Call Packages & Read Data

# ---- Packages ----
library(lavaan)
## This is lavaan 0.6-19
## lavaan is FREE software! Please report any bugs.
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(tidyr)
library(stringr)
library(knitr)
library(kableExtra)
## Warning: package 'kableExtra' was built under R version 4.5.1
## 
## Attaching package: 'kableExtra'
## The following object is masked from 'package:dplyr':
## 
##     group_rows
options(scipen = 999, digits = 3)


ScaledData <- read.csv(
  "C:/Users/woodph/OneDrive - University of Missouri/Documents/bartholow/May202025/ScaledVars.csv")

# Drink dummies (as given)
ScaledData$A <- 1 * (ScaledData$Drink == 100)
ScaledData$P <- 1 * (ScaledData$Drink == 1)
ScaledData$Both <- 1 * (ScaledData$ISD == 0)
ScaledData$IX <- ScaledData$A * ScaledData$Both

Best Fitting Model with AS and General Effects

Ascending and Descending factor variances vary

ModifiedModelFVI <- "
! regressions 
AS=~1.0*Antisac1+AN2*Antisac2+AN3*Antisac3
STR=~1.0*Stroop1+S2*Stroop2+S3*Stroop3
Keep=~1.0*Keeptrk1+K2*Keeptrk2+K3*Keeptrk3
Let=~1.0*Letmem1+L2*Letmem2+L3*Letmem3
NB=~1.0*Nback1+N2*Nback2+N3*Nback3
cat=~1.0*Catswt1+A2*Catswt2+A3*Catswt3
col=~1.0*Colswt1+O2*Colswt2+O3*Colswt3
Num=~1.0*Numswt1+U2*Numswt2+U3*Numswt3
EF1=~EFAntisac*Antisac1+EFStroop*Stroop1+EFKeeptrk*Keeptrk1+EFLetmem*Letmem1+EFNback*Nback1+
  EFCatswt*Catswt1+EFColswt*Colswt1+EFNumswt*Numswt1
EF2=~EFAntisac*Antisac2+EFStroop*Stroop2+EFKeeptrk*Keeptrk2+EFLetmem*Letmem2+EFNback*Nback2+
  EFCatswt*Catswt2+EFColswt*Colswt2+EFNumswt*Numswt2
EF3=~EFAntisac*Antisac3+EFStroop*Stroop3+EFKeeptrk*Keeptrk3+EFLetmem*Letmem3+EFNback*Nback3+
  EFCatswt*Catswt3+EFColswt*Colswt3+EFNumswt*Numswt3

UP1=~UPKeeptrk*Keeptrk1+start(0.38)*Keeptrk1+UPLetmem*Letmem1+UPNback*Nback1
UP2=~UPKeeptrk*Keeptrk2+start(0.65)*Keeptrk2+UPLetmem*Letmem2+UPNback*Nback2
UP3=~UPKeeptrk*Keeptrk3+UPLetmem*Letmem3+UPNback*Nback3

SW1=~SWCatswt*Catswt1+SWColswt*Colswt1+SWNumswt*Numswt1
SW2=~SWCatswt*Catswt2+SWColswt*Colswt2+SWNumswt*Numswt2
SW3=~SWCatswt*Catswt3+SWColswt*Colswt3+SWNumswt*Numswt3

EF1 ~ A__EF1*A
EF2 ~ A__EF2*A
EF3 ~ A__EF3*A
EF1 ~ P__EF1*P
EF2 ~ P__EF2*P
EF3 ~ P__EF3*P
EF3 ~ Both__EF3*Both
EF3 ~ IX__EF3*IX
UP1 ~ A__UP1*A
UP1 ~ P__UP1*P
UP2 ~ A__UP2*A
UP2 ~ P__UP2*P
UP3 ~ A__UP3*A
UP3 ~ P__UP3*P
UP3 ~ Both__UP3*Both
UP3 ~ IX__UP3*IX
SW1 ~ A__SW1*A
SW1 ~ P__SW1*P
SW2 ~ A__SW2*A
SW3 ~ P__SW3*P
SW2 ~ P__SW2*P
SW3 ~ A__SW3*A
SW3 ~ IX__SW3*IX
SW3 ~ Both__SW3*Both
#Task Modifications
Antisac1 ~ A_Antisac1*A
Antisac1 ~ P_Antisac1*P
Antisac2 ~ A_Antisac2*A
Antisac3 ~ P_Antisac3*P

Antisac2 ~ P_Antisac2*P
Antisac3 ~ A_Antisac3*A
Antisac3 ~ IX_Antisac3*IX
Antisac3 ~ Both_Antisac3*Both

! residuals, variances and covariances

!manifest variances
Antisac1 ~~ VAR_Antisac1*Antisac1
Antisac2 ~~ VAR_Antisac2*Antisac2
Antisac3 ~~ VAR_Antisac3*Antisac3
Stroop1 ~~ VAR_Stroop1*Stroop1
Stroop2 ~~ VAR_Stroop2*Stroop2
Stroop3 ~~ VAR_Stroop3*Stroop3
Keeptrk1 ~~ VAR_Keeptrk1*Keeptrk1
Keeptrk2 ~~ VAR_Keeptrk2*Keeptrk2
Keeptrk3 ~~ VAR_Keeptrk3*Keeptrk3
Letmem1 ~~ VAR_Letmem1*Letmem1
Letmem2 ~~ VAR_Letmem2*Letmem2
Letmem3 ~~ VAR_Letmem3*Letmem3
!Covariances of Letmem
!Letmem1 ~~ C_Letmem1_Letmem2*Letmem2
!Letmem1 ~~ C_Letmem1_Letmem3*Letmem3
!Letmem2 ~~ C_Letmem2_Letmem3*Letmem3
Nback1 ~~ VAR_Nback1*Nback1
Nback2 ~~ VAR_Nback2*Nback2
Nback3 ~~ VAR_Nback3*Nback3
Catswt1 ~~ VAR_Catswt1*Catswt1
Catswt2 ~~ VAR_Catswt2*Catswt2
Catswt3 ~~ VAR_Catswt3*Catswt3
Colswt1 ~~ VAR_Colswt1*Colswt1
Colswt2 ~~ VAR_Colswt2*Colswt2
Colswt3 ~~ VAR_Colswt3*Colswt3
Numswt1 ~~ VAR_Numswt1*Numswt1
Numswt2 ~~ VAR_Numswt2*Numswt2
Numswt3 ~~ VAR_Numswt3*Numswt3
!Task variances
AS ~~ VAR_AS*AS
STR ~~ VAR_STR*STR
Keep ~~ VAR_Keep*Keep
Let ~~ VAR_Let*Let
NB ~~ VAR_NB*NB
cat ~~ VAR_cat*cat
col ~~ VAR_col*col
Num ~~ VAR_Num*Num

!Superfactor Variances & Covariances
EF1 ~~ 1.0*EF1
EF2 ~~ 1.0*EF2
EF3 ~~ 1.0*EF3
EF1 ~~ 1*EF2
EF1 ~~ 1*EF3
EF2 ~~ 1*EF3
UP1 ~~ 1.0*UP1
UP2 ~~ 1.0*UP2
UP3 ~~ 1.0*UP3
UP1 ~~ 1*UP2
UP2 ~~ 1*UP3
UP1 ~~ 1*UP3
SW1 ~~ 1.0*SW1
SW2 ~~ 1.0*SW2
SW3 ~~ 1.0*SW3
SW1 ~~ 1*SW2
SW1 ~~ 1*SW3
SW2 ~~ 1*SW3
!Covariances of Updating with Switch
UP1 ~~ COV_UP1_SW1*SW1
UP2 ~~ COV_UP2_SW1*SW2
UP3 ~~ COV_UP3_SW1*SW3

! means

!Superfactor means for Ascending and Descending
EF2~const__EF2*1
EF3~const__EF3*1
UP2~const__UP2*1
UP3~const__UP3*1
SW2~const__SW2*1
SW3~const__SW3*1
!Task factor means
AS~0*1
STR~0*1
Keep~0*1
Let~0*1
NB~0*1
cat~0*1
col~0*1
Num~0*1
!Manifest Variable intercepts Free
Antisac1~Intercept*1;
Antisac2~Intercept*1;
Antisac3~Intercept*1;
Stroop1~Intercept*1;
Stroop2~Intercept*1;
Stroop3~Intercept*1;
Keeptrk1~Intercept*1;
Keeptrk2~Intercept*1;
Keeptrk3~Intercept*1;
Letmem1~Intercept*1;
Letmem2~Intercept*1;
Letmem3~Intercept*1;
Nback1~Intercept*1;
Nback2~Intercept*1;
Nback3~Intercept*1;
Catswt1~Intercept*1;
Catswt2~Intercept*1;
Catswt3~Intercept*1;
Colswt1~Intercept*1;
Colswt2~Intercept*1;
Colswt3~Intercept*1;
Numswt1~Intercept*1;
Numswt2~Intercept*1;
Numswt3~Intercept*1;
!Baseline superfactor means zeroed out
EF1~0*1;
EF2~NA*1;
EF3~NA*1;
UP1~0*1;
UP2~NA*1;
UP3~NA*1;
SW1~0*1;
SW2~NA*1;
SW3~NA*1;
"
GrowthModelResult<-lavaan(ModifiedModelFVI, data=ScaledData, fixed.x=TRUE, missing="FIML", 
                          control   = list(
                            optim.method = "NLMINB",        # try "NLMINB" if needed
                            optim.maxit  = 20000,         # raise iteration cap
                            rel.tol      = 1e-10,         # tighter convergence tolerance
                            ftol         = 1e-10          # function tolerance (if available in your lavaan)
                          ));
## Warning: lavaan->lav_object_post_check():  
##    covariance matrix of latent variables is not positive definite ; use 
##    lavInspect(fit, "cov.lv") to investigate.

Summary Statistics from Modified Model

summary(GrowthModelResult, fit.measures=TRUE,standardized=TRUE);
## Warning in pchisq(X2, df = df, ncp = ncp): NaNs produced
## Warning in pchisq(X2, df = df, ncp = ncp): NaNs produced
## lavaan 0.6-19 ended normally after 201 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       155
##   Number of equality constraints                    51
## 
##   Number of observations                           694
##   Number of missing patterns                       103
## 
## Model Test User Model:
##                                                       
##   Test statistic                               397.565
##   Degrees of freedom                               316
##   P-value (Chi-square)                           0.001
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4046.313
##   Degrees of freedom                               372
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.978
##   Tucker-Lewis Index (TLI)                       0.974
##                                                       
##   Robust Comparative Fit Index (CFI)             0.006
##   Robust Tucker-Lewis Index (TLI)               -0.170
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12348.847
##   Loglikelihood unrestricted model (H1)     -12150.064
##                                                       
##   Akaike (AIC)                               24905.693
##   Bayesian (BIC)                             25378.110
##   Sample-size adjusted Bayesian (SABIC)      25047.892
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.019
##   90 Percent confidence interval - lower         0.013
##   90 Percent confidence interval - upper         0.025
##   P-value H_0: RMSEA <= 0.050                    1.000
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   2.434
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: Robust RMSEA <= 0.050               NaN
##   P-value H_0: Robust RMSEA >= 0.080               NaN
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.056
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   AS =~                                                                 
##     Antisc1           1.000                               0.495    0.512
##     Antisc2  (AN2)    1.479    0.171    8.670    0.000    0.733    0.724
##     Antisc3  (AN3)    1.078    0.100   10.811    0.000    0.534    0.557
##   STR =~                                                                
##     Stroop1           1.000                               0.617    0.595
##     Stroop2   (S2)    0.847    0.160    5.293    0.000    0.523    0.600
##     Stroop3   (S3)    0.827    0.159    5.193    0.000    0.510    0.539
##   Keep =~                                                               
##     Keptrk1           1.000                               0.500    0.507
##     Keptrk2   (K2)    1.359    0.196    6.927    0.000    0.679    0.708
##     Keptrk3   (K3)    1.089    0.160    6.823    0.000    0.544    0.555
##   Let =~                                                                
##     Letmem1           1.000                               0.251    0.280
##     Letmem2   (L2)    2.426    0.980    2.475    0.013    0.609    0.594
##     Letmem3   (L3)    1.545    0.443    3.486    0.000    0.388    0.368
##   NB =~                                                                 
##     Nback1            1.000                               0.556    0.584
##     Nback2    (N2)    1.233    0.113   10.879    0.000    0.686    0.710
##     Nback3    (N3)    1.392    0.125   11.110    0.000    0.775    0.730
##   cat =~                                                                
##     Catswt1           1.000                               0.523    0.528
##     Catswt2   (A2)    0.718    0.255    2.811    0.005    0.376    0.388
##     Catswt3   (A3)    0.615    0.212    2.906    0.004    0.322    0.342
##   col =~                                                                
##     Colswt1           1.000                               0.309    0.294
##     Colswt2   (O2)    2.016    0.645    3.124    0.002    0.622    0.634
##     Colswt3   (O3)    1.143    0.280    4.084    0.000    0.353    0.396
##   Num =~                                                                
##     Numswt1           1.000                               0.428    0.419
##     Numswt2   (U2)    1.021    0.209    4.875    0.000    0.437    0.452
##     Numswt3   (U3)    1.018    0.179    5.681    0.000    0.435    0.455
##   EF1 =~                                                                
##     Antisc1 (EFAn)    0.600    0.052   11.531    0.000    0.602    0.622
##     Stroop1 (EFSt)    0.337    0.037    9.142    0.000    0.338    0.326
##     Keptrk1 (EFKp)    0.220    0.040    5.469    0.000    0.220    0.224
##     Letmem1 (EFLt)    0.276    0.042    6.537    0.000    0.277    0.309
##     Nback1  (EFNb)    0.380    0.038    9.926    0.000    0.381    0.400
##     Catswt1 (EFCt)    0.297    0.042    7.079    0.000    0.298    0.300
##     Colswt1 (EFCl)    0.230    0.042    5.492    0.000    0.231    0.220
##     Numswt1 (EFNm)    0.331    0.047    7.074    0.000    0.332    0.325
##   EF2 =~                                                                
##     Antisc2 (EFAn)    0.600    0.052   11.531    0.000    0.623    0.615
##     Stroop2 (EFSt)    0.337    0.037    9.142    0.000    0.350    0.402
##     Keptrk2 (EFKp)    0.220    0.040    5.469    0.000    0.228    0.238
##     Letmem2 (EFLt)    0.276    0.042    6.537    0.000    0.287    0.280
##     Nback2  (EFNb)    0.380    0.038    9.926    0.000    0.395    0.408
##     Catswt2 (EFCt)    0.297    0.042    7.079    0.000    0.308    0.318
##     Colswt2 (EFCl)    0.230    0.042    5.492    0.000    0.239    0.244
##     Numswt2 (EFNm)    0.331    0.047    7.074    0.000    0.343    0.356
##   EF3 =~                                                                
##     Antisc3 (EFAn)    0.600    0.052   11.531    0.000    0.614    0.640
##     Stroop3 (EFSt)    0.337    0.037    9.142    0.000    0.344    0.364
##     Keptrk3 (EFKp)    0.220    0.040    5.469    0.000    0.225    0.229
##     Letmem3 (EFLt)    0.276    0.042    6.537    0.000    0.283    0.268
##     Nback3  (EFNb)    0.380    0.038    9.926    0.000    0.389    0.366
##     Catswt3 (EFCt)    0.297    0.042    7.079    0.000    0.304    0.323
##     Colswt3 (EFCl)    0.230    0.042    5.492    0.000    0.236    0.264
##     Numswt3 (EFNm)    0.331    0.047    7.074    0.000    0.338    0.353
##   UP1 =~                                                                
##     Keptrk1 (UPKp)    0.396    0.037   10.718    0.000    0.397    0.403
##     Letmem1 (UPLt)    0.544    0.045   12.066    0.000    0.546    0.609
##     Nback1  (UPNb)    0.307    0.038    8.001    0.000    0.308    0.323
##   UP2 =~                                                                
##     Keptrk2 (UPKp)    0.396    0.037   10.718    0.000    0.486    0.507
##     Letmem2 (UPLt)    0.544    0.045   12.066    0.000    0.669    0.651
##     Nback2  (UPNb)    0.307    0.038    8.001    0.000    0.377    0.391
##   UP3 =~                                                                
##     Keptrk3 (UPKp)    0.396    0.037   10.718    0.000    0.471    0.480
##     Letmem3 (UPLt)    0.544    0.045   12.066    0.000    0.648    0.614
##     Nback3  (UPNb)    0.307    0.038    8.001    0.000    0.366    0.345
##   SW1 =~                                                                
##     Catswt1 (SWCt)    0.508    0.038   13.368    0.000    0.508    0.512
##     Colswt1 (SWCl)    0.544    0.037   14.724    0.000    0.545    0.519
##     Numswt1 (SWNm)    0.636    0.040   15.886    0.000    0.636    0.623
##   SW2 =~                                                                
##     Catswt2 (SWCt)    0.508    0.038   13.368    0.000    0.549    0.566
##     Colswt2 (SWCl)    0.544    0.037   14.724    0.000    0.588    0.600
##     Numswt2 (SWNm)    0.636    0.040   15.886    0.000    0.687    0.712
##   SW3 =~                                                                
##     Catswt3 (SWCt)    0.508    0.038   13.368    0.000    0.543    0.578
##     Colswt3 (SWCl)    0.544    0.037   14.724    0.000    0.582    0.653
##     Numswt3 (SWNm)    0.636    0.040   15.886    0.000    0.680    0.709
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   EF1 ~                                                                 
##     A     (A__EF1)    0.094    0.187    0.503    0.615    0.094    0.044
##   EF2 ~                                                                 
##     A     (A__EF2)    0.383    0.303    1.262    0.207    0.368    0.174
##   EF3 ~                                                                 
##     A     (A__EF3)   -0.176    0.339   -0.518    0.604   -0.172   -0.081
##   EF1 ~                                                                 
##     P     (P__EF1)   -0.103    0.191   -0.539    0.590   -0.103   -0.048
##   EF2 ~                                                                 
##     P     (P__EF2)   -0.308    0.285   -1.079    0.280   -0.297   -0.139
##   EF3 ~                                                                 
##     P     (P__EF3)   -0.168    0.262   -0.639    0.523   -0.164   -0.077
##     Both    (B__E)   -0.470    0.226   -2.077    0.038   -0.459   -0.230
##     IX     (IX__E)    0.222    0.432    0.514    0.607    0.217    0.083
##   UP1 ~                                                                 
##     A     (A__UP1)   -0.180    0.135   -1.335    0.182   -0.179   -0.085
##     P     (P__UP1)   -0.013    0.137   -0.097    0.923   -0.013   -0.006
##   UP2 ~                                                                 
##     A     (A__UP2)   -1.519    0.287   -5.289    0.000   -1.237   -0.584
##     P     (P__UP2)   -0.016    0.262   -0.060    0.952   -0.013   -0.006
##   UP3 ~                                                                 
##     A     (A__UP3)   -0.928    0.304   -3.052    0.002   -0.780   -0.368
##     P     (P__UP3)    0.100    0.229    0.438    0.661    0.084    0.039
##     Both    (B__U)    0.929    0.222    4.178    0.000    0.780    0.390
##     IX     (IX__U)    0.054    0.379    0.143    0.887    0.045    0.017
##   SW1 ~                                                                 
##     A     (A__SW1)   -0.064    0.116   -0.550    0.582   -0.064   -0.030
##     P     (P__SW1)    0.015    0.120    0.128    0.898    0.015    0.007
##   SW2 ~                                                                 
##     A     (A__SW2)   -0.756    0.210   -3.597    0.000   -0.699   -0.330
##   SW3 ~                                                                 
##     P     (P__SW3)    0.010    0.168    0.057    0.954    0.009    0.004
##   SW2 ~                                                                 
##     P     (P__SW2)    0.195    0.198    0.984    0.325    0.180    0.084
##   SW3 ~                                                                 
##     A     (A__SW3)   -0.060    0.216   -0.278    0.781   -0.056   -0.026
##     IX     (IX__S)   -0.411    0.271   -1.514    0.130   -0.384   -0.146
##     Both    (B__S)    0.825    0.157    5.242    0.000    0.772    0.386
##   Antisac1 ~                                                            
##     A       (A_A1)   -0.140    0.107   -1.316    0.188   -0.140   -0.068
##     P       (P_A1)    0.017    0.109    0.160    0.873    0.017    0.008
##   Antisac2 ~                                                            
##     A       (A_A2)   -0.870    0.191   -4.560    0.000   -0.870   -0.406
##   Antisac3 ~                                                            
##     P       (P_A3)    0.014    0.157    0.086    0.931    0.014    0.007
##   Antisac2 ~                                                            
##     P       (P_A2)    0.028    0.171    0.162    0.871    0.028    0.013
##   Antisac3 ~                                                            
##     A       (A_A3)   -0.555    0.202   -2.748    0.006   -0.555   -0.274
##     IX      (IX_A)   -0.095    0.280   -0.339    0.735   -0.095   -0.038
##     Both    (B_A3)    0.412    0.139    2.962    0.003    0.412    0.215
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .EF1 ~~                                                                
##    .EF2               1.000                               1.000    1.000
##    .EF3               1.000                               1.000    1.000
##  .EF2 ~~                                                                
##    .EF3               1.000                               1.000    1.000
##  .UP1 ~~                                                                
##    .UP2               1.000                               1.000    1.000
##  .UP2 ~~                                                                
##    .UP3               1.000                               1.000    1.000
##  .UP1 ~~                                                                
##    .UP3               1.000                               1.000    1.000
##  .SW1 ~~                                                                
##    .SW2               1.000                               1.000    1.000
##    .SW3               1.000                               1.000    1.000
##  .SW2 ~~                                                                
##    .SW3               1.000                               1.000    1.000
##  .UP1 ~~                                                                
##    .SW1  (COV_UP1)   -0.007    0.040   -0.165    0.869   -0.007   -0.007
##  .UP2 ~~                                                                
##    .SW2  (COV_UP2)    0.007    0.059    0.118    0.906    0.007    0.007
##  .UP3 ~~                                                                
##    .SW3  (COV_UP3)   -0.012    0.051   -0.235    0.815   -0.012   -0.012
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .EF2   (c__EF2)    0.871    0.128    6.819    0.000    0.838    0.838
##    .EF3   (c__EF3)    1.056    0.136    7.778    0.000    1.032    1.032
##    .UP2   (c__UP2)    0.604    0.164    3.673    0.000    0.491    0.491
##    .UP3   (c__UP3)    0.395    0.176    2.240    0.025    0.332    0.332
##    .SW2   (c__SW2)    0.170    0.126    1.347    0.178    0.157    0.157
##    .SW3   (c__SW3)   -0.053    0.129   -0.410    0.682   -0.049   -0.049
##     AS                0.000                               0.000    0.000
##     STR               0.000                               0.000    0.000
##     Keep              0.000                               0.000    0.000
##     Let               0.000                               0.000    0.000
##     NB                0.000                               0.000    0.000
##     cat               0.000                               0.000    0.000
##     col               0.000                               0.000    0.000
##     Num               0.000                               0.000    0.000
##    .Ants1   (Intr)    9.853    0.032  308.951    0.000    9.853   10.188
##    .Ants2   (Intr)    9.853    0.032  308.951    0.000    9.853    9.732
##    .Ants3   (Intr)    9.853    0.032  308.951    0.000    9.853   10.284
##    .Strp1   (Intr)    9.853    0.032  308.951    0.000    9.853    9.505
##    .Strp2   (Intr)    9.853    0.032  308.951    0.000    9.853   11.314
##    .Strp3   (Intr)    9.853    0.032  308.951    0.000    9.853   10.412
##    .Kptr1   (Intr)    9.853    0.032  308.951    0.000    9.853   10.001
##    .Kptr2   (Intr)    9.853    0.032  308.951    0.000    9.853   10.276
##    .Kptr3   (Intr)    9.853    0.032  308.951    0.000    9.853   10.043
##    .Ltmm1   (Intr)    9.853    0.032  308.951    0.000    9.853   10.985
##    .Ltmm2   (Intr)    9.853    0.032  308.951    0.000    9.853    9.601
##    .Ltmm3   (Intr)    9.853    0.032  308.951    0.000    9.853    9.343
##    .Nbck1   (Intr)    9.853    0.032  308.951    0.000    9.853   10.334
##    .Nbck2   (Intr)    9.853    0.032  308.951    0.000    9.853   10.200
##    .Nbck3   (Intr)    9.853    0.032  308.951    0.000    9.853    9.291
##    .Ctsw1   (Intr)    9.853    0.032  308.951    0.000    9.853    9.933
##    .Ctsw2   (Intr)    9.853    0.032  308.951    0.000    9.853   10.165
##    .Ctsw3   (Intr)    9.853    0.032  308.951    0.000    9.853   10.483
##    .Clsw1   (Intr)    9.853    0.032  308.951    0.000    9.853    9.396
##    .Clsw2   (Intr)    9.853    0.032  308.951    0.000    9.853   10.041
##    .Clsw3   (Intr)    9.853    0.032  308.951    0.000    9.853   11.050
##    .Nmsw1   (Intr)    9.853    0.032  308.951    0.000    9.853    9.647
##    .Nmsw2   (Intr)    9.853    0.032  308.951    0.000    9.853   10.205
##    .Nmsw3   (Intr)    9.853    0.032  308.951    0.000    9.853   10.284
##    .EF1               0.000                               0.000    0.000
##    .UP1               0.000                               0.000    0.000
##    .SW1               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Ant1  (VAR_A1)    0.329    0.029   11.417    0.000    0.329    0.352
##    .Ant2  (VAR_A2)    0.053    0.039    1.344    0.179    0.053    0.052
##    .Ant3  (VAR_A3)    0.188    0.024    7.883    0.000    0.188    0.204
##    .Str1  (VAR_S1)    0.579    0.080    7.198    0.000    0.579    0.539
##    .Str2  (VAR_S2)    0.363    0.062    5.869    0.000    0.363    0.478
##    .Str3  (VAR_S3)    0.516    0.061    8.395    0.000    0.516    0.576
##    .Kpt1  (VAR_K1)    0.515    0.049   10.585    0.000    0.515    0.531
##    .Kpt2  (VAR_K2)    0.201    0.065    3.083    0.002    0.201    0.218
##    .Kpt3  (VAR_K3)    0.411    0.051    8.015    0.000    0.411    0.427
##    .Ltm1  (VAR_L1)    0.368    0.034   10.987    0.000    0.368    0.458
##    .Ltm2  (VAR_L2)    0.206    0.131    1.579    0.114    0.206    0.196
##    .Ltm3  (VAR_L3)    0.492    0.059    8.302    0.000    0.492    0.442
##    .Nbc1 (VAR_Nb1)    0.361    0.034   10.710    0.000    0.361    0.397
##    .Nbc2 (VAR_Nb2)    0.206    0.041    4.996    0.000    0.206    0.221
##    .Nbc3 (VAR_Nb3)    0.263    0.048    5.507    0.000    0.263    0.234
##    .Cts1 (VAR_Ct1)    0.364    0.095    3.836    0.000    0.364    0.370
##    .Cts2 (VAR_Ct2)    0.436    0.064    6.777    0.000    0.436    0.464
##    .Cts3 (VAR_Ct3)    0.415    0.046    9.095    0.000    0.415    0.470
##    .Cls1 (VAR_Cl1)    0.655    0.048   13.695    0.000    0.655    0.595
##    .Cls2 (VAR_Cl2)    0.200    0.118    1.698    0.090    0.200    0.208
##    .Cls3 (VAR_Cl3)    0.295    0.041    7.263    0.000    0.295    0.371
##    .Nms1 (VAR_Nm1)    0.347    0.037    9.491    0.000    0.347    0.332
##    .Nms2 (VAR_Nm2)    0.198    0.035    5.583    0.000    0.198    0.213
##    .Nms3 (VAR_Nm3)    0.183    0.032    5.810    0.000    0.183    0.199
##     AS    (VAR_AS)    0.245    0.061    4.034    0.000    1.000    1.000
##     STR   (VAR_ST)    0.381    0.088    4.331    0.000    1.000    1.000
##     Keep  (VAR_Kp)    0.250    0.055    4.537    0.000    1.000    1.000
##     Let   (VAR_Lt)    0.063    0.041    1.524    0.127    1.000    1.000
##     NB    (VAR_NB)    0.310    0.045    6.928    0.000    1.000    1.000
##     cat   (VAR_ct)    0.274    0.102    2.688    0.007    1.000    1.000
##     col   (VAR_cl)    0.095    0.044    2.157    0.031    1.000    1.000
##     Num   (VAR_Nm)    0.183    0.052    3.541    0.000    1.000    1.000
##    .EF1               1.000                               0.994    0.994
##    .EF2               1.000                               0.927    0.927
##    .EF3               1.000                               0.955    0.955
##    .UP1               1.000                               0.993    0.993
##    .UP2               1.000                               0.662    0.662
##    .UP3               1.000                               0.706    0.706
##    .SW1               1.000                               0.999    0.999
##    .SW2               1.000                               0.856    0.856
##    .SW3               1.000                               0.875    0.875

StrongCH

strongCH <- '
CEF1 =~  l1*Antisac1 + l2*Stroop1 + l4*Keeptrk1 +  l5*Letmem1 + l6*Nback1 + l7*Catswt1 + l8*Colswt1 + l9*Numswt1
CEF2 =~  l1*Antisac2 + l2*Stroop2 + l4*Keeptrk2 +  l5*Letmem2 + l6*Nback2 + l7*Catswt2 + l8*Colswt2 + l9*Numswt2
CEF3 =~  l1*Antisac3 + l2*Stroop3 + l4*Keeptrk3 +  l5*Letmem3 + l6*Nback3 + l7*Catswt3 + l8*Colswt3 + l9*Numswt3

UPD1 =~  l10*Keeptrk1 + l11*Letmem1 + l12*Nback1
UPD2 =~  l10*Keeptrk2 + l11*Letmem2 + l12*Nback2
UPD3 =~  l10*Keeptrk3 + l11*Letmem3 + l12*Nback3

SHI1 =~  l13*Catswt1 + l14*Colswt1 + l15*Numswt1
SHI2 =~  l13*Catswt2 + l14*Colswt2 + l15*Numswt2
SHI3 =~  l13*Catswt3 + l14*Colswt3 + l15*Numswt3

#Cholesky decomposition on factor residual covariance matrix
CEF1 ~~ 0*CEF1
UPD1 ~~ 0*UPD1
SHI1 ~~ 0*SHI1

CEF2 ~~ 0*CEF2
UPD2 ~~ 0*UPD2
SHI2 ~~ 0*SHI2

CEF3 ~~ 0*CEF3
UPD3 ~~ 0*UPD3
SHI3 ~~ 0*SHI3

ch1CEF =~ NA*CEF1 + CEF2 + CEF3
ch2CEF =~ NA*CEF2 + CEF3
ch3CEF =~ NA*CEF3
ch1CEF ~~ 1*ch1CEF
ch2CEF ~~ 1*ch2CEF
ch3CEF ~~ 1*ch3CEF

ch1UPD =~ NA*UPD1 + UPD2 + UPD3
ch2UPD =~ NA*UPD2 + UPD3
ch3UPD =~ NA*UPD3
ch1UPD ~~ 1*ch1UPD
ch2UPD ~~ 1*ch2UPD
ch3UPD ~~ 1*ch3UPD

ch1SHI =~ NA*SHI1 + SHI2 + SHI3
ch2SHI =~ NA*SHI2 + SHI3
ch3SHI =~ NA*SHI3
ch1SHI ~~ 1*ch1SHI
ch2SHI ~~ 1*ch2SHI
ch3SHI ~~ 1*ch3SHI

Antisac1 ~~ Antisac2 + Antisac3
Antisac2 ~~ Antisac3
Stroop1 ~~ Stroop2 + Stroop3
Stroop2 ~~ Stroop3
Keeptrk1 ~~ Keeptrk2 + Keeptrk3
Keeptrk2 ~~ Keeptrk3
Letmem1 ~~ Letmem2 + Letmem3
Letmem2 ~~ Letmem3
Nback1 ~~ Nback2 + Nback3
Nback2 ~~ Nback3
Catswt1 ~~ Catswt2 + Catswt3
Catswt2 ~~ Catswt3
Colswt1 ~~ Colswt2 + Colswt3
Colswt2 ~~ Colswt3
Numswt1 ~~ Numswt2 + Numswt3
Numswt2 ~~ Numswt3

CEF1 + CEF2 + CEF3 ~ A + P
UPD1 + UPD2 + UPD3 ~ A + P
SHI1 + SHI2 + SHI3 ~ A + P
CEF3 + UPD3 + SHI3 ~ Both + IX

#constrain intercepts
Antisac1 + Antisac2 + Antisac3 ~ m1*1
Stroop1 + Stroop2 + Stroop3 ~ m2*1
Keeptrk1 + Keeptrk2 + Keeptrk3 ~ m4*1
Letmem1 + Letmem2 + Letmem3 ~ m5*1
Nback1 + Nback2 + Nback3 ~ m6*1
Catswt1 + Catswt2 + Catswt3 ~ m7*1
Colswt1 + Colswt2 + Colswt3 ~ m8*1
Numswt1 + Numswt2 + Numswt3 ~ m9*1
CEF1 ~ 0*1
CEF2 ~ 1
CEF3 ~ 1

UPD1 ~ 0*1
UPD2 ~ 1
UPD3 ~ 1

SHI1 ~ 0*1
SHI2 ~ 1
SHI3 ~ 1
'

StrongCH Fit

fit_strongCH <- sem(strongCH, data = ScaledData,
                    missing = "ML", orthogonal = TRUE)
summary(fit_strongCH, fit.measures=TRUE,standardized=TRUE);
## Warning in pchisq(X2, df = df, ncp = ncp): NaNs produced
## Warning in pchisq(X2, df = df, ncp = ncp): NaNs produced
## lavaan 0.6-19 ended normally after 153 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       153
##   Number of equality constraints                    38
## 
##   Number of observations                           694
##   Number of missing patterns                       103
## 
## Model Test User Model:
##                                                       
##   Test statistic                               402.503
##   Degrees of freedom                               305
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4046.313
##   Degrees of freedom                               372
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.973
##   Tucker-Lewis Index (TLI)                       0.968
##                                                       
##   Robust Comparative Fit Index (CFI)             0.006
##   Robust Tucker-Lewis Index (TLI)               -0.212
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12351.316
##   Loglikelihood unrestricted model (H1)     -12150.064
##                                                       
##   Akaike (AIC)                               24932.632
##   Bayesian (BIC)                             25455.016
##   Sample-size adjusted Bayesian (SABIC)      25089.871
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.021
##   90 Percent confidence interval - lower         0.015
##   90 Percent confidence interval - upper         0.027
##   P-value H_0: RMSEA <= 0.050                    1.000
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   2.478
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: Robust RMSEA <= 0.050               NaN
##   P-value H_0: Robust RMSEA >= 0.080               NaN
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.057
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   CEF1 =~                                                               
##     Antisac1  (l1)    1.000                               0.595    0.617
##     Stroop1   (l2)    0.461    0.066    7.014    0.000    0.274    0.266
##     Keeptrk1  (l4)    0.424    0.111    3.820    0.000    0.252    0.255
##     Letmem1   (l5)    0.460    0.090    5.101    0.000    0.274    0.306
##     Nback1    (l6)    0.662    0.107    6.178    0.000    0.393    0.418
##     Catswt1   (l7)    0.429    0.074    5.782    0.000    0.255    0.256
##     Colswt1   (l8)    0.351    0.082    4.287    0.000    0.209    0.197
##     Numswt1   (l9)    0.574    0.104    5.528    0.000    0.341    0.330
##   CEF2 =~                                                               
##     Antisac2  (l1)    1.000                               0.720    0.714
##     Stroop2   (l2)    0.461    0.066    7.014    0.000    0.332    0.375
##     Keeptrk2  (l4)    0.424    0.111    3.820    0.000    0.305    0.316
##     Letmem2   (l5)    0.460    0.090    5.101    0.000    0.331    0.320
##     Nback2    (l6)    0.662    0.107    6.178    0.000    0.476    0.481
##     Catswt2   (l7)    0.429    0.074    5.782    0.000    0.309    0.323
##     Colswt2   (l8)    0.351    0.082    4.287    0.000    0.253    0.258
##     Numswt2   (l9)    0.574    0.104    5.528    0.000    0.413    0.433
##   CEF3 =~                                                               
##     Antisac3  (l1)    1.000                               0.687    0.727
##     Stroop3   (l2)    0.461    0.066    7.014    0.000    0.316    0.332
##     Keeptrk3  (l4)    0.424    0.111    3.820    0.000    0.291    0.298
##     Letmem3   (l5)    0.460    0.090    5.101    0.000    0.316    0.300
##     Nback3    (l6)    0.662    0.107    6.178    0.000    0.454    0.424
##     Catswt3   (l7)    0.429    0.074    5.782    0.000    0.294    0.315
##     Colswt3   (l8)    0.351    0.082    4.287    0.000    0.241    0.275
##     Numswt3   (l9)    0.574    0.104    5.528    0.000    0.394    0.417
##   UPD1 =~                                                               
##     Keeptrk1 (l10)    1.000                               0.346    0.350
##     Letmem1  (l11)    1.795    0.515    3.483    0.000    0.621    0.694
##     Nback1   (l12)    0.664    0.141    4.704    0.000    0.230    0.244
##   UPD2 =~                                                               
##     Keeptrk2 (l10)    1.000                               0.392    0.407
##     Letmem2  (l11)    1.795    0.515    3.483    0.000    0.705    0.680
##     Nback2   (l12)    0.664    0.141    4.704    0.000    0.261    0.263
##   UPD3 =~                                                               
##     Keeptrk3 (l10)    1.000                               0.371    0.380
##     Letmem3  (l11)    1.795    0.515    3.483    0.000    0.666    0.633
##     Nback3   (l12)    0.664    0.141    4.704    0.000    0.247    0.230
##   SHI1 =~                                                               
##     Catswt1  (l13)    1.000                               0.565    0.566
##     Colswt1  (l14)    1.080    0.101   10.694    0.000    0.610    0.575
##     Numswt1  (l15)    1.150    0.115   10.008    0.000    0.650    0.628
##   SHI2 =~                                                               
##     Catswt2  (l13)    1.000                               0.503    0.525
##     Colswt2  (l14)    1.080    0.101   10.694    0.000    0.543    0.555
##     Numswt2  (l15)    1.150    0.115   10.008    0.000    0.578    0.605
##   SHI3 =~                                                               
##     Catswt3  (l13)    1.000                               0.520    0.556
##     Colswt3  (l14)    1.080    0.101   10.694    0.000    0.562    0.641
##     Numswt3  (l15)    1.150    0.115   10.008    0.000    0.598    0.632
##   ch1CEF =~                                                             
##     CEF1              0.595    0.061    9.808    0.000    1.000    1.000
##     CEF2              0.637    0.073    8.679    0.000    0.885    0.885
##     CEF3              0.593    0.065    9.185    0.000    0.864    0.864
##   ch2CEF =~                                                             
##     CEF2              0.284    0.066    4.317    0.000    0.395    0.395
##     CEF3              0.179    0.074    2.402    0.016    0.260    0.260
##   ch3CEF =~                                                             
##     CEF3             -0.188    0.063   -2.995    0.003   -0.273   -0.273
##   ch1UPD =~                                                             
##     UPD1              0.346    0.063    5.488    0.000    0.999    0.999
##     UPD2              0.373    0.079    4.696    0.000    0.951    0.951
##     UPD3              0.351    0.069    5.112    0.000    0.946    0.946
##   ch2UPD =~                                                             
##     UPD2              0.000    0.106    0.000    1.000    0.000    0.000
##     UPD3              0.000    0.134    0.000    1.000    0.000    0.000
##   ch3UPD =~                                                             
##     UPD3             -0.000    0.104   -0.000    1.000   -0.000   -0.000
##   ch1SHI =~                                                             
##     SHI1              0.565    0.043   13.125    0.000    1.000    1.000
##     SHI2              0.488    0.050    9.663    0.000    0.971    0.971
##     SHI3              0.480    0.042   11.516    0.000    0.923    0.923
##   ch2SHI =~                                                             
##     SHI2              0.093    0.060    1.544    0.123    0.185    0.185
##     SHI3             -0.162    0.051   -3.195    0.001   -0.312   -0.312
##   ch3SHI =~                                                             
##     SHI3              0.000    0.343    0.000    1.000    0.000    0.000
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   CEF1 ~                                                                
##     A                 0.009    0.082    0.112    0.911    0.016    0.007
##     P                -0.001    0.083   -0.013    0.990   -0.002   -0.001
##   CEF2 ~                                                                
##     A                -0.416    0.121   -3.448    0.001   -0.578   -0.273
##     P                -0.116    0.112   -1.034    0.301   -0.161   -0.075
##   CEF3 ~                                                                
##     A                -0.552    0.116   -4.759    0.000   -0.804   -0.380
##     P                -0.060    0.095   -0.628    0.530   -0.087   -0.041
##   UPD1 ~                                                                
##     A                -0.001    0.046   -0.014    0.989   -0.002   -0.001
##     P                 0.026    0.047    0.564    0.573    0.076    0.036
##   UPD2 ~                                                                
##     A                -0.249    0.099   -2.532    0.011   -0.636   -0.300
##     P                 0.015    0.076    0.196    0.844    0.038    0.018
##   UPD3 ~                                                                
##     A                -0.087    0.109   -0.805    0.421   -0.235   -0.111
##     P                 0.073    0.063    1.169    0.243    0.198    0.093
##   SHI1 ~                                                                
##     A                -0.024    0.070   -0.348    0.728   -0.043   -0.020
##     P                -0.029    0.071   -0.412    0.681   -0.051   -0.024
##   SHI2 ~                                                                
##     A                -0.125    0.093   -1.342    0.179   -0.249   -0.118
##     P                 0.060    0.089    0.678    0.498    0.120    0.056
##   SHI3 ~                                                                
##     A                 0.158    0.100    1.579    0.114    0.304    0.144
##     P                -0.019    0.072   -0.269    0.788   -0.037   -0.017
##   CEF3 ~                                                                
##     Both              0.075    0.074    1.013    0.311    0.109    0.055
##     IX                0.104    0.129    0.809    0.419    0.152    0.058
##   UPD3 ~                                                                
##     Both              0.205    0.063    3.271    0.001    0.552    0.276
##     IX               -0.002    0.100   -0.019    0.985   -0.005   -0.002
##   SHI3 ~                                                                
##     Both              0.275    0.058    4.755    0.000    0.529    0.264
##     IX               -0.211    0.101   -2.094    0.036   -0.405   -0.154
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .Antisac1 ~~                                                           
##    .Antisac2          0.352    0.074    4.766    0.000    0.352    0.657
##    .Antisac3          0.271    0.066    4.106    0.000    0.271    0.550
##  .Antisac2 ~~                                                           
##    .Antisac3          0.342    0.085    4.045    0.000    0.342    0.748
##  .Stroop1 ~~                                                            
##    .Stroop2           0.345    0.054    6.447    0.000    0.345    0.424
##    .Stroop3           0.342    0.047    7.211    0.000    0.342    0.383
##  .Stroop2 ~~                                                            
##    .Stroop3           0.290    0.054    5.361    0.000    0.290    0.393
##  .Keeptrk1 ~~                                                           
##    .Keeptrk2          0.366    0.058    6.259    0.000    0.366    0.503
##    .Keeptrk3          0.298    0.049    6.087    0.000    0.298    0.394
##  .Keeptrk2 ~~                                                           
##    .Keeptrk3          0.383    0.056    6.797    0.000    0.383    0.553
##  .Letmem1 ~~                                                            
##    .Letmem2           0.044    0.114    0.390    0.696    0.044    0.115
##    .Letmem3           0.006    0.109    0.054    0.957    0.006    0.014
##  .Letmem2 ~~                                                            
##    .Letmem3           0.113    0.124    0.908    0.364    0.113    0.234
##  .Nback1 ~~                                                             
##    .Nback2            0.393    0.048    8.178    0.000    0.393    0.585
##    .Nback3            0.452    0.045   10.053    0.000    0.452    0.590
##  .Nback2 ~~                                                             
##    .Nback3            0.526    0.060    8.771    0.000    0.526    0.692
##  .Catswt1 ~~                                                            
##    .Catswt2           0.187    0.053    3.510    0.000    0.187    0.321
##    .Catswt3           0.176    0.039    4.552    0.000    0.176    0.314
##  .Catswt2 ~~                                                            
##    .Catswt3           0.140    0.048    2.916    0.004    0.140    0.260
##  .Colswt1 ~~                                                            
##    .Colswt2           0.184    0.052    3.510    0.000    0.184    0.284
##    .Colswt3           0.103    0.039    2.637    0.008    0.103    0.194
##  .Colswt2 ~~                                                            
##    .Colswt3           0.250    0.047    5.355    0.000    0.250    0.517
##  .Numswt1 ~~                                                            
##    .Numswt2           0.218    0.046    4.703    0.000    0.218    0.478
##    .Numswt3           0.227    0.040    5.689    0.000    0.227    0.502
##  .Numswt2 ~~                                                            
##    .Numswt3           0.251    0.048    5.281    0.000    0.251    0.647
##   ch1CEF ~~                                                             
##     ch2CEF            0.000                               0.000    0.000
##     ch3CEF            0.000                               0.000    0.000
##     ch1UPD            0.000                               0.000    0.000
##     ch2UPD            0.000                               0.000    0.000
##     ch3UPD            0.000                               0.000    0.000
##     ch1SHI            0.000                               0.000    0.000
##     ch2SHI            0.000                               0.000    0.000
##     ch3SHI            0.000                               0.000    0.000
##   ch2CEF ~~                                                             
##     ch3CEF            0.000                               0.000    0.000
##     ch1UPD            0.000                               0.000    0.000
##     ch2UPD            0.000                               0.000    0.000
##     ch3UPD            0.000                               0.000    0.000
##     ch1SHI            0.000                               0.000    0.000
##     ch2SHI            0.000                               0.000    0.000
##     ch3SHI            0.000                               0.000    0.000
##   ch3CEF ~~                                                             
##     ch1UPD            0.000                               0.000    0.000
##     ch2UPD            0.000                               0.000    0.000
##     ch3UPD            0.000                               0.000    0.000
##     ch1SHI            0.000                               0.000    0.000
##     ch2SHI            0.000                               0.000    0.000
##     ch3SHI            0.000                               0.000    0.000
##   ch1UPD ~~                                                             
##     ch2UPD            0.000                               0.000    0.000
##     ch3UPD            0.000                               0.000    0.000
##     ch1SHI            0.000                               0.000    0.000
##     ch2SHI            0.000                               0.000    0.000
##     ch3SHI            0.000                               0.000    0.000
##   ch2UPD ~~                                                             
##     ch3UPD            0.000                               0.000    0.000
##     ch1SHI            0.000                               0.000    0.000
##     ch2SHI            0.000                               0.000    0.000
##     ch3SHI            0.000                               0.000    0.000
##   ch3UPD ~~                                                             
##     ch1SHI            0.000                               0.000    0.000
##     ch2SHI            0.000                               0.000    0.000
##     ch3SHI            0.000                               0.000    0.000
##   ch1SHI ~~                                                             
##     ch2SHI            0.000                               0.000    0.000
##     ch3SHI            0.000                               0.000    0.000
##   ch2SHI ~~                                                             
##     ch3SHI            0.000                               0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Antisac1  (m1)    9.772    0.060  164.163    0.000    9.772   10.137
##    .Antisac2  (m1)    9.772    0.060  164.163    0.000    9.772    9.697
##    .Antisac3  (m1)    9.772    0.060  164.163    0.000    9.772   10.348
##    .Stroop1   (m2)    9.902    0.043  231.418    0.000    9.902    9.627
##    .Stroop2   (m2)    9.902    0.043  231.418    0.000    9.902   11.189
##    .Stroop3   (m2)    9.902    0.043  231.418    0.000    9.902   10.382
##    .Keeptrk1  (m4)    9.830    0.045  217.311    0.000    9.830    9.938
##    .Keeptrk2  (m4)    9.830    0.045  217.311    0.000    9.830   10.191
##    .Keeptrk3  (m4)    9.830    0.045  217.311    0.000    9.830   10.060
##    .Letmem1   (m5)    9.769    0.057  170.529    0.000    9.769   10.912
##    .Letmem2   (m5)    9.769    0.057  170.529    0.000    9.769    9.432
##    .Letmem3   (m5)    9.769    0.057  170.529    0.000    9.769    9.281
##    .Nback1    (m6)    9.805    0.047  208.920    0.000    9.805   10.414
##    .Nback2    (m6)    9.805    0.047  208.920    0.000    9.805    9.906
##    .Nback3    (m6)    9.805    0.047  208.920    0.000    9.805    9.154
##    .Catswt1   (m7)    9.878    0.054  183.189    0.000    9.878    9.904
##    .Catswt2   (m7)    9.878    0.054  183.189    0.000    9.878   10.323
##    .Catswt3   (m7)    9.878    0.054  183.189    0.000    9.878   10.569
##    .Colswt1   (m8)    9.890    0.056  175.283    0.000    9.890    9.328
##    .Colswt2   (m8)    9.890    0.056  175.283    0.000    9.890   10.112
##    .Colswt3   (m8)    9.890    0.056  175.283    0.000    9.890   11.281
##    .Numswt1   (m9)    9.838    0.060  162.845    0.000    9.838    9.516
##    .Numswt2   (m9)    9.838    0.060  162.845    0.000    9.838   10.297
##    .Numswt3   (m9)    9.838    0.060  162.845    0.000    9.838   10.401
##    .CEF1              0.000                               0.000    0.000
##    .CEF2              0.547    0.070    7.829    0.000    0.760    0.760
##    .CEF3              0.686    0.067   10.228    0.000    0.999    0.999
##    .UPD1              0.000                               0.000    0.000
##    .UPD2              0.196    0.084    2.345    0.019    0.500    0.500
##    .UPD3              0.092    0.092    0.997    0.319    0.247    0.247
##    .SHI1              0.000                               0.000    0.000
##    .SHI2              0.084    0.070    1.188    0.235    0.167    0.167
##    .SHI3             -0.050    0.077   -0.648    0.517   -0.096   -0.096
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .CEF1              0.000                               0.000    0.000
##    .UPD1              0.000                               0.000    0.000
##    .SHI1              0.000                               0.000    0.000
##    .CEF2              0.000                               0.000    0.000
##    .UPD2              0.000                               0.000    0.000
##    .SHI2              0.000                               0.000    0.000
##    .CEF3              0.000                               0.000    0.000
##    .UPD3              0.000                               0.000    0.000
##    .SHI3              0.000                               0.000    0.000
##     ch1CEF            1.000                               1.000    1.000
##     ch2CEF            1.000                               1.000    1.000
##     ch3CEF            1.000                               1.000    1.000
##     ch1UPD            1.000                               1.000    1.000
##     ch2UPD            1.000                               1.000    1.000
##     ch3UPD            1.000                               1.000    1.000
##     ch1SHI            1.000                               1.000    1.000
##     ch2SHI            1.000                               1.000    1.000
##     ch3SHI            1.000                               1.000    1.000
##    .Antisac1          0.576    0.070    8.269    0.000    0.576    0.619
##    .Stroop1           0.983    0.056   17.513    0.000    0.983    0.929
##    .Keeptrk1          0.795    0.054   14.791    0.000    0.795    0.813
##    .Letmem1           0.341    0.107    3.196    0.001    0.341    0.425
##    .Nback1            0.679    0.042   16.232    0.000    0.679    0.766
##    .Catswt1           0.611    0.045   13.669    0.000    0.611    0.614
##    .Colswt1           0.708    0.052   13.526    0.000    0.708    0.630
##    .Numswt1           0.530    0.047   11.289    0.000    0.530    0.496
##    .Antisac2          0.497    0.104    4.804    0.000    0.497    0.490
##    .Stroop2           0.673    0.070    9.577    0.000    0.673    0.859
##    .Keeptrk2          0.666    0.074    9.029    0.000    0.666    0.716
##    .Letmem2           0.433    0.140    3.094    0.002    0.433    0.404
##    .Nback2            0.667    0.072    9.274    0.000    0.667    0.681
##    .Catswt2           0.558    0.071    7.814    0.000    0.558    0.610
##    .Colswt2           0.590    0.073    8.107    0.000    0.590    0.616
##    .Numswt2           0.393    0.063    6.214    0.000    0.393    0.431
##    .Antisac3          0.420    0.083    5.070    0.000    0.420    0.471
##    .Stroop3           0.810    0.061   13.182    0.000    0.810    0.890
##    .Keeptrk3          0.718    0.060   11.873    0.000    0.718    0.752
##    .Letmem3           0.536    0.130    4.133    0.000    0.536    0.483
##    .Nback3            0.865    0.068   12.705    0.000    0.865    0.754
##    .Catswt3           0.518    0.048   10.748    0.000    0.518    0.593
##    .Colswt3           0.397    0.044    9.120    0.000    0.397    0.516
##    .Numswt3           0.384    0.047    8.150    0.000    0.384    0.430

Model fit indices (unscaled). ΔBIC (Modified FVI − Strong CH) = -82.977.
Measure Modified FVI Strong CH ChiSq 411.121 402.503 df 319 305 p 0 0 CFI 0.975 0.973 TLI 0.971 0.968 RMSEA 0.02 0.021 SRMR 0.057 0.057 AIC 24913.25 24932.632 BIC 25372.039 25455.016