  mentalizing =~ tasit2_ssar     2     2     1 4.403 -0.418  -0.138   -0.273
## 157  simulation =~  tasit3_sar     3     3     1 4.038 -0.243  -0.149   -0.139
## 138  er40_total ~~ tasit2_psar     2     2     1 3.878 -0.065  -0.065   -0.177
## 154 tasit2_psar ~~  tasit3_sar     2     2     1 3.603  0.057   0.057    0.187
##     sepc.nox
## 178    0.206
## 156    0.232
## 179   -0.226
## 123   -0.259
## 129    0.182
## 136    0.165
## 31    -0.273
## 157   -0.139
## 138   -0.177
## 154    0.187