CFA and EFA model testing
In this project, I will conduct a measurement model and a structural model to investigate the relationship between executive function components and the two types of category learning. The data of this project was inherited from previous lab member’s dissertation work.
Data preprocessing
library(dplyr)
library(lavaan)
library(semPlot)
library(data.table)#to get path to folder, cmd+opt+c
setwd('/Users/tzhu9/Documents/OneDrive - The University of Western Ontario/Grad School Course Work/9555/Assignment/Project')
data<-read.csv('sarahdata.csv')
data<-select(data,
"Subj",
"Antisaccade",
#"Stroop",
"StroopPerf",
"SSRTavg",
"LetMem",
"KeepTrack",
"SpatialBack",
"NumLett",
#"NumLetPerf",
"ColShape",
#"ColShapePerf",
"CatSwitch",
#"CatSwitchPerf",
"FR1", "FR2", "FR3", "FR4",
"SD1", "SD2", "SD3", "SD4")
head(data)#think about how to simulate 3 columns based on previous trajectory#convert Subj variable from numeric to factor
data$Subj<-as.factor(data$Subj)#Standardize all columns in the data, except for Subj
data[,-c(1)]<-scale(data[,-c(1)])
head(data)Confirmatory Factor Analysis
Three factor CFA based on Miyake et al., (2000)
cfa3f<-'
Inhibit=~StroopPerf+SSRTavg+Antisaccade
Update=~KeepTrack+SpatialBack+LetMem
Shift=~ NumLett+ColShape+CatSwitch
'Three factor model fit
Previous analysis used listwise deletion to handle missing data, which led to a loss of 70 Subj (i.e., more than 1/3 of total Subj). The current analysis adopted Miximum Likelihood estimation.
cfa3f_fit <- cfa(cfa3f, data, std.lv=TRUE, missing='ml')
summary(cfa3f_fit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 29 iterations
##
## Optimization method NLMINB
## Number of free parameters 30
##
## Number of observations 176
## Number of missing patterns 19
##
## Estimator ML
## Model Fit Test Statistic 23.986
## Degrees of freedom 24
## P-value (Chi-square) 0.462
##
## Model test baseline model:
##
## Minimum Function Test Statistic 189.969
## Degrees of freedom 36
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2016.781
## Loglikelihood unrestricted model (H1) -2004.788
##
## Number of free parameters 30
## Akaike (AIC) 4093.561
## Bayesian (BIC) 4188.676
## Sample-size adjusted Bayesian (BIC) 4093.673
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.061
## P-value RMSEA <= 0.05 0.876
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.047
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit =~
## StroopPerf 0.164 0.100 1.647 0.100 0.164 0.165
## SSRTavg 0.152 0.110 1.381 0.167 0.152 0.153
## Antisaccade 0.711 0.225 3.156 0.002 0.711 0.713
## Update =~
## KeepTrack 0.420 0.106 3.977 0.000 0.420 0.421
## SpatialBack 0.515 0.121 4.272 0.000 0.515 0.510
## LetMem 0.221 0.102 2.161 0.031 0.221 0.221
## Shift =~
## NumLett 0.766 0.082 9.288 0.000 0.766 0.767
## ColShape 0.710 0.081 8.753 0.000 0.710 0.713
## CatSwitch 0.519 0.083 6.260 0.000 0.519 0.520
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit ~~
## Update 0.922 0.309 2.981 0.003 0.922 0.922
## Shift 0.576 0.196 2.935 0.003 0.576 0.576
## Update ~~
## Shift 0.672 0.150 4.474 0.000 0.672 0.672
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.075 0.000 1.000 0.000 0.000
## .SSRTavg -0.007 0.084 -0.089 0.929 -0.007 -0.007
## .Antisaccade -0.024 0.078 -0.311 0.755 -0.024 -0.024
## .KeepTrack -0.009 0.077 -0.116 0.908 -0.009 -0.009
## .SpatialBack -0.048 0.084 -0.573 0.566 -0.048 -0.048
## .LetMem -0.000 0.075 -0.006 0.995 -0.000 -0.000
## .NumLett -0.015 0.076 -0.199 0.842 -0.015 -0.015
## .ColShape -0.000 0.075 -0.001 0.999 -0.000 -0.000
## .CatSwitch -0.004 0.076 -0.050 0.961 -0.004 -0.004
## Inhibit 0.000 0.000 0.000
## Update 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.967 0.105 9.179 0.000 0.967 0.973
## .SSRTavg 0.969 0.118 8.237 0.000 0.969 0.977
## .Antisaccade 0.489 0.309 1.582 0.114 0.489 0.492
## .KeepTrack 0.819 0.109 7.480 0.000 0.819 0.823
## .SpatialBack 0.754 0.122 6.181 0.000 0.754 0.740
## .LetMem 0.945 0.106 8.944 0.000 0.945 0.951
## .NumLett 0.410 0.090 4.536 0.000 0.410 0.411
## .ColShape 0.489 0.087 5.644 0.000 0.489 0.492
## .CatSwitch 0.726 0.090 8.058 0.000 0.726 0.730
## Inhibit 1.000 1.000 1.000
## Update 1.000 1.000 1.000
## Shift 1.000 1.000 1.000
##
## R-Square:
## Estimate
## StroopPerf 0.027
## SSRTavg 0.023
## Antisaccade 0.508
## KeepTrack 0.177
## SpatialBack 0.260
## LetMem 0.049
## NumLett 0.589
## ColShape 0.508
## CatSwitch 0.270Fit indices indicated good model fit. However, covariance between Inhibit and Shift is .92. Question, should we see them as separate latent variables?
A visual representation of the three factor model
semPaths(cfa3f_fit, 'std', layout='tree')
Two factor CFA, combining Inhibit and Update
cfa2f<-'
Inhibit=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~ NumLett+ColShape+CatSwitch
'
cfa2f_fit <- cfa(cfa2f, std.lv=T, data, missing='ml')
summary(cfa2f_fit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 18 iterations
##
## Optimization method NLMINB
## Number of free parameters 28
##
## Number of observations 176
## Number of missing patterns 19
##
## Estimator ML
## Model Fit Test Statistic 24.146
## Degrees of freedom 26
## P-value (Chi-square) 0.568
##
## Model test baseline model:
##
## Minimum Function Test Statistic 189.969
## Degrees of freedom 36
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.017
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2016.861
## Loglikelihood unrestricted model (H1) -2004.788
##
## Number of free parameters 28
## Akaike (AIC) 4089.722
## Bayesian (BIC) 4178.495
## Sample-size adjusted Bayesian (BIC) 4089.826
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.054
## P-value RMSEA <= 0.05 0.926
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.047
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit =~
## StroopPerf 0.155 0.098 1.579 0.114 0.155 0.156
## SSRTavg 0.154 0.107 1.438 0.150 0.154 0.155
## Antisaccade 0.645 0.103 6.281 0.000 0.645 0.646
## KeepTrack 0.425 0.099 4.316 0.000 0.425 0.426
## SpatialBack 0.521 0.113 4.613 0.000 0.521 0.516
## LetMem 0.227 0.098 2.321 0.020 0.227 0.227
## Shift =~
## NumLett 0.764 0.082 9.280 0.000 0.764 0.765
## ColShape 0.713 0.081 8.815 0.000 0.713 0.716
## CatSwitch 0.519 0.083 6.267 0.000 0.519 0.520
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit ~~
## Shift 0.645 0.103 6.266 0.000 0.645 0.645
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf -0.000 0.075 -0.000 1.000 -0.000 -0.000
## .SSRTavg -0.007 0.084 -0.086 0.931 -0.007 -0.007
## .Antisaccade -0.023 0.078 -0.290 0.772 -0.023 -0.023
## .KeepTrack -0.009 0.077 -0.122 0.903 -0.009 -0.009
## .SpatialBack -0.048 0.084 -0.572 0.568 -0.048 -0.048
## .LetMem -0.000 0.075 -0.006 0.995 -0.000 -0.000
## .NumLett -0.015 0.076 -0.199 0.842 -0.015 -0.015
## .ColShape 0.000 0.075 0.000 1.000 0.000 0.000
## .CatSwitch -0.004 0.076 -0.051 0.960 -0.004 -0.004
## Inhibit 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.970 0.105 9.213 0.000 0.970 0.976
## .SSRTavg 0.968 0.117 8.251 0.000 0.968 0.976
## .Antisaccade 0.579 0.116 4.996 0.000 0.579 0.582
## .KeepTrack 0.814 0.105 7.755 0.000 0.814 0.818
## .SpatialBack 0.747 0.115 6.521 0.000 0.747 0.734
## .LetMem 0.943 0.105 8.996 0.000 0.943 0.948
## .NumLett 0.414 0.090 4.616 0.000 0.414 0.415
## .ColShape 0.485 0.086 5.618 0.000 0.485 0.488
## .CatSwitch 0.726 0.090 8.066 0.000 0.726 0.730
## Inhibit 1.000 1.000 1.000
## Shift 1.000 1.000 1.000
##
## R-Square:
## Estimate
## StroopPerf 0.024
## SSRTavg 0.024
## Antisaccade 0.418
## KeepTrack 0.182
## SpatialBack 0.266
## LetMem 0.052
## NumLett 0.585
## ColShape 0.512
## CatSwitch 0.270A visual representation of the two factor model
semPaths(cfa2f_fit, 'std', layout='tree')
Stroop and SSR load load regardless of the 3 or 2 factor model.
Chi-square difference test of the 3-factor and 2-factor model
anova(cfa2f_fit, cfa3f_fit)These model did not differ significantly.
One factor CFA model fit
cfa1f<-'
Inhibit=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem+NumLett+ColShape+CatSwitch
'
cfa1f_fit <- cfa(cfa1f, std.lv=T, data, missing='ml')
summary(cfa1f_fit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 16 iterations
##
## Optimization method NLMINB
## Number of free parameters 27
##
## Number of observations 176
## Number of missing patterns 19
##
## Estimator ML
## Model Fit Test Statistic 35.748
## Degrees of freedom 27
## P-value (Chi-square) 0.121
##
## Model test baseline model:
##
## Minimum Function Test Statistic 189.969
## Degrees of freedom 36
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.943
## Tucker-Lewis Index (TLI) 0.924
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2022.662
## Loglikelihood unrestricted model (H1) -2004.788
##
## Number of free parameters 27
## Akaike (AIC) 4099.324
## Bayesian (BIC) 4184.927
## Sample-size adjusted Bayesian (BIC) 4099.424
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.043
## 90 Percent Confidence Interval 0.000 0.077
## P-value RMSEA <= 0.05 0.593
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.057
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit =~
## StroopPerf 0.078 0.088 0.885 0.376 0.078 0.078
## SSRTavg 0.135 0.093 1.448 0.148 0.135 0.135
## Antisaccade 0.472 0.087 5.444 0.000 0.472 0.474
## KeepTrack 0.369 0.086 4.291 0.000 0.369 0.370
## SpatialBack 0.383 0.106 3.622 0.000 0.383 0.381
## LetMem 0.122 0.087 1.406 0.160 0.122 0.123
## NumLett 0.748 0.079 9.457 0.000 0.748 0.748
## ColShape 0.690 0.079 8.779 0.000 0.690 0.693
## CatSwitch 0.527 0.082 6.424 0.000 0.527 0.529
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.075 0.000 1.000 0.000 0.000
## .SSRTavg -0.002 0.084 -0.020 0.984 -0.002 -0.002
## .Antisaccade -0.006 0.078 -0.077 0.938 -0.006 -0.006
## .KeepTrack 0.000 0.077 0.003 0.998 0.000 0.000
## .SpatialBack -0.032 0.084 -0.386 0.699 -0.032 -0.032
## .LetMem -0.000 0.075 -0.000 1.000 -0.000 -0.000
## .NumLett -0.017 0.076 -0.219 0.827 -0.017 -0.017
## .ColShape -0.000 0.075 -0.002 0.999 -0.000 -0.000
## .CatSwitch -0.004 0.076 -0.055 0.956 -0.004 -0.004
## Inhibit 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.988 0.106 9.358 0.000 0.988 0.994
## .SSRTavg 0.974 0.117 8.343 0.000 0.974 0.982
## .Antisaccade 0.770 0.096 8.015 0.000 0.770 0.775
## .KeepTrack 0.857 0.099 8.645 0.000 0.857 0.863
## .SpatialBack 0.866 0.110 7.868 0.000 0.866 0.855
## .LetMem 0.979 0.105 9.305 0.000 0.979 0.985
## .NumLett 0.439 0.082 5.345 0.000 0.439 0.440
## .ColShape 0.517 0.081 6.343 0.000 0.517 0.520
## .CatSwitch 0.716 0.089 8.049 0.000 0.716 0.721
## Inhibit 1.000 1.000 1.000
##
## R-Square:
## Estimate
## StroopPerf 0.006
## SSRTavg 0.018
## Antisaccade 0.225
## KeepTrack 0.137
## SpatialBack 0.145
## LetMem 0.015
## NumLett 0.560
## ColShape 0.480
## CatSwitch 0.279Chi-square difference test of the 3-factor and 1-factor model
anova(cfa1f_fit, cfa2f_fit)Chi_square difference test suggests that 2-factor model fits siginificantly better than the 1 factor model (delta df = 1).
Full CFA including Executive functions side and Category side
cfa_all3f<-'
Inhibit=~StroopPerf+SSRTavg+Antisaccade
Update=~KeepTrack+SpatialBack+LetMem
Shift=~NumLett+ColShape+CatSwitch
FR =~ FR1 + FR2 + FR3 + FR4
SD =~ SD1 + SD2 + SD3 + SD4
'Three factors on the EF side
cfa_all3f_fit <- cfa(cfa_all3f, std.lv=T, data, missing='ml')## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.summary(cfa_all3f_fit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 44 iterations
##
## Optimization method NLMINB
## Number of free parameters 61
##
## Number of observations 176
## Number of missing patterns 21
##
## Estimator ML
## Model Fit Test Statistic 167.933
## Degrees of freedom 109
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 1191.672
## Degrees of freedom 136
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.944
## Tucker-Lewis Index (TLI) 0.930
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3547.702
## Loglikelihood unrestricted model (H1) -3463.735
##
## Number of free parameters 61
## Akaike (AIC) 7217.403
## Bayesian (BIC) 7410.803
## Sample-size adjusted Bayesian (BIC) 7217.631
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.055
## 90 Percent Confidence Interval 0.038 0.071
## P-value RMSEA <= 0.05 0.284
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit =~
## StroopPerf 0.213 0.093 2.294 0.022 0.213 0.214
## SSRTavg 0.210 0.101 2.080 0.038 0.210 0.211
## Antisaccade 0.589 0.148 3.988 0.000 0.589 0.590
## Update =~
## KeepTrack 0.364 0.103 3.535 0.000 0.364 0.364
## SpatialBack 0.587 0.127 4.642 0.000 0.587 0.581
## LetMem 0.179 0.097 1.845 0.065 0.179 0.179
## Shift =~
## NumLett 0.758 0.083 9.162 0.000 0.758 0.760
## ColShape 0.718 0.082 8.793 0.000 0.718 0.721
## CatSwitch 0.518 0.083 6.263 0.000 0.518 0.519
## FR =~
## FR1 0.536 0.076 7.078 0.000 0.536 0.537
## FR2 0.770 0.068 11.284 0.000 0.770 0.772
## FR3 0.839 0.065 12.805 0.000 0.839 0.841
## FR4 0.821 0.066 12.424 0.000 0.821 0.824
## SD =~
## SD1 0.660 0.069 9.526 0.000 0.660 0.662
## SD2 0.865 0.061 14.093 0.000 0.865 0.867
## SD3 0.943 0.058 16.372 0.000 0.943 0.946
## SD4 0.894 0.060 14.991 0.000 0.894 0.896
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit ~~
## Update 1.060 0.279 3.799 0.000 1.060 1.060
## Shift 0.629 0.178 3.538 0.000 0.629 0.629
## FR 0.593 0.177 3.355 0.001 0.593 0.593
## SD 0.610 0.158 3.858 0.000 0.610 0.610
## Update ~~
## Shift 0.615 0.161 3.833 0.000 0.615 0.615
## FR 0.343 0.141 2.436 0.015 0.343 0.343
## SD 0.576 0.135 4.275 0.000 0.576 0.576
## Shift ~~
## FR 0.238 0.092 2.583 0.010 0.238 0.238
## SD 0.109 0.092 1.181 0.238 0.109 0.109
## FR ~~
## SD 0.370 0.075 4.930 0.000 0.370 0.370
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf -0.000 0.075 -0.000 1.000 -0.000 -0.000
## .SSRTavg -0.016 0.084 -0.192 0.848 -0.016 -0.016
## .Antisaccade -0.024 0.078 -0.311 0.756 -0.024 -0.024
## .KeepTrack -0.012 0.077 -0.154 0.878 -0.012 -0.012
## .SpatialBack -0.066 0.084 -0.789 0.430 -0.066 -0.065
## .LetMem -0.000 0.075 -0.005 0.996 -0.000 -0.000
## .NumLett -0.014 0.076 -0.179 0.858 -0.014 -0.014
## .ColShape 0.000 0.075 0.001 0.999 0.000 0.000
## .CatSwitch -0.004 0.076 -0.049 0.961 -0.004 -0.004
## .FR1 0.004 0.076 0.047 0.962 0.004 0.004
## .FR2 0.005 0.076 0.068 0.946 0.005 0.005
## .FR3 0.006 0.076 0.074 0.941 0.006 0.006
## .FR4 0.005 0.076 0.073 0.942 0.005 0.006
## .SD1 -0.001 0.076 -0.015 0.988 -0.001 -0.001
## .SD2 -0.002 0.076 -0.020 0.984 -0.002 -0.002
## .SD3 -0.002 0.076 -0.022 0.983 -0.002 -0.002
## .SD4 -0.002 0.076 -0.021 0.984 -0.002 -0.002
## Inhibit 0.000 0.000 0.000
## Update 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
## FR 0.000 0.000 0.000
## SD 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.949 0.104 9.134 0.000 0.949 0.954
## .SSRTavg 0.950 0.116 8.217 0.000 0.950 0.956
## .Antisaccade 0.649 0.166 3.901 0.000 0.649 0.652
## .KeepTrack 0.863 0.107 8.045 0.000 0.863 0.867
## .SpatialBack 0.675 0.135 4.988 0.000 0.675 0.662
## .LetMem 0.962 0.105 9.148 0.000 0.962 0.968
## .NumLett 0.421 0.091 4.645 0.000 0.421 0.422
## .ColShape 0.477 0.088 5.418 0.000 0.477 0.480
## .CatSwitch 0.726 0.090 8.074 0.000 0.726 0.730
## .FR1 0.708 0.082 8.638 0.000 0.708 0.712
## .FR2 0.402 0.058 6.979 0.000 0.402 0.404
## .FR3 0.291 0.051 5.722 0.000 0.291 0.293
## .FR4 0.320 0.052 6.137 0.000 0.320 0.322
## .SD1 0.559 0.064 8.667 0.000 0.559 0.562
## .SD2 0.247 0.035 7.019 0.000 0.247 0.248
## .SD3 0.105 0.025 4.209 0.000 0.105 0.105
## .SD4 0.196 0.028 6.896 0.000 0.196 0.197
## Inhibit 1.000 1.000 1.000
## Update 1.000 1.000 1.000
## Shift 1.000 1.000 1.000
## FR 1.000 1.000 1.000
## SD 1.000 1.000 1.000
##
## R-Square:
## Estimate
## StroopPerf 0.046
## SSRTavg 0.044
## Antisaccade 0.348
## KeepTrack 0.133
## SpatialBack 0.338
## LetMem 0.032
## NumLett 0.578
## ColShape 0.520
## CatSwitch 0.270
## FR1 0.288
## FR2 0.596
## FR3 0.707
## FR4 0.678
## SD1 0.438
## SD2 0.752
## SD3 0.895
## SD4 0.803Lavaan spitted out warning, let’s check the figure with loadings to find out where problem lays.
Visual representation of CFA all 3 factors EF
semPaths(cfa_all3f_fit, "std", layout = "tree")
Covariance between Inhibit and Update is over 1, which usually suggests these should not be seen as separate.
Two factors on the EF side
cfa_all2f<-'
InhUpd=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~NumLett+ColShape+CatSwitch
FR =~ FR1 + FR2 + FR3 + FR4
SD =~ SD1 + SD2 + SD3 + SD4
'
cfa_all2f_fit <- cfa(cfa_all2f, std.lv=T, data, missing='ml',std.lv=T)
summary(cfa_all2f_fit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 30 iterations
##
## Optimization method NLMINB
## Number of free parameters 57
##
## Number of observations 176
## Number of missing patterns 21
##
## Estimator ML
## Model Fit Test Statistic 170.211
## Degrees of freedom 113
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 1191.672
## Degrees of freedom 136
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.946
## Tucker-Lewis Index (TLI) 0.935
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3548.841
## Loglikelihood unrestricted model (H1) -3463.735
##
## Number of free parameters 57
## Akaike (AIC) 7211.682
## Bayesian (BIC) 7392.399
## Sample-size adjusted Bayesian (BIC) 7211.894
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.054
## 90 Percent Confidence Interval 0.036 0.070
## P-value RMSEA <= 0.05 0.345
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd =~
## StroopPerf 0.220 0.090 2.451 0.014 0.220 0.221
## SSRTavg 0.195 0.102 1.912 0.056 0.195 0.195
## Antisaccade 0.641 0.091 7.044 0.000 0.641 0.643
## KeepTrack 0.331 0.093 3.540 0.000 0.331 0.331
## SpatialBack 0.585 0.098 5.987 0.000 0.585 0.581
## LetMem 0.182 0.092 1.992 0.046 0.182 0.183
## Shift =~
## NumLett 0.757 0.083 9.166 0.000 0.757 0.759
## ColShape 0.720 0.081 8.843 0.000 0.720 0.722
## CatSwitch 0.518 0.083 6.257 0.000 0.518 0.519
## FR =~
## FR1 0.536 0.076 7.078 0.000 0.536 0.537
## FR2 0.770 0.068 11.279 0.000 0.770 0.772
## FR3 0.839 0.066 12.809 0.000 0.839 0.841
## FR4 0.821 0.066 12.409 0.000 0.821 0.823
## SD =~
## SD1 0.661 0.069 9.540 0.000 0.661 0.663
## SD2 0.865 0.061 14.113 0.000 0.865 0.868
## SD3 0.942 0.058 16.356 0.000 0.942 0.945
## SD4 0.894 0.060 14.992 0.000 0.894 0.896
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd ~~
## Shift 0.596 0.104 5.751 0.000 0.596 0.596
## FR 0.462 0.102 4.534 0.000 0.462 0.462
## SD 0.581 0.090 6.465 0.000 0.581 0.581
## Shift ~~
## FR 0.237 0.092 2.574 0.010 0.237 0.237
## SD 0.108 0.092 1.178 0.239 0.108 0.108
## FR ~~
## SD 0.370 0.075 4.924 0.000 0.370 0.370
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf -0.000 0.075 -0.000 1.000 -0.000 -0.000
## .SSRTavg -0.014 0.084 -0.167 0.867 -0.014 -0.014
## .Antisaccade -0.026 0.078 -0.332 0.740 -0.026 -0.026
## .KeepTrack -0.012 0.077 -0.149 0.881 -0.012 -0.012
## .SpatialBack -0.066 0.083 -0.796 0.426 -0.066 -0.066
## .LetMem -0.000 0.075 -0.005 0.996 -0.000 -0.000
## .NumLett -0.014 0.076 -0.180 0.857 -0.014 -0.014
## .ColShape 0.000 0.075 0.002 0.998 0.000 0.000
## .CatSwitch -0.004 0.076 -0.050 0.961 -0.004 -0.004
## .FR1 0.004 0.076 0.048 0.962 0.004 0.004
## .FR2 0.005 0.076 0.069 0.945 0.005 0.005
## .FR3 0.006 0.076 0.076 0.940 0.006 0.006
## .FR4 0.006 0.076 0.074 0.941 0.006 0.006
## .SD1 -0.001 0.076 -0.017 0.987 -0.001 -0.001
## .SD2 -0.002 0.076 -0.022 0.983 -0.002 -0.002
## .SD3 -0.002 0.076 -0.024 0.981 -0.002 -0.002
## .SD4 -0.002 0.076 -0.023 0.982 -0.002 -0.002
## InhUpd 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
## FR 0.000 0.000 0.000
## SD 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.946 0.103 9.160 0.000 0.946 0.951
## .SSRTavg 0.955 0.116 8.239 0.000 0.955 0.962
## .Antisaccade 0.583 0.098 5.947 0.000 0.583 0.587
## .KeepTrack 0.886 0.103 8.566 0.000 0.886 0.890
## .SpatialBack 0.673 0.101 6.637 0.000 0.673 0.663
## .LetMem 0.961 0.105 9.192 0.000 0.961 0.967
## .NumLett 0.422 0.090 4.686 0.000 0.422 0.424
## .ColShape 0.475 0.088 5.425 0.000 0.475 0.478
## .CatSwitch 0.727 0.090 8.075 0.000 0.727 0.731
## .FR1 0.707 0.082 8.636 0.000 0.707 0.711
## .FR2 0.402 0.058 6.968 0.000 0.402 0.404
## .FR3 0.290 0.051 5.696 0.000 0.290 0.292
## .FR4 0.321 0.052 6.143 0.000 0.321 0.323
## .SD1 0.557 0.064 8.661 0.000 0.557 0.561
## .SD2 0.245 0.035 6.998 0.000 0.245 0.247
## .SD3 0.106 0.025 4.259 0.000 0.106 0.107
## .SD4 0.196 0.028 6.877 0.000 0.196 0.197
## InhUpd 1.000 1.000 1.000
## Shift 1.000 1.000 1.000
## FR 1.000 1.000 1.000
## SD 1.000 1.000 1.000
##
## R-Square:
## Estimate
## StroopPerf 0.049
## SSRTavg 0.038
## Antisaccade 0.413
## KeepTrack 0.110
## SpatialBack 0.337
## LetMem 0.033
## NumLett 0.576
## ColShape 0.522
## CatSwitch 0.269
## FR1 0.289
## FR2 0.596
## FR3 0.708
## FR4 0.677
## SD1 0.439
## SD2 0.753
## SD3 0.893
## SD4 0.803Visual representation of CFA all 2 factors EF
semPaths(cfa_all2f_fit, "std", layout = "tree")
Seems like the 2 facors EF solution fits better than 3 factor solution
Full structural model
Two latent factors of EF predict SD category performance
sem2f_sd<-'
InhUpd=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~NumLett+ColShape+CatSwitch
#FR =~ FR1 + FR2 + FR3 + FR4
SD =~ SD1 + SD2 + SD3 + SD4
SD~InhUpd+Shift
'sem2f_fit_sd <- sem(sem2f_sd, data, missing='ml')
summary(sem2f_fit_sd, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 73 iterations
##
## Optimization method NLMINB
## Number of free parameters 42
##
## Number of observations 176
## Number of missing patterns 20
##
## Estimator ML
## Model Fit Test Statistic 104.015
## Degrees of freedom 62
## P-value (Chi-square) 0.001
##
## Model test baseline model:
##
## Minimum Function Test Statistic 818.597
## Degrees of freedom 78
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.943
## Tucker-Lewis Index (TLI) 0.929
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2722.381
## Loglikelihood unrestricted model (H1) -2670.373
##
## Number of free parameters 42
## Akaike (AIC) 5528.761
## Bayesian (BIC) 5661.922
## Sample-size adjusted Bayesian (BIC) 5528.918
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.062
## 90 Percent Confidence Interval 0.040 0.082
## P-value RMSEA <= 0.05 0.166
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.053
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd =~
## StroopPerf 1.000 0.211 0.211
## SSRTavg 0.764 0.576 1.326 0.185 0.161 0.161
## Antisaccade 3.018 1.353 2.230 0.026 0.636 0.638
## KeepTrack 1.710 0.848 2.017 0.044 0.360 0.361
## SpatialBack 2.830 1.281 2.209 0.027 0.596 0.590
## LetMem 0.839 0.573 1.465 0.143 0.177 0.177
## Shift =~
## NumLett 1.000 0.756 0.758
## ColShape 0.947 0.147 6.462 0.000 0.716 0.719
## CatSwitch 0.692 0.129 5.360 0.000 0.523 0.525
## SD =~
## SD1 1.000 0.658 0.660
## SD2 1.312 0.130 10.086 0.000 0.864 0.867
## SD3 1.432 0.139 10.337 0.000 0.943 0.946
## SD4 1.357 0.135 10.020 0.000 0.893 0.896
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SD ~
## InhUpd 2.544 1.262 2.017 0.044 0.814 0.814
## Shift -0.343 0.162 -2.117 0.034 -0.394 -0.394
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd ~~
## Shift 0.097 0.045 2.146 0.032 0.606 0.606
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf -0.000 0.075 -0.000 1.000 -0.000 -0.000
## .SSRTavg -0.011 0.084 -0.134 0.894 -0.011 -0.011
## .Antisaccade -0.027 0.078 -0.350 0.727 -0.027 -0.027
## .KeepTrack -0.012 0.077 -0.157 0.875 -0.012 -0.012
## .SpatialBack -0.068 0.083 -0.814 0.415 -0.068 -0.067
## .LetMem -0.000 0.075 -0.006 0.995 -0.000 -0.000
## .NumLett -0.014 0.076 -0.186 0.853 -0.014 -0.014
## .ColShape -0.000 0.075 -0.001 0.999 -0.000 -0.000
## .CatSwitch -0.004 0.076 -0.050 0.960 -0.004 -0.004
## .SD1 -0.000 0.076 -0.006 0.995 -0.000 -0.000
## .SD2 -0.001 0.076 -0.008 0.994 -0.001 -0.001
## .SD3 -0.001 0.076 -0.009 0.993 -0.001 -0.001
## .SD4 -0.001 0.076 -0.008 0.993 -0.001 -0.001
## InhUpd 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
## .SD 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.950 0.104 9.169 0.000 0.950 0.955
## .SSRTavg 0.967 0.117 8.292 0.000 0.967 0.974
## .Antisaccade 0.590 0.098 6.020 0.000 0.590 0.593
## .KeepTrack 0.866 0.102 8.488 0.000 0.866 0.870
## .SpatialBack 0.667 0.103 6.462 0.000 0.667 0.652
## .LetMem 0.963 0.105 9.198 0.000 0.963 0.969
## .NumLett 0.424 0.089 4.736 0.000 0.424 0.425
## .ColShape 0.480 0.087 5.528 0.000 0.480 0.483
## .CatSwitch 0.721 0.090 8.014 0.000 0.721 0.724
## .SD1 0.560 0.065 8.676 0.000 0.560 0.564
## .SD2 0.247 0.035 7.026 0.000 0.247 0.249
## .SD3 0.104 0.025 4.177 0.000 0.104 0.105
## .SD4 0.195 0.028 6.886 0.000 0.195 0.196
## InhUpd 0.044 0.038 1.161 0.246 1.000 1.000
## Shift 0.572 0.124 4.595 0.000 1.000 1.000
## .SD 0.247 0.075 3.291 0.001 0.571 0.571
##
## R-Square:
## Estimate
## StroopPerf 0.045
## SSRTavg 0.026
## Antisaccade 0.407
## KeepTrack 0.130
## SpatialBack 0.348
## LetMem 0.031
## NumLett 0.575
## ColShape 0.517
## CatSwitch 0.276
## SD1 0.436
## SD2 0.751
## SD3 0.895
## SD4 0.804
## SD 0.429semPaths(sem2f_fit_sd, "std", layout = "tree")
Two latent factors of EF predict FR category performance
sem2f_fr<-'
InhUpd=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~NumLett+ColShape+CatSwitch
FR =~ FR1 + FR2 + FR3 + FR4
#SD =~ SD1 + SD2 + SD3 + SD4
FR~InhUpd+Shift
'sem2f_fit_fr <- sem(sem2f_fr, data, missing='ml')
summary(sem2f_fit_fr, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 73 iterations
##
## Optimization method NLMINB
## Number of free parameters 42
##
## Number of observations 176
## Number of missing patterns 20
##
## Estimator ML
## Model Fit Test Statistic 78.596
## Degrees of freedom 62
## P-value (Chi-square) 0.076
##
## Model test baseline model:
##
## Minimum Function Test Statistic 540.364
## Degrees of freedom 78
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.964
## Tucker-Lewis Index (TLI) 0.955
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2848.788
## Loglikelihood unrestricted model (H1) -2809.490
##
## Number of free parameters 42
## Akaike (AIC) 5781.575
## Bayesian (BIC) 5914.736
## Sample-size adjusted Bayesian (BIC) 5781.732
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.039
## 90 Percent Confidence Interval 0.000 0.063
## P-value RMSEA <= 0.05 0.750
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.063
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd =~
## StroopPerf 1.000 0.183 0.183
## SSRTavg 1.152 0.815 1.413 0.158 0.211 0.211
## Antisaccade 3.688 1.988 1.855 0.064 0.674 0.674
## KeepTrack 1.976 1.151 1.717 0.086 0.361 0.362
## SpatialBack 2.828 1.559 1.814 0.070 0.517 0.515
## LetMem 1.259 0.849 1.483 0.138 0.230 0.231
## Shift =~
## NumLett 1.000 0.762 0.763
## ColShape 0.943 0.148 6.377 0.000 0.718 0.721
## CatSwitch 0.675 0.127 5.297 0.000 0.514 0.516
## FR =~
## FR1 1.000 0.530 0.532
## FR2 1.452 0.213 6.826 0.000 0.770 0.772
## FR3 1.593 0.233 6.852 0.000 0.845 0.847
## FR4 1.542 0.231 6.689 0.000 0.818 0.820
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FR ~
## InhUpd 1.460 0.919 1.589 0.112 0.503 0.503
## Shift -0.051 0.113 -0.451 0.652 -0.073 -0.073
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd ~~
## Shift 0.085 0.047 1.815 0.070 0.614 0.614
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.075 0.000 1.000 0.000 0.000
## .SSRTavg -0.011 0.084 -0.134 0.893 -0.011 -0.011
## .Antisaccade -0.022 0.078 -0.284 0.776 -0.022 -0.022
## .KeepTrack -0.010 0.077 -0.129 0.897 -0.010 -0.010
## .SpatialBack -0.049 0.083 -0.586 0.558 -0.049 -0.049
## .LetMem -0.000 0.075 -0.004 0.997 -0.000 -0.000
## .NumLett -0.015 0.076 -0.193 0.847 -0.015 -0.015
## .ColShape 0.000 0.075 0.004 0.996 0.000 0.000
## .CatSwitch -0.004 0.076 -0.050 0.960 -0.004 -0.004
## .FR1 0.003 0.076 0.043 0.966 0.003 0.003
## .FR2 0.005 0.076 0.063 0.950 0.005 0.005
## .FR3 0.005 0.076 0.069 0.945 0.005 0.005
## .FR4 0.005 0.076 0.067 0.947 0.005 0.005
## InhUpd 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
## .FR 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.961 0.105 9.178 0.000 0.961 0.966
## .SSRTavg 0.948 0.116 8.137 0.000 0.948 0.955
## .Antisaccade 0.544 0.112 4.879 0.000 0.544 0.545
## .KeepTrack 0.865 0.104 8.300 0.000 0.865 0.869
## .SpatialBack 0.741 0.109 6.822 0.000 0.741 0.735
## .LetMem 0.941 0.104 9.033 0.000 0.941 0.947
## .NumLett 0.416 0.091 4.579 0.000 0.416 0.417
## .ColShape 0.477 0.088 5.453 0.000 0.477 0.480
## .CatSwitch 0.730 0.090 8.104 0.000 0.730 0.734
## .FR1 0.713 0.082 8.661 0.000 0.713 0.717
## .FR2 0.402 0.058 6.922 0.000 0.402 0.404
## .FR3 0.281 0.051 5.478 0.000 0.281 0.283
## .FR4 0.326 0.053 6.209 0.000 0.326 0.328
## InhUpd 0.033 0.035 0.959 0.337 1.000 1.000
## Shift 0.581 0.126 4.593 0.000 1.000 1.000
## .FR 0.221 0.067 3.310 0.001 0.787 0.787
##
## R-Square:
## Estimate
## StroopPerf 0.034
## SSRTavg 0.045
## Antisaccade 0.455
## KeepTrack 0.131
## SpatialBack 0.265
## LetMem 0.053
## NumLett 0.583
## ColShape 0.520
## CatSwitch 0.266
## FR1 0.283
## FR2 0.596
## FR3 0.717
## FR4 0.672
## FR 0.213semPaths(sem2f_fit_fr, "std", layout = "tree")
Two latent factors of EF predict both SD & FR category performance
sem2f_both<-'
InhUpd=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~NumLett+ColShape+CatSwitch
FR =~ FR1 + FR2 + FR3 + FR4
SD =~ SD1 + SD2 + SD3 + SD4
FR~InhUpd+Shift
SD~InhUpd+Shift
'sem2f_fit_both <- sem(sem2f_both, data, missing='ml',std.lv=T)
sum<-summary(sem2f_fit_both, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 38 iterations
##
## Optimization method NLMINB
## Number of free parameters 57
##
## Number of observations 176
## Number of missing patterns 21
##
## Estimator ML
## Model Fit Test Statistic 170.211
## Degrees of freedom 113
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 1191.672
## Degrees of freedom 136
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.946
## Tucker-Lewis Index (TLI) 0.935
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3548.841
## Loglikelihood unrestricted model (H1) -3463.735
##
## Number of free parameters 57
## Akaike (AIC) 7211.682
## Bayesian (BIC) 7392.399
## Sample-size adjusted Bayesian (BIC) 7211.894
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.054
## 90 Percent Confidence Interval 0.036 0.070
## P-value RMSEA <= 0.05 0.345
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd =~
## StroopPerf 0.220 0.090 2.451 0.014 0.220 0.221
## SSRTavg 0.195 0.102 1.912 0.056 0.195 0.195
## Antisaccade 0.641 0.091 7.044 0.000 0.641 0.643
## KeepTrack 0.331 0.093 3.540 0.000 0.331 0.331
## SpatialBack 0.585 0.098 5.987 0.000 0.585 0.581
## LetMem 0.182 0.092 1.992 0.046 0.182 0.183
## Shift =~
## NumLett 0.757 0.083 9.166 0.000 0.757 0.759
## ColShape 0.720 0.081 8.843 0.000 0.720 0.722
## CatSwitch 0.518 0.083 6.257 0.000 0.518 0.519
## FR =~
## FR1 0.474 0.071 6.693 0.000 0.536 0.537
## FR2 0.682 0.070 9.691 0.000 0.770 0.772
## FR3 0.743 0.071 10.467 0.000 0.839 0.841
## FR4 0.727 0.069 10.477 0.000 0.821 0.823
## SD =~
## SD1 0.501 0.076 6.613 0.000 0.661 0.663
## SD2 0.656 0.086 7.647 0.000 0.865 0.868
## SD3 0.714 0.091 7.818 0.000 0.942 0.945
## SD4 0.677 0.088 7.724 0.000 0.894 0.896
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FR ~
## InhUpd 0.562 0.216 2.607 0.009 0.498 0.498
## Shift -0.068 0.177 -0.381 0.703 -0.060 -0.060
## SD ~
## InhUpd 1.058 0.341 3.101 0.002 0.802 0.802
## Shift -0.488 0.269 -1.813 0.070 -0.370 -0.370
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd ~~
## Shift 0.596 0.104 5.751 0.000 0.596 0.596
## .FR ~~
## .SD 0.130 0.140 0.927 0.354 0.130 0.130
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.075 0.000 1.000 0.000 0.000
## .SSRTavg -0.014 0.084 -0.167 0.867 -0.014 -0.014
## .Antisaccade -0.026 0.078 -0.332 0.740 -0.026 -0.026
## .KeepTrack -0.012 0.077 -0.149 0.881 -0.012 -0.012
## .SpatialBack -0.066 0.083 -0.796 0.426 -0.066 -0.066
## .LetMem -0.000 0.075 -0.005 0.996 -0.000 -0.000
## .NumLett -0.014 0.076 -0.180 0.857 -0.014 -0.014
## .ColShape 0.000 0.075 0.002 0.998 0.000 0.000
## .CatSwitch -0.004 0.076 -0.050 0.961 -0.004 -0.004
## .FR1 0.004 0.076 0.048 0.962 0.004 0.004
## .FR2 0.005 0.076 0.069 0.945 0.005 0.005
## .FR3 0.006 0.076 0.076 0.940 0.006 0.006
## .FR4 0.006 0.076 0.074 0.941 0.006 0.006
## .SD1 -0.001 0.076 -0.017 0.987 -0.001 -0.001
## .SD2 -0.002 0.076 -0.022 0.983 -0.002 -0.002
## .SD3 -0.002 0.076 -0.024 0.981 -0.002 -0.002
## .SD4 -0.002 0.076 -0.023 0.982 -0.002 -0.002
## InhUpd 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
## .FR 0.000 0.000 0.000
## .SD 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.946 0.103 9.160 0.000 0.946 0.951
## .SSRTavg 0.955 0.116 8.239 0.000 0.955 0.962
## .Antisaccade 0.583 0.098 5.947 0.000 0.583 0.587
## .KeepTrack 0.886 0.103 8.566 0.000 0.886 0.890
## .SpatialBack 0.673 0.101 6.637 0.000 0.673 0.663
## .LetMem 0.961 0.105 9.192 0.000 0.961 0.967
## .NumLett 0.422 0.090 4.686 0.000 0.422 0.424
## .ColShape 0.475 0.088 5.425 0.000 0.475 0.478
## .CatSwitch 0.727 0.090 8.075 0.000 0.727 0.731
## .FR1 0.707 0.082 8.636 0.000 0.707 0.711
## .FR2 0.402 0.058 6.968 0.000 0.402 0.404
## .FR3 0.290 0.051 5.696 0.000 0.290 0.292
## .FR4 0.321 0.052 6.143 0.000 0.321 0.323
## .SD1 0.557 0.064 8.661 0.000 0.557 0.561
## .SD2 0.245 0.035 6.998 0.000 0.245 0.247
## .SD3 0.106 0.025 4.259 0.000 0.106 0.107
## .SD4 0.196 0.028 6.877 0.000 0.196 0.197
## InhUpd 1.000 1.000 1.000
## Shift 1.000 1.000 1.000
## .FR 1.000 0.784 0.784
## .SD 1.000 0.574 0.574
##
## R-Square:
## Estimate
## StroopPerf 0.049
## SSRTavg 0.038
## Antisaccade 0.413
## KeepTrack 0.110
## SpatialBack 0.337
## LetMem 0.033
## NumLett 0.576
## ColShape 0.522
## CatSwitch 0.269
## FR1 0.289
## FR2 0.596
## FR3 0.708
## FR4 0.677
## SD1 0.439
## SD2 0.753
## SD3 0.893
## SD4 0.803
## FR 0.216
## SD 0.426semPaths(sem2f_fit_both, "std", layout = "tree")
Two-factor EF predict both SD & FR, equality constraint on reg-coeff
test<-'
InhUpd=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~NumLett+ColShape+CatSwitch
FR =~ FR1 + FR2 + FR3 + FR4
SD =~ SD1 + SD2 + SD3 + SD4
FR ~ d1*InhUpd + d2*Shift
SD ~ d1*InhUpd + d2*Shift
'test_fit <- sem(test, data, missing='ml',std.lv=T)
sum_path<-summary(test_fit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 34 iterations
##
## Optimization method NLMINB
## Number of free parameters 57
## Number of equality constraints 2
##
## Number of observations 176
## Number of missing patterns 21
##
## Estimator ML
## Model Fit Test Statistic 173.868
## Degrees of freedom 115
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 1191.672
## Degrees of freedom 136
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.944
## Tucker-Lewis Index (TLI) 0.934
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3550.669
## Loglikelihood unrestricted model (H1) -3463.735
##
## Number of free parameters 55
## Akaike (AIC) 7211.338
## Bayesian (BIC) 7385.715
## Sample-size adjusted Bayesian (BIC) 7211.543
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.054
## 90 Percent Confidence Interval 0.037 0.070
## P-value RMSEA <= 0.05 0.333
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.063
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd =~
## StroopPerf 0.218 0.090 2.414 0.016 0.218 0.219
## SSRTavg 0.214 0.101 2.118 0.034 0.214 0.214
## Antisaccade 0.649 0.092 7.020 0.000 0.649 0.650
## KeepTrack 0.322 0.094 3.418 0.001 0.322 0.322
## SpatialBack 0.567 0.097 5.845 0.000 0.567 0.564
## LetMem 0.193 0.092 2.100 0.036 0.193 0.193
## Shift =~
## NumLett 0.755 0.083 9.083 0.000 0.755 0.756
## ColShape 0.721 0.082 8.835 0.000 0.721 0.723
## CatSwitch 0.521 0.083 6.284 0.000 0.521 0.523
## FR =~
## FR1 0.447 0.068 6.540 0.000 0.539 0.540
## FR2 0.642 0.069 9.250 0.000 0.773 0.773
## FR3 0.698 0.070 9.966 0.000 0.841 0.840
## FR4 0.686 0.069 9.919 0.000 0.826 0.826
## SD =~
## SD1 0.545 0.066 8.203 0.000 0.657 0.660
## SD2 0.714 0.067 10.583 0.000 0.861 0.866
## SD3 0.780 0.069 11.315 0.000 0.940 0.946
## SD4 0.739 0.068 10.896 0.000 0.890 0.895
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FR ~
## InhUpd (d1) 0.800 0.223 3.587 0.000 0.664 0.664
## Shift (d2) -0.275 0.185 -1.493 0.136 -0.229 -0.229
## SD ~
## InhUpd (d1) 0.800 0.223 3.587 0.000 0.664 0.664
## Shift (d2) -0.275 0.185 -1.493 0.136 -0.229 -0.229
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd ~~
## Shift 0.599 0.104 5.765 0.000 0.599 0.599
## .FR ~~
## .SD 0.092 0.143 0.644 0.520 0.092 0.092
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.075 0.000 1.000 0.000 0.000
## .SSRTavg -0.015 0.084 -0.177 0.859 -0.015 -0.015
## .Antisaccade -0.024 0.078 -0.314 0.754 -0.024 -0.024
## .KeepTrack -0.011 0.077 -0.142 0.887 -0.011 -0.011
## .SpatialBack -0.062 0.083 -0.746 0.455 -0.062 -0.062
## .LetMem -0.000 0.075 -0.004 0.997 -0.000 -0.000
## .NumLett -0.015 0.076 -0.191 0.849 -0.015 -0.015
## .ColShape 0.000 0.075 0.002 0.998 0.000 0.000
## .CatSwitch -0.004 0.076 -0.051 0.959 -0.004 -0.004
## .FR1 0.005 0.076 0.062 0.951 0.005 0.005
## .FR2 0.007 0.076 0.089 0.929 0.007 0.007
## .FR3 0.007 0.076 0.097 0.923 0.007 0.007
## .FR4 0.007 0.076 0.095 0.924 0.007 0.007
## .SD1 -0.002 0.076 -0.023 0.982 -0.002 -0.002
## .SD2 -0.002 0.075 -0.030 0.976 -0.002 -0.002
## .SD3 -0.002 0.075 -0.032 0.974 -0.002 -0.002
## .SD4 -0.002 0.075 -0.031 0.976 -0.002 -0.002
## InhUpd 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
## .FR 0.000 0.000 0.000
## .SD 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.947 0.103 9.156 0.000 0.947 0.952
## .SSRTavg 0.947 0.115 8.207 0.000 0.947 0.954
## .Antisaccade 0.574 0.100 5.733 0.000 0.574 0.577
## .KeepTrack 0.892 0.104 8.582 0.000 0.892 0.896
## .SpatialBack 0.688 0.102 6.770 0.000 0.688 0.682
## .LetMem 0.957 0.104 9.168 0.000 0.957 0.963
## .NumLett 0.427 0.091 4.706 0.000 0.427 0.428
## .ColShape 0.474 0.088 5.388 0.000 0.474 0.477
## .CatSwitch 0.723 0.090 8.029 0.000 0.723 0.727
## .FR1 0.707 0.082 8.632 0.000 0.707 0.709
## .FR2 0.403 0.058 6.981 0.000 0.403 0.402
## .FR3 0.294 0.051 5.781 0.000 0.294 0.294
## .FR4 0.319 0.052 6.110 0.000 0.319 0.318
## .SD1 0.560 0.065 8.675 0.000 0.560 0.565
## .SD2 0.248 0.035 7.038 0.000 0.248 0.251
## .SD3 0.103 0.025 4.157 0.000 0.103 0.104
## .SD4 0.196 0.028 6.919 0.000 0.196 0.198
## InhUpd 1.000 1.000 1.000
## Shift 1.000 1.000 1.000
## .FR 1.000 0.689 0.689
## .SD 1.000 0.689 0.689
##
## R-Square:
## Estimate
## StroopPerf 0.048
## SSRTavg 0.046
## Antisaccade 0.423
## KeepTrack 0.104
## SpatialBack 0.318
## LetMem 0.037
## NumLett 0.572
## ColShape 0.523
## CatSwitch 0.273
## FR1 0.291
## FR2 0.598
## FR3 0.706
## FR4 0.682
## SD1 0.435
## SD2 0.749
## SD3 0.896
## SD4 0.802
## FR 0.311
## SD 0.311semPaths(test_fit, "std", layout = "tree")
EF components predict larger proportion of performance variance in SD than in FR. Inhibit+Update positively predict FR and SD, while Shift negatively predict FR and SD. Recall that Shift is measured by task switch RT, which means, people with longer delays in response tend to have lower performance in category learning.
Two latent factors of EF, Path model of Category performance
This is a path model where InhUpd and Shift predict FR1 and SD1, and the each following block predicts the block after
sem2f_path<-'
InhUpd=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~NumLett+ColShape+CatSwitch
FR1~InhUpd+Shift
SD1~InhUpd+Shift
FR2~FR1
FR3~FR2
FR4~FR3
SD2~SD1
SD3~SD2
SD4~SD3
'sem2f_path_fit <- sem(sem2f_path, data, missing='ml',std.lv=T)
sum_path<-summary(sem2f_path_fit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 29 iterations
##
## Optimization method NLMINB
## Number of free parameters 55
##
## Number of observations 176
## Number of missing patterns 21
##
## Estimator ML
## Model Fit Test Statistic 172.945
## Degrees of freedom 115
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 1191.672
## Degrees of freedom 136
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.945
## Tucker-Lewis Index (TLI) 0.935
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3550.208
## Loglikelihood unrestricted model (H1) -3463.735
##
## Number of free parameters 55
## Akaike (AIC) 7210.416
## Bayesian (BIC) 7384.793
## Sample-size adjusted Bayesian (BIC) 7210.621
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.054
## 90 Percent Confidence Interval 0.036 0.069
## P-value RMSEA <= 0.05 0.349
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.100
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd =~
## StroopPerf 0.191 0.091 2.091 0.037 0.191 0.191
## SSRTavg 0.196 0.102 1.920 0.055 0.196 0.197
## Antisaccade 0.670 0.090 7.452 0.000 0.670 0.673
## KeepTrack 0.337 0.092 3.656 0.000 0.337 0.338
## SpatialBack 0.539 0.099 5.461 0.000 0.539 0.536
## LetMem 0.212 0.092 2.314 0.021 0.212 0.213
## Shift =~
## NumLett 0.744 0.083 9.015 0.000 0.744 0.746
## ColShape 0.726 0.081 8.945 0.000 0.726 0.728
## CatSwitch 0.528 0.083 6.367 0.000 0.528 0.529
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FR1 ~
## InhUpd 0.421 0.134 3.135 0.002 0.421 0.423
## Shift -0.073 0.132 -0.555 0.579 -0.073 -0.073
## SD1 ~
## InhUpd 0.679 0.161 4.226 0.000 0.679 0.682
## Shift -0.346 0.162 -2.130 0.033 -0.346 -0.347
## FR2 ~
## FR1 0.504 0.066 7.673 0.000 0.504 0.504
## FR3 ~
## FR2 0.641 0.058 10.983 0.000 0.641 0.641
## FR4 ~
## FR3 0.711 0.053 13.416 0.000 0.711 0.712
## SD2 ~
## SD1 0.711 0.053 13.301 0.000 0.711 0.711
## SD3 ~
## SD2 0.811 0.044 18.259 0.000 0.811 0.811
## SD4 ~
## SD3 0.854 0.039 22.055 0.000 0.854 0.862
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd ~~
## Shift 0.608 0.104 5.861 0.000 0.608 0.608
## .FR4 ~~
## .SD4 0.038 0.027 1.402 0.161 0.038 0.110
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf -0.000 0.075 -0.000 1.000 -0.000 -0.000
## .SSRTavg -0.013 0.084 -0.152 0.879 -0.013 -0.013
## .Antisaccade -0.028 0.078 -0.357 0.721 -0.028 -0.028
## .KeepTrack -0.012 0.077 -0.156 0.876 -0.012 -0.012
## .SpatialBack -0.059 0.083 -0.710 0.477 -0.059 -0.059
## .LetMem -0.001 0.075 -0.013 0.990 -0.001 -0.001
## .NumLett -0.015 0.076 -0.201 0.841 -0.015 -0.015
## .ColShape -0.000 0.075 -0.006 0.995 -0.000 -0.000
## .CatSwitch -0.004 0.076 -0.052 0.959 -0.004 -0.004
## .FR1 0.005 0.076 0.064 0.949 0.005 0.005
## .SD1 -0.003 0.076 -0.046 0.963 -0.003 -0.003
## .FR2 0.000 0.065 0.000 1.000 0.000 0.000
## .FR3 0.000 0.058 0.000 1.000 0.000 0.000
## .FR4 0.001 0.053 0.018 0.986 0.001 0.001
## .SD2 0.000 0.053 0.000 1.000 0.000 0.000
## .SD3 0.000 0.044 0.000 1.000 0.000 0.000
## .SD4 -0.000 0.038 -0.011 0.991 -0.000 -0.000
## InhUpd 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.958 0.104 9.203 0.000 0.958 0.963
## .SSRTavg 0.954 0.116 8.226 0.000 0.954 0.961
## .Antisaccade 0.543 0.098 5.567 0.000 0.543 0.547
## .KeepTrack 0.882 0.103 8.578 0.000 0.882 0.886
## .SpatialBack 0.720 0.104 6.953 0.000 0.720 0.713
## .LetMem 0.949 0.104 9.131 0.000 0.949 0.955
## .NumLett 0.443 0.089 4.976 0.000 0.443 0.444
## .ColShape 0.467 0.087 5.349 0.000 0.467 0.470
## .CatSwitch 0.716 0.090 7.967 0.000 0.716 0.720
## .FR1 0.849 0.102 8.285 0.000 0.849 0.854
## .SD1 0.699 0.116 6.020 0.000 0.699 0.703
## .FR2 0.742 0.080 9.301 0.000 0.742 0.746
## .FR3 0.586 0.063 9.301 0.000 0.586 0.589
## .FR4 0.488 0.052 9.301 0.000 0.488 0.493
## .SD2 0.492 0.053 9.301 0.000 0.492 0.494
## .SD3 0.340 0.037 9.301 0.000 0.340 0.342
## .SD4 0.250 0.027 9.297 0.000 0.250 0.256
## InhUpd 1.000 1.000 1.000
## Shift 1.000 1.000 1.000
##
## R-Square:
## Estimate
## StroopPerf 0.037
## SSRTavg 0.039
## Antisaccade 0.453
## KeepTrack 0.114
## SpatialBack 0.287
## LetMem 0.045
## NumLett 0.556
## ColShape 0.530
## CatSwitch 0.280
## FR1 0.146
## SD1 0.297
## FR2 0.254
## FR3 0.411
## FR4 0.507
## SD2 0.506
## SD3 0.658
## SD4 0.744semPaths(sem2f_path_fit, "std", layout = "tree")
Two latent factors of EF drop StroopPerf and SSR
sem2f_norm<-'
InhUpd=~Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~NumLett+ColShape+CatSwitch
FR =~ FR1 + FR2 + FR3 + FR4
SD =~ SD1 + SD2 + SD3 + SD4
FR ~ d1*InhUpd + d2*Shift
SD ~ d1*InhUpd + d2*Shift
#FR=~0*SD
'sem2f_norm_fit <- sem(sem2f_norm, data, missing='ml', std.lv=T)
sum_drop<-summary(sem2f_norm_fit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 34 iterations
##
## Optimization method NLMINB
## Number of free parameters 51
## Number of equality constraints 2
##
## Number of observations 176
## Number of missing patterns 14
##
## Estimator ML
## Model Fit Test Statistic 132.988
## Degrees of freedom 86
## P-value (Chi-square) 0.001
##
## Model test baseline model:
##
## Minimum Function Test Statistic 1140.886
## Degrees of freedom 105
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.955
## Tucker-Lewis Index (TLI) 0.945
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3106.822
## Loglikelihood unrestricted model (H1) -3040.328
##
## Number of free parameters 49
## Akaike (AIC) 6311.644
## Bayesian (BIC) 6466.997
## Sample-size adjusted Bayesian (BIC) 6311.826
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.056
## 90 Percent Confidence Interval 0.036 0.074
## P-value RMSEA <= 0.05 0.294
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.060
##
## Parameter Estimates:
##
## Information Observed
## Observed information based on Hessian
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd =~
## Antisaccade 0.665 0.093 7.149 0.000 0.665 0.668
## KeepTrack 0.329 0.094 3.511 0.000 0.329 0.330
## SpatialBack 0.577 0.099 5.844 0.000 0.577 0.574
## LetMem 0.206 0.092 2.222 0.026 0.206 0.206
## Shift =~
## NumLett 0.769 0.083 9.262 0.000 0.769 0.770
## ColShape 0.708 0.081 8.710 0.000 0.708 0.710
## CatSwitch 0.517 0.083 6.217 0.000 0.517 0.519
## FR =~
## FR1 0.461 0.069 6.660 0.000 0.538 0.539
## FR2 0.663 0.068 9.709 0.000 0.774 0.774
## FR3 0.720 0.069 10.471 0.000 0.840 0.840
## FR4 0.708 0.068 10.463 0.000 0.827 0.826
## SD =~
## SD1 0.562 0.066 8.476 0.000 0.657 0.660
## SD2 0.737 0.066 11.193 0.000 0.861 0.866
## SD3 0.806 0.067 12.067 0.000 0.940 0.946
## SD4 0.763 0.066 11.575 0.000 0.890 0.895
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FR ~
## InhUpd (d1) 0.721 0.211 3.413 0.001 0.618 0.618
## Shift (d2) -0.246 0.180 -1.368 0.171 -0.211 -0.211
## SD ~
## InhUpd (d1) 0.721 0.211 3.413 0.001 0.618 0.618
## Shift (d2) -0.246 0.180 -1.368 0.171 -0.211 -0.211
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## InhUpd ~~
## Shift 0.615 0.103 5.948 0.000 0.615 0.615
## .FR ~~
## .SD 0.148 0.126 1.171 0.242 0.148 0.148
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Antisaccade -0.021 0.078 -0.266 0.790 -0.021 -0.021
## .KeepTrack -0.010 0.077 -0.132 0.895 -0.010 -0.010
## .SpatialBack -0.062 0.083 -0.747 0.455 -0.062 -0.062
## .LetMem -0.000 0.075 -0.006 0.995 -0.000 -0.000
## .NumLett -0.015 0.076 -0.199 0.842 -0.015 -0.015
## .ColShape -0.000 0.075 -0.003 0.998 -0.000 -0.000
## .CatSwitch -0.004 0.076 -0.047 0.963 -0.004 -0.004
## .FR1 0.004 0.076 0.059 0.953 0.004 0.004
## .FR2 0.006 0.076 0.084 0.933 0.006 0.006
## .FR3 0.007 0.076 0.091 0.927 0.007 0.007
## .FR4 0.007 0.076 0.090 0.928 0.007 0.007
## .SD1 -0.002 0.076 -0.026 0.979 -0.002 -0.002
## .SD2 -0.003 0.076 -0.034 0.973 -0.003 -0.003
## .SD3 -0.003 0.075 -0.037 0.970 -0.003 -0.003
## .SD4 -0.003 0.075 -0.035 0.972 -0.003 -0.003
## InhUpd 0.000 0.000 0.000
## Shift 0.000 0.000 0.000
## .FR 0.000 0.000 0.000
## .SD 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Antisaccade 0.550 0.102 5.375 0.000 0.550 0.554
## .KeepTrack 0.887 0.104 8.559 0.000 0.887 0.891
## .SpatialBack 0.679 0.103 6.570 0.000 0.679 0.671
## .LetMem 0.952 0.104 9.132 0.000 0.952 0.958
## .NumLett 0.406 0.092 4.432 0.000 0.406 0.407
## .ColShape 0.492 0.087 5.672 0.000 0.492 0.496
## .CatSwitch 0.727 0.090 8.034 0.000 0.727 0.731
## .FR1 0.708 0.082 8.634 0.000 0.708 0.710
## .FR2 0.401 0.058 6.953 0.000 0.401 0.401
## .FR3 0.295 0.051 5.791 0.000 0.295 0.295
## .FR4 0.318 0.052 6.087 0.000 0.318 0.318
## .SD1 0.560 0.065 8.674 0.000 0.560 0.565
## .SD2 0.248 0.035 7.036 0.000 0.248 0.251
## .SD3 0.103 0.025 4.159 0.000 0.103 0.105
## .SD4 0.196 0.028 6.908 0.000 0.196 0.198
## InhUpd 1.000 1.000 1.000
## Shift 1.000 1.000 1.000
## .FR 1.000 0.734 0.734
## .SD 1.000 0.734 0.734
##
## R-Square:
## Estimate
## Antisaccade 0.446
## KeepTrack 0.109
## SpatialBack 0.329
## LetMem 0.042
## NumLett 0.593
## ColShape 0.504
## CatSwitch 0.269
## FR1 0.290
## FR2 0.599
## FR3 0.705
## FR4 0.682
## SD1 0.435
## SD2 0.749
## SD3 0.895
## SD4 0.802
## FR 0.266
## SD 0.266semPaths(sem2f_norm_fit, "std", layout = "tree")