Latent Growth Model
In this post, I will show why LGM was not suitable for modeling our data.
Data preprocessing
library(dplyr)
library(lavaan)
library(semPlot)
library(data.table)
#library(apaTables)
library(psych)table<-as.matrix(describe(data))
table<-table[-c(1),c(3,4,12,13)]
library(knitr)
kable(print(table, digits=2))## mean sd kurtosis se
## Antisaccade 0.75 0.143 -0.611 0.0113
## StroopPerf 0.95 0.066 12.920 0.0050
## SSRTavg -280.07 99.543 1.403 8.3831
## LetMem 0.72 0.136 0.379 0.0103
## KeepTrack 0.79 0.090 -0.707 0.0070
## SpatialBack 0.84 0.101 -0.507 0.0085
## NumLett -399.56 195.024 3.172 14.9139
## ColShape -318.26 159.535 1.957 12.0597
## CatSwitch -245.36 135.915 0.368 10.3037
## FR1 0.63 0.071 0.338 0.0054
## FR2 0.67 0.083 0.054 0.0063
## FR3 0.68 0.088 0.161 0.0067
## FR4 0.70 0.098 -0.221 0.0074
## SD1 0.67 0.129 -1.131 0.0098
## SD2 0.77 0.138 -0.327 0.0105
## SD3 0.78 0.124 0.528 0.0094
## SD4 0.79 0.131 1.303 0.0099| mean | sd | kurtosis | se | |
|---|---|---|---|---|
| Antisaccade | 0.7507246 | 0.1434301 | -0.6112679 | 0.0113039 |
| StroopPerf | 0.9491435 | 0.0664097 | 12.9195476 | 0.0050058 |
| SSRTavg | -280.0650482 | 99.5432562 | 1.4029271 | 8.3830544 |
| LetMem | 0.7161578 | 0.1360090 | 0.3785893 | 0.0102813 |
| KeepTrack | 0.7909182 | 0.0899232 | -0.7068257 | 0.0069585 |
| SpatialBack | 0.8445645 | 0.1013671 | -0.5070834 | 0.0084767 |
| NumLett | -399.5594896 | 195.0239674 | 3.1722474 | 14.9138555 |
| ColShape | -318.2554522 | 159.5351990 | 1.9574696 | 12.0597275 |
| CatSwitch | -245.3623021 | 135.9154801 | 0.3684109 | 10.3037260 |
| FR1 | 0.6330925 | 0.0708614 | 0.3380205 | 0.0053875 |
| FR2 | 0.6715318 | 0.0828865 | 0.0543777 | 0.0063017 |
| FR3 | 0.6838873 | 0.0883038 | 0.1607651 | 0.0067136 |
| FR4 | 0.6955425 | 0.0978952 | -0.2209053 | 0.0074428 |
| SD1 | 0.6663589 | 0.1290260 | -1.1305562 | 0.0098097 |
| SD2 | 0.7679913 | 0.1379110 | -0.3267983 | 0.0104852 |
| SD3 | 0.7845376 | 0.1238585 | 0.5275628 | 0.0094168 |
| SD4 | 0.7895954 | 0.1307547 | 1.3029919 | 0.0099411 |
#convert Subj variable from numeric to factor
data$Subj<-as.factor(data$Subj)#Standardize all columns in the data, except for Subj and category blocks
data[,c(2:10)]<-scale(data[,c(2:10)])
head(data)Measurement model looking at whether SD and FR fits linear model
Latent Growth Model for SD category
Bad fit indices
sdcat<-'
i=~1*SD1+1*SD2+1*SD3+1*SD4
s=~0*SD1+1*SD2+2*SD3+3*SD4
'
sdcatfit <- growth(sdcat, data, missing='ml')## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 86 128 175summary(sdcatfit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 74 iterations
##
## Optimization method NLMINB
## Number of free parameters 9
##
## Used Total
## Number of observations 173 176
## Number of missing patterns 1
##
## Estimator ML
## Model Fit Test Statistic 115.897
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 553.253
## Degrees of freedom 6
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.797
## Tucker-Lewis Index (TLI) 0.757
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) 649.064
## Loglikelihood unrestricted model (H1) 707.012
##
## Number of free parameters 9
## Akaike (AIC) -1280.127
## Bayesian (BIC) -1251.748
## Sample-size adjusted Bayesian (BIC) -1280.247
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.358
## 90 Percent Confidence Interval 0.303 0.416
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.169
##
## 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
## i =~
## SD1 1.000 0.110 0.731
## SD2 1.000 0.110 0.845
## SD3 1.000 0.110 0.897
## SD4 1.000 0.110 0.825
## s =~
## SD1 0.000 0.000 0.000
## SD2 1.000 0.023 0.178
## SD3 2.000 0.047 0.378
## SD4 3.000 0.070 0.522
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~~
## s -0.000 0.001 -0.577 0.564 -0.113 -0.113
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SD1 0.000 0.000 0.000
## .SD2 0.000 0.000 0.000
## .SD3 0.000 0.000 0.000
## .SD4 0.000 0.000 0.000
## i 0.717 0.011 64.760 0.000 6.505 6.505
## s 0.028 0.004 7.498 0.000 1.223 1.223
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SD1 0.011 0.002 6.157 0.000 0.011 0.465
## .SD2 0.005 0.001 6.553 0.000 0.005 0.289
## .SD3 0.002 0.000 4.644 0.000 0.002 0.129
## .SD4 0.003 0.001 3.524 0.000 0.003 0.143
## i 0.012 0.002 6.283 0.000 1.000 1.000
## s 0.001 0.000 2.502 0.012 1.000 1.000
##
## R-Square:
## Estimate
## SD1 0.535
## SD2 0.711
## SD3 0.871
## SD4 0.857Latent Growth Model for FR category
Not so bad, but not optimal model fit because of RMSEA
frcat<-'
i=~1*FR1+1*FR2+1*FR3+1*FR4
s=~0*FR1+1*FR2+2*FR3+3*FR4
'
frcatfit <- growth(frcat, data, missing='ml')## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 91 116 133summary(frcatfit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 88 iterations
##
## Optimization method NLMINB
## Number of free parameters 9
##
## Used Total
## Number of observations 173 176
## Number of missing patterns 1
##
## Estimator ML
## Model Fit Test Statistic 18.535
## Degrees of freedom 5
## P-value (Chi-square) 0.002
##
## Model test baseline model:
##
## Minimum Function Test Statistic 287.656
## Degrees of freedom 6
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.952
## Tucker-Lewis Index (TLI) 0.942
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) 865.310
## Loglikelihood unrestricted model (H1) 874.577
##
## Number of free parameters 9
## Akaike (AIC) -1712.619
## Bayesian (BIC) -1684.240
## Sample-size adjusted Bayesian (BIC) -1712.739
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.125
## 90 Percent Confidence Interval 0.068 0.188
## P-value RMSEA <= 0.05 0.019
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.066
##
## 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
## i =~
## FR1 1.000 0.053 0.729
## FR2 1.000 0.053 0.668
## FR3 1.000 0.053 0.610
## FR4 1.000 0.053 0.536
## s =~
## FR1 0.000 0.000 0.000
## FR2 1.000 0.023 0.287
## FR3 2.000 0.046 0.525
## FR4 3.000 0.069 0.692
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~~
## s 0.000 0.000 0.222 0.824 0.039 0.039
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .FR1 0.000 0.000 0.000
## .FR2 0.000 0.000 0.000
## .FR3 0.000 0.000 0.000
## .FR4 0.000 0.000 0.000
## i 0.641 0.005 120.318 0.000 12.034 12.034
## s 0.020 0.002 8.080 0.000 0.864 0.864
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .FR1 0.003 0.001 4.750 0.000 0.003 0.469
## .FR2 0.003 0.000 7.444 0.000 0.003 0.456
## .FR3 0.002 0.000 6.409 0.000 0.002 0.328
## .FR4 0.002 0.001 3.399 0.001 0.002 0.204
## i 0.003 0.001 5.156 0.000 1.000 1.000
## s 0.001 0.000 3.848 0.000 1.000 1.000
##
## R-Square:
## Estimate
## FR1 0.531
## FR2 0.544
## FR3 0.672
## FR4 0.796Structural Model where EF predict i and s of SD
Same as seen in measurement model, not good fit. i and s are both significant, and both EF components siginificantly prefict i of FR learning, but neither significantly predict s.
sdmodel<- '
Inhibit=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~ NumLett+ColShape+CatSwitch
i~Inhibit+Shift
s~Inhibit+Shift
i=~1*SD1+1*SD2+1*SD3+1*SD4
s=~0*SD1+1*SD2+2*SD3+3*SD4
'
sdfit <- growth(sdmodel, data, missing='ml')
summary(sdfit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 124 iterations
##
## Optimization method NLMINB
## Number of free parameters 34
##
## Number of observations 176
## Number of missing patterns 20
##
## Estimator ML
## Model Fit Test Statistic 181.922
## Degrees of freedom 70
## P-value (Chi-square) 0.000
##
## 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) 0.849
## Tucker-Lewis Index (TLI) 0.832
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1351.049
## Loglikelihood unrestricted model (H1) -1260.088
##
## Number of free parameters 34
## Akaike (AIC) 2770.098
## Bayesian (BIC) 2877.895
## Sample-size adjusted Bayesian (BIC) 2770.225
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.095
## 90 Percent Confidence Interval 0.078 0.112
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.080
##
## 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 1.000 0.209 0.210
## SSRTavg 0.762 0.576 1.322 0.186 0.160 0.160
## Antisaccade 3.103 1.385 2.240 0.025 0.650 0.652
## KeepTrack 1.694 0.840 2.016 0.044 0.355 0.356
## SpatialBack 2.764 1.256 2.201 0.028 0.579 0.574
## LetMem 0.865 0.579 1.493 0.135 0.181 0.182
## Shift =~
## NumLett 1.000 0.756 0.757
## ColShape 0.949 0.148 6.394 0.000 0.717 0.720
## CatSwitch 0.691 0.131 5.287 0.000 0.523 0.524
## i =~
## SD1 1.000 0.111 0.736
## SD2 1.000 0.111 0.850
## SD3 1.000 0.111 0.897
## SD4 1.000 0.111 0.832
## s =~
## SD1 0.000 0.000 0.000
## SD2 1.000 0.024 0.185
## SD3 2.000 0.048 0.390
## SD4 3.000 0.072 0.543
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~
## Inhibit 0.449 0.220 2.036 0.042 0.850 0.850
## Shift -0.058 0.030 -1.950 0.051 -0.397 -0.397
## s ~
## Inhibit -0.001 0.029 -0.038 0.970 -0.009 -0.009
## Shift -0.001 0.007 -0.150 0.881 -0.035 -0.035
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit ~~
## Shift 0.096 0.045 2.146 0.032 0.604 0.604
## .i ~~
## .s -0.000 0.001 -0.637 0.524 -0.171 -0.171
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.000 0.000
## .SSRTavg 0.000 0.000 0.000
## .Antisaccade 0.000 0.000 0.000
## .KeepTrack 0.000 0.000 0.000
## .SpatialBack 0.000 0.000 0.000
## .LetMem 0.000 0.000 0.000
## .NumLett 0.000 0.000 0.000
## .ColShape 0.000 0.000 0.000
## .CatSwitch 0.000 0.000 0.000
## .SD1 0.000 0.000 0.000
## .SD2 0.000 0.000 0.000
## .SD3 0.000 0.000 0.000
## .SD4 0.000 0.000 0.000
## Inhibit -0.013 0.022 -0.591 0.555 -0.062 -0.062
## Shift -0.007 0.067 -0.111 0.911 -0.010 -0.010
## .i 0.722 0.012 61.966 0.000 6.530 6.530
## .s 0.028 0.004 7.377 0.000 1.172 1.172
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.950 0.104 9.178 0.000 0.950 0.956
## .SSRTavg 0.968 0.117 8.296 0.000 0.968 0.974
## .Antisaccade 0.571 0.099 5.782 0.000 0.571 0.575
## .KeepTrack 0.869 0.102 8.525 0.000 0.869 0.874
## .SpatialBack 0.683 0.104 6.600 0.000 0.683 0.671
## .LetMem 0.961 0.105 9.191 0.000 0.961 0.967
## .NumLett 0.424 0.091 4.666 0.000 0.424 0.426
## .ColShape 0.479 0.087 5.486 0.000 0.479 0.482
## .CatSwitch 0.722 0.090 7.984 0.000 0.722 0.725
## .SD1 0.010 0.002 6.141 0.000 0.010 0.459
## .SD2 0.005 0.001 6.507 0.000 0.005 0.286
## .SD3 0.002 0.000 4.909 0.000 0.002 0.138
## .SD4 0.002 0.001 3.256 0.001 0.002 0.134
## Inhibit 0.044 0.038 1.164 0.244 1.000 1.000
## Shift 0.571 0.125 4.554 0.000 1.000 1.000
## .i 0.006 0.002 2.964 0.003 0.528 0.528
## .s 0.001 0.000 2.666 0.008 0.998 0.998
##
## R-Square:
## Estimate
## StroopPerf 0.044
## SSRTavg 0.026
## Antisaccade 0.425
## KeepTrack 0.126
## SpatialBack 0.329
## LetMem 0.033
## NumLett 0.574
## ColShape 0.518
## CatSwitch 0.275
## SD1 0.541
## SD2 0.714
## SD3 0.862
## SD4 0.866
## i 0.472
## s 0.002Structural Model where EF predict i and s of FR
Actually the fit is good here. i and s are both significant, but neither of the EF components siginificantly prefict FR learning
frmodel<- '
Inhibit=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~ NumLett+ColShape+CatSwitch
i~Inhibit+Shift
s~Inhibit+Shift
i=~1*FR1+1*FR2+1*FR3+1*FR4
s=~0*FR1+1*FR2+2*FR3+3*FR4
'
frfit <- growth(frmodel, data, missing='ml')
summary(frfit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 160 iterations
##
## Optimization method NLMINB
## Number of free parameters 34
##
## Number of observations 176
## Number of missing patterns 20
##
## Estimator ML
## Model Fit Test Statistic 85.250
## Degrees of freedom 70
## P-value (Chi-square) 0.104
##
## 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) 0.967
## Tucker-Lewis Index (TLI) 0.963
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1141.466
## Loglikelihood unrestricted model (H1) -1098.841
##
## Number of free parameters 34
## Akaike (AIC) 2350.931
## Bayesian (BIC) 2458.728
## Sample-size adjusted Bayesian (BIC) 2351.058
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.035
## 90 Percent Confidence Interval 0.000 0.059
## P-value RMSEA <= 0.05 0.831
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.064
##
## 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 1.000 0.188 0.188
## SSRTavg 1.146 0.791 1.448 0.148 0.215 0.216
## Antisaccade 3.586 1.878 1.910 0.056 0.673 0.673
## KeepTrack 1.900 1.083 1.755 0.079 0.356 0.357
## SpatialBack 2.739 1.469 1.865 0.062 0.514 0.512
## LetMem 1.242 0.817 1.520 0.128 0.233 0.234
## Shift =~
## NumLett 1.000 0.761 0.763
## ColShape 0.944 0.149 6.353 0.000 0.719 0.721
## CatSwitch 0.676 0.128 5.294 0.000 0.515 0.516
## i =~
## FR1 1.000 0.054 0.740
## FR2 1.000 0.054 0.671
## FR3 1.000 0.054 0.612
## FR4 1.000 0.054 0.544
## s =~
## FR1 0.000 0.000 0.000
## FR2 1.000 0.023 0.294
## FR3 2.000 0.047 0.535
## FR4 3.000 0.070 0.713
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~
## Inhibit 0.134 0.088 1.510 0.131 0.466 0.466
## Shift -0.003 0.013 -0.246 0.806 -0.046 -0.046
## s ~
## Inhibit 0.034 0.031 1.091 0.275 0.273 0.273
## Shift -0.003 0.006 -0.441 0.659 -0.086 -0.086
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit ~~
## Shift 0.087 0.047 1.862 0.063 0.610 0.610
## .i ~~
## .s -0.000 0.000 -0.528 0.597 -0.104 -0.104
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.000 0.000
## .SSRTavg 0.000 0.000 0.000
## .Antisaccade 0.000 0.000 0.000
## .KeepTrack 0.000 0.000 0.000
## .SpatialBack 0.000 0.000 0.000
## .LetMem 0.000 0.000 0.000
## .NumLett 0.000 0.000 0.000
## .ColShape 0.000 0.000 0.000
## .CatSwitch 0.000 0.000 0.000
## .FR1 0.000 0.000 0.000
## .FR2 0.000 0.000 0.000
## .FR3 0.000 0.000 0.000
## .FR4 0.000 0.000 0.000
## Inhibit -0.009 0.019 -0.440 0.660 -0.046 -0.046
## Shift -0.008 0.067 -0.122 0.903 -0.011 -0.011
## .i 0.642 0.005 120.947 0.000 11.947 11.947
## .s 0.020 0.002 8.173 0.000 0.857 0.857
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.959 0.105 9.171 0.000 0.959 0.965
## .SSRTavg 0.946 0.116 8.125 0.000 0.946 0.953
## .Antisaccade 0.546 0.111 4.910 0.000 0.546 0.547
## .KeepTrack 0.869 0.104 8.339 0.000 0.869 0.872
## .SpatialBack 0.742 0.108 6.872 0.000 0.742 0.738
## .LetMem 0.940 0.104 9.029 0.000 0.940 0.945
## .NumLett 0.417 0.091 4.582 0.000 0.417 0.419
## .ColShape 0.477 0.088 5.432 0.000 0.477 0.480
## .CatSwitch 0.730 0.090 8.098 0.000 0.730 0.734
## .FR1 0.002 0.001 4.620 0.000 0.002 0.452
## .FR2 0.003 0.000 7.497 0.000 0.003 0.460
## .FR3 0.003 0.000 6.523 0.000 0.003 0.334
## .FR4 0.002 0.001 3.161 0.002 0.002 0.189
## Inhibit 0.035 0.036 0.991 0.322 1.000 1.000
## Shift 0.580 0.127 4.579 0.000 1.000 1.000
## .i 0.002 0.001 4.212 0.000 0.806 0.806
## .s 0.001 0.000 3.810 0.000 0.947 0.947
##
## R-Square:
## Estimate
## StroopPerf 0.035
## SSRTavg 0.047
## Antisaccade 0.453
## KeepTrack 0.128
## SpatialBack 0.262
## LetMem 0.055
## NumLett 0.581
## ColShape 0.520
## CatSwitch 0.266
## FR1 0.548
## FR2 0.540
## FR3 0.666
## FR4 0.811
## i 0.194
## s 0.053Structural Model where EF predict both SD and FR
With equality constraints for i and s across categories
equalmodel<- '
Inhibit=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~ NumLett+ColShape+CatSwitch
NRD_i~d1*Inhibit+d2*Shift
NRD_s~d3*Inhibit+d4*Shift
NRD_i=~1*FR1+1*FR2+1*FR3+1*FR4
NRD_s=~0*FR1+1*FR2+2*FR3+3*FR4
RD_i~d1*Inhibit+d2*Shift
RD_s~d3*Inhibit+d4*Shift
RD_i=~1*SD1+1*SD2+1*SD3+1*SD4
RD_s=~0*SD1+1*SD2+2*SD3+3*SD4
'
equalfit <- growth(equalmodel, data, missing='ml')
summary(equalfit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 306 iterations
##
## Optimization method NLMINB
## Number of free parameters 51
## Number of equality constraints 4
##
## Number of observations 176
## Number of missing patterns 21
##
## Estimator ML
## Model Fit Test Statistic 265.381
## Degrees of freedom 123
## 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) 0.865
## Tucker-Lewis Index (TLI) 0.851
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -475.492
## Loglikelihood unrestricted model (H1) -342.802
##
## Number of free parameters 47
## Akaike (AIC) 1044.985
## Bayesian (BIC) 1193.997
## Sample-size adjusted Bayesian (BIC) 1045.160
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent Confidence Interval 0.068 0.094
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.084
##
## 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 1.000 0.207 0.207
## SSRTavg 1.116 0.690 1.617 0.106 0.230 0.231
## Antisaccade 3.167 1.479 2.141 0.032 0.654 0.655
## KeepTrack 1.601 0.848 1.887 0.059 0.331 0.331
## SpatialBack 2.634 1.246 2.115 0.034 0.544 0.542
## LetMem 1.038 0.656 1.581 0.114 0.214 0.215
## Shift =~
## NumLett 1.000 0.758 0.759
## ColShape 0.950 0.151 6.297 0.000 0.720 0.723
## CatSwitch 0.682 0.129 5.276 0.000 0.517 0.519
## NRD_i =~
## FR1 1.000 0.057 0.767
## FR2 1.000 0.057 0.693
## FR3 1.000 0.057 0.634
## FR4 1.000 0.057 0.572
## NRD_s =~
## FR1 0.000 0.000 0.000
## FR2 1.000 0.024 0.293
## FR3 2.000 0.048 0.536
## FR4 3.000 0.072 0.725
## RD_i =~
## SD1 1.000 0.105 0.718
## SD2 1.000 0.105 0.830
## SD3 1.000 0.105 0.881
## SD4 1.000 0.105 0.807
## RD_s =~
## SD1 0.000 0.000 0.000
## SD2 1.000 0.024 0.191
## SD3 2.000 0.048 0.405
## SD4 3.000 0.072 0.556
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NRD_i ~
## Inhibit (d1) 0.186 0.097 1.910 0.056 0.678 0.678
## Shift (d2) -0.013 0.014 -0.942 0.346 -0.171 -0.171
## NRD_s ~
## Inhibit (d3) 0.021 0.021 1.016 0.309 0.181 0.181
## Shift (d4) -0.002 0.005 -0.531 0.595 -0.077 -0.077
## RD_i ~
## Inhibit (d1) 0.186 0.097 1.910 0.056 0.367 0.367
## Shift (d2) -0.013 0.014 -0.942 0.346 -0.093 -0.093
## RD_s ~
## Inhibit (d3) 0.021 0.021 1.016 0.309 0.180 0.180
## Shift (d4) -0.002 0.005 -0.531 0.595 -0.077 -0.077
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit ~~
## Shift 0.094 0.045 2.066 0.039 0.599 0.599
## .NRD_i ~~
## .NRD_s -0.000 0.000 -0.744 0.457 -0.150 -0.150
## .RD_i 0.001 0.001 0.815 0.415 0.135 0.135
## .RD_s 0.000 0.000 0.077 0.939 0.015 0.015
## .NRD_s ~~
## .RD_i 0.000 0.000 1.004 0.316 0.136 0.136
## .RD_s -0.000 0.000 -0.486 0.627 -0.084 -0.084
## .RD_i ~~
## .RD_s -0.000 0.000 -0.842 0.400 -0.177 -0.177
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.000 0.000
## .SSRTavg 0.000 0.000 0.000
## .Antisaccade 0.000 0.000 0.000
## .KeepTrack 0.000 0.000 0.000
## .SpatialBack 0.000 0.000 0.000
## .LetMem 0.000 0.000 0.000
## .NumLett 0.000 0.000 0.000
## .ColShape 0.000 0.000 0.000
## .CatSwitch 0.000 0.000 0.000
## .FR1 0.000 0.000 0.000
## .FR2 0.000 0.000 0.000
## .FR3 0.000 0.000 0.000
## .FR4 0.000 0.000 0.000
## .SD1 0.000 0.000 0.000
## .SD2 0.000 0.000 0.000
## .SD3 0.000 0.000 0.000
## .SD4 0.000 0.000 0.000
## Inhibit -0.011 0.022 -0.509 0.611 -0.053 -0.053
## Shift -0.008 0.067 -0.120 0.904 -0.011 -0.011
## .NRD_i 0.643 0.006 115.885 0.000 11.337 11.337
## .NRD_s 0.020 0.002 8.167 0.000 0.839 0.839
## .RD_i 0.718 0.011 66.426 0.000 6.863 6.863
## .RD_s 0.029 0.004 7.533 0.000 1.197 1.197
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.952 0.104 9.157 0.000 0.952 0.957
## .SSRTavg 0.939 0.115 8.136 0.000 0.939 0.946
## .Antisaccade 0.568 0.104 5.461 0.000 0.568 0.570
## .KeepTrack 0.886 0.104 8.502 0.000 0.886 0.890
## .SpatialBack 0.710 0.104 6.801 0.000 0.710 0.706
## .LetMem 0.948 0.104 9.103 0.000 0.948 0.954
## .NumLett 0.422 0.092 4.599 0.000 0.422 0.424
## .ColShape 0.474 0.088 5.362 0.000 0.474 0.478
## .CatSwitch 0.727 0.090 8.060 0.000 0.727 0.731
## .FR1 0.002 0.001 4.428 0.000 0.002 0.412
## .FR2 0.003 0.000 7.517 0.000 0.003 0.448
## .FR3 0.003 0.000 6.582 0.000 0.003 0.333
## .FR4 0.002 0.001 2.940 0.003 0.002 0.175
## .SD1 0.010 0.002 6.082 0.000 0.010 0.484
## .SD2 0.005 0.001 6.596 0.000 0.005 0.313
## .SD3 0.002 0.000 4.796 0.000 0.002 0.144
## .SD4 0.002 0.001 3.367 0.001 0.002 0.147
## Inhibit 0.043 0.038 1.122 0.262 1.000 1.000
## Shift 0.575 0.127 4.530 0.000 1.000 1.000
## .NRD_i 0.002 0.001 3.565 0.000 0.650 0.650
## .NRD_s 0.001 0.000 4.053 0.000 0.978 0.978
## .RD_i 0.010 0.002 5.393 0.000 0.897 0.897
## .RD_s 0.001 0.000 2.614 0.009 0.978 0.978
##
## R-Square:
## Estimate
## StroopPerf 0.043
## SSRTavg 0.054
## Antisaccade 0.430
## KeepTrack 0.110
## SpatialBack 0.294
## LetMem 0.046
## NumLett 0.576
## ColShape 0.522
## CatSwitch 0.269
## FR1 0.588
## FR2 0.552
## FR3 0.667
## FR4 0.825
## SD1 0.516
## SD2 0.687
## SD3 0.856
## SD4 0.853
## NRD_i 0.350
## NRD_s 0.022
## RD_i 0.103
## RD_s 0.022unconstrained
allmodel<- '
Inhibit=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~ NumLett+ColShape+CatSwitch
NRD_i~Inhibit+Shift
NRD_s~Inhibit+Shift
NRD_i=~1*FR1+1*FR2+1*FR3+1*FR4
NRD_s=~0*FR1+1*FR2+2*FR3+3*FR4
RD_i~Inhibit+Shift
RD_s~Inhibit+Shift
RD_i=~1*SD1+1*SD2+1*SD3+1*SD4
RD_s=~0*SD1+1*SD2+2*SD3+3*SD4
'
allfit <- growth(allmodel, data, missing='ml')
summary(allfit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 299 iterations
##
## Optimization method NLMINB
## Number of free parameters 51
##
## Number of observations 176
## Number of missing patterns 21
##
## Estimator ML
## Model Fit Test Statistic 251.297
## Degrees of freedom 119
## 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) 0.875
## Tucker-Lewis Index (TLI) 0.857
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -468.450
## Loglikelihood unrestricted model (H1) -342.802
##
## Number of free parameters 51
## Akaike (AIC) 1038.900
## Bayesian (BIC) 1200.595
## Sample-size adjusted Bayesian (BIC) 1039.090
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent Confidence Interval 0.066 0.093
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.075
##
## 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 1.000 0.220 0.221
## SSRTavg 0.884 0.575 1.537 0.124 0.195 0.195
## Antisaccade 2.965 1.256 2.361 0.018 0.653 0.655
## KeepTrack 1.481 0.729 2.031 0.042 0.326 0.327
## SpatialBack 2.588 1.116 2.319 0.020 0.570 0.567
## LetMem 0.858 0.545 1.573 0.116 0.189 0.189
## Shift =~
## NumLett 1.000 0.756 0.758
## ColShape 0.953 0.151 6.329 0.000 0.721 0.723
## CatSwitch 0.684 0.130 5.272 0.000 0.517 0.519
## NRD_i =~
## FR1 1.000 0.054 0.751
## FR2 1.000 0.054 0.674
## FR3 1.000 0.054 0.614
## FR4 1.000 0.054 0.550
## NRD_s =~
## FR1 0.000 0.000 0.000
## FR2 1.000 0.024 0.298
## FR3 2.000 0.048 0.543
## FR4 3.000 0.072 0.730
## RD_i =~
## SD1 1.000 0.111 0.737
## SD2 1.000 0.111 0.849
## SD3 1.000 0.111 0.896
## SD4 1.000 0.111 0.831
## RD_s =~
## SD1 0.000 0.000 0.000
## SD2 1.000 0.024 0.184
## SD3 2.000 0.048 0.389
## SD4 3.000 0.072 0.542
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NRD_i ~
## Inhibit 0.117 0.067 1.749 0.080 0.476 0.476
## Shift -0.003 0.013 -0.248 0.804 -0.044 -0.044
## NRD_s ~
## Inhibit 0.025 0.024 1.046 0.296 0.232 0.232
## Shift -0.002 0.006 -0.322 0.747 -0.060 -0.060
## RD_i ~
## Inhibit 0.420 0.196 2.142 0.032 0.836 0.836
## Shift -0.054 0.029 -1.866 0.062 -0.369 -0.369
## RD_s ~
## Inhibit -0.001 0.027 -0.029 0.977 -0.007 -0.007
## Shift -0.001 0.007 -0.163 0.871 -0.037 -0.037
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit ~~
## Shift 0.099 0.044 2.236 0.025 0.593 0.593
## .NRD_i ~~
## .NRD_s -0.000 0.000 -0.644 0.520 -0.123 -0.123
## .RD_i 0.000 0.001 0.639 0.523 0.127 0.127
## .RD_s 0.000 0.000 0.224 0.823 0.040 0.040
## .NRD_s ~~
## .RD_i 0.000 0.000 0.482 0.630 0.088 0.088
## .RD_s -0.000 0.000 -0.381 0.703 -0.066 -0.066
## .RD_i ~~
## .RD_s -0.000 0.001 -0.634 0.526 -0.169 -0.169
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.000 0.000
## .SSRTavg 0.000 0.000 0.000
## .Antisaccade 0.000 0.000 0.000
## .KeepTrack 0.000 0.000 0.000
## .SpatialBack 0.000 0.000 0.000
## .LetMem 0.000 0.000 0.000
## .NumLett 0.000 0.000 0.000
## .ColShape 0.000 0.000 0.000
## .CatSwitch 0.000 0.000 0.000
## .FR1 0.000 0.000 0.000
## .FR2 0.000 0.000 0.000
## .FR3 0.000 0.000 0.000
## .FR4 0.000 0.000 0.000
## .SD1 0.000 0.000 0.000
## .SD2 0.000 0.000 0.000
## .SD3 0.000 0.000 0.000
## .SD4 0.000 0.000 0.000
## Inhibit -0.013 0.023 -0.584 0.559 -0.061 -0.061
## Shift -0.008 0.067 -0.114 0.909 -0.010 -0.010
## .NRD_i 0.642 0.005 120.815 0.000 11.851 11.851
## .NRD_s 0.020 0.002 8.182 0.000 0.843 0.843
## .RD_i 0.721 0.012 62.236 0.000 6.522 6.522
## .RD_s 0.028 0.004 7.415 0.000 1.179 1.179
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.946 0.103 9.167 0.000 0.946 0.951
## .SSRTavg 0.956 0.116 8.239 0.000 0.956 0.962
## .Antisaccade 0.567 0.099 5.757 0.000 0.567 0.571
## .KeepTrack 0.889 0.103 8.600 0.000 0.889 0.893
## .SpatialBack 0.686 0.102 6.759 0.000 0.686 0.679
## .LetMem 0.958 0.104 9.182 0.000 0.958 0.964
## .NumLett 0.424 0.092 4.630 0.000 0.424 0.426
## .ColShape 0.474 0.088 5.377 0.000 0.474 0.477
## .CatSwitch 0.727 0.090 8.042 0.000 0.727 0.731
## .FR1 0.002 0.001 4.478 0.000 0.002 0.437
## .FR2 0.003 0.000 7.534 0.000 0.003 0.463
## .FR3 0.003 0.000 6.574 0.000 0.003 0.339
## .FR4 0.002 0.001 2.970 0.003 0.002 0.179
## .SD1 0.010 0.002 6.119 0.000 0.010 0.456
## .SD2 0.005 0.001 6.543 0.000 0.005 0.287
## .SD3 0.002 0.000 4.915 0.000 0.002 0.138
## .SD4 0.002 0.001 3.262 0.001 0.002 0.135
## Inhibit 0.048 0.039 1.236 0.217 1.000 1.000
## Shift 0.572 0.126 4.535 0.000 1.000 1.000
## .NRD_i 0.002 0.001 4.242 0.000 0.796 0.796
## .NRD_s 0.001 0.000 3.995 0.000 0.959 0.959
## .RD_i 0.006 0.002 3.002 0.003 0.531 0.531
## .RD_s 0.001 0.000 2.667 0.008 0.998 0.998
##
## R-Square:
## Estimate
## StroopPerf 0.049
## SSRTavg 0.038
## Antisaccade 0.429
## KeepTrack 0.107
## SpatialBack 0.321
## LetMem 0.036
## NumLett 0.574
## ColShape 0.523
## CatSwitch 0.269
## FR1 0.563
## FR2 0.537
## FR3 0.661
## FR4 0.821
## SD1 0.544
## SD2 0.713
## SD3 0.862
## SD4 0.865
## NRD_i 0.204
## NRD_s 0.041
## RD_i 0.469
## RD_s 0.002Chi-square difference test compare unconstrained and constrained
anova(allfit, equalfit)semPaths(allfit, layout='tree')
Auto-regressive Paths Analysis of SD and FR
pathmodel<- '
Inhibit=~StroopPerf+SSRTavg+Antisaccade+KeepTrack+SpatialBack+LetMem
Shift=~ NumLett+ColShape+CatSwitch
NRD_i~Inhibit+Shift
NRD_i=~1*FR1+1*FR2+1*FR3+1*FR4
FR2~FR1
FR3~FR2
FR4~FR3
RD_i~Inhibit+Shift
RD_i=~1*SD1+1*SD2+1*SD3+1*SD4
SD2~SD1
SD3~SD2
SD4~SD3
'
pathfit <- growth(pathmodel, data, missing='ml')
summary(pathfit, fit.measures=T, standardized=T, rsquare=T)## lavaan 0.6-3 ended normally after 194 iterations
##
## Optimization method NLMINB
## Number of free parameters 44
##
## Number of observations 176
## Number of missing patterns 21
##
## Estimator ML
## Model Fit Test Statistic 176.268
## Degrees of freedom 126
## P-value (Chi-square) 0.002
##
## 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) 0.952
## Tucker-Lewis Index (TLI) 0.949
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -430.936
## Loglikelihood unrestricted model (H1) -342.802
##
## Number of free parameters 44
## Akaike (AIC) 949.871
## Bayesian (BIC) 1089.373
## Sample-size adjusted Bayesian (BIC) 950.036
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.048
## 90 Percent Confidence Interval 0.029 0.063
## P-value RMSEA <= 0.05 0.580
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.075
##
## 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 1.000 0.218 0.219
## SSRTavg 0.891 0.582 1.531 0.126 0.194 0.195
## Antisaccade 2.949 1.265 2.332 0.020 0.643 0.645
## KeepTrack 1.503 0.746 2.015 0.044 0.328 0.328
## SpatialBack 2.677 1.162 2.305 0.021 0.584 0.580
## LetMem 0.836 0.546 1.532 0.126 0.182 0.183
## Shift =~
## NumLett 1.000 0.757 0.759
## ColShape 0.951 0.149 6.390 0.000 0.720 0.723
## CatSwitch 0.683 0.128 5.332 0.000 0.517 0.519
## NRD_i =~
## FR1 1.000 0.059 0.710
## FR2 1.000 0.059 0.722
## FR3 1.000 0.059 0.699
## FR4 1.000 0.059 0.654
## RD_i =~
## SD1 1.000 0.096 0.698
## SD2 1.000 0.096 0.726
## SD3 1.000 0.096 0.773
## SD4 1.000 0.096 0.750
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NRD_i ~
## Inhibit 0.144 0.074 1.930 0.054 0.530 0.530
## Shift -0.005 0.012 -0.410 0.682 -0.065 -0.065
## FR2 ~
## FR1 0.065 0.009 6.935 0.000 0.065 0.066
## FR3 ~
## FR2 0.080 0.009 8.873 0.000 0.080 0.077
## FR4 ~
## FR3 0.098 0.009 10.385 0.000 0.098 0.091
## RD_i ~
## Inhibit 0.364 0.170 2.144 0.032 0.824 0.824
## Shift -0.049 0.023 -2.117 0.034 -0.382 -0.382
## SD2 ~
## SD1 0.165 0.013 12.252 0.000 0.165 0.171
## SD3 ~
## SD2 0.160 0.011 14.982 0.000 0.160 0.170
## SD4 ~
## SD3 0.165 0.011 15.188 0.000 0.165 0.160
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Inhibit ~~
## Shift 0.098 0.044 2.219 0.027 0.594 0.594
## .NRD_i ~~
## .RD_i 0.001 0.001 0.855 0.393 0.144 0.144
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.000 0.000 0.000
## .SSRTavg 0.000 0.000 0.000
## .Antisaccade 0.000 0.000 0.000
## .KeepTrack 0.000 0.000 0.000
## .SpatialBack 0.000 0.000 0.000
## .LetMem 0.000 0.000 0.000
## .NumLett 0.000 0.000 0.000
## .ColShape 0.000 0.000 0.000
## .CatSwitch 0.000 0.000 0.000
## .FR1 0.000 0.000 0.000
## .FR2 0.000 0.000 0.000
## .FR3 0.000 0.000 0.000
## .FR4 0.000 0.000 0.000
## .SD1 0.000 0.000 0.000
## .SD2 0.000 0.000 0.000
## .SD3 0.000 0.000 0.000
## .SD4 0.000 0.000 0.000
## Inhibit -0.013 0.023 -0.590 0.555 -0.062 -0.062
## Shift -0.007 0.067 -0.110 0.912 -0.010 -0.010
## .NRD_i 0.633 0.006 100.293 0.000 10.724 10.724
## .RD_i 0.665 0.011 61.448 0.000 6.910 6.910
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .StroopPerf 0.947 0.103 9.169 0.000 0.947 0.952
## .SSRTavg 0.956 0.116 8.241 0.000 0.956 0.962
## .Antisaccade 0.581 0.098 5.937 0.000 0.581 0.585
## .KeepTrack 0.888 0.104 8.582 0.000 0.888 0.892
## .SpatialBack 0.673 0.101 6.660 0.000 0.673 0.664
## .LetMem 0.961 0.105 9.194 0.000 0.961 0.967
## .NumLett 0.423 0.090 4.684 0.000 0.423 0.424
## .ColShape 0.475 0.088 5.410 0.000 0.475 0.478
## .CatSwitch 0.727 0.090 8.078 0.000 0.727 0.731
## .FR1 0.003 0.000 7.311 0.000 0.003 0.496
## .FR2 0.003 0.000 7.047 0.000 0.003 0.406
## .FR3 0.003 0.000 7.175 0.000 0.003 0.423
## .FR4 0.004 0.001 7.589 0.000 0.004 0.474
## .SD1 0.010 0.001 8.340 0.000 0.010 0.513
## .SD2 0.005 0.001 7.508 0.000 0.005 0.271
## .SD3 0.002 0.000 5.813 0.000 0.002 0.152
## .SD4 0.003 0.000 6.750 0.000 0.003 0.192
## Inhibit 0.047 0.039 1.220 0.223 1.000 1.000
## Shift 0.573 0.125 4.578 0.000 1.000 1.000
## .NRD_i 0.003 0.000 5.392 0.000 0.756 0.756
## .RD_i 0.005 0.001 3.658 0.000 0.549 0.549
##
## R-Square:
## Estimate
## StroopPerf 0.048
## SSRTavg 0.038
## Antisaccade 0.415
## KeepTrack 0.108
## SpatialBack 0.336
## LetMem 0.033
## NumLett 0.576
## ColShape 0.522
## CatSwitch 0.269
## FR1 0.504
## FR2 0.594
## FR3 0.577
## FR4 0.526
## SD1 0.487
## SD2 0.729
## SD3 0.848
## SD4 0.808
## NRD_i 0.244
## RD_i 0.451semPaths(pathfit,layout='tree')