Construct Validity of the WASI and WRIT - Reanalysis
Setup
#Packages
library(pacman); p_load(psych, lavaan, semPlot)
#Functions
CONGO <- function(F1, F2) {
PHI = sum(F1*F2) / sqrt(sum(F1^2)*sum(F2^2))
return(PHI)}
CRITR <- function(n, alpha = .05) {
df <- n - 2; CRITT <- qt(alpha/2, df, lower.tail = F)
CRITR <- sqrt((CRITT^2)/((CRITT^2) + df ))
return(CRITR)}
NP <- function(N, S = 2) {
NP = 1-pnorm(qnorm(1-(N^(-6/5))/S))
return(NP)}
#Model Fit Measures
FITM <- c("chisq", "df", "nPar", "cfi", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "aic", "bic")#Data
##Correlation Matrices
lowerCANEA <-'
1
0.57 1
0.79 0.57 1
0.62 0.65 0.6 1
0.69 0.51 0.7 0.53 1
0.83 0.54 0.74 0.57 0.71 1
0.56 0.59 0.58 0.71 0.65 0.58 1
0.51 0.66 0.55 0.62 0.51 0.53 0.62 1'
lowerCANEAWASI <- '
1
0.57 1
0.79 0.57 1
0.62 0.65 0.6 1'
lowerCANEAWRIT <- '
1
0.71 1
0.65 0.58 1
0.51 0.53 0.62 1'
CANEA.cor = getCov(lowerCANEA, names = c("VocWA", "BD", "SIM", "MR", "VA", "VocWR", "MAT", "DIA"))
CANEAWASI.cor = getCov(lowerCANEAWASI, names = c("VocWA", "BD", "SIM", "MR"))
CANEAWRIT.cor = getCov(lowerCANEAWRIT, names = c("VA", "VocWR", "MAT", "DIA"))
##Sample Size
nCANEA <- 152Analysis
Parallel Analyses
fa.parallel(CANEA.cor, n.obs = nCANEA)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1fa.parallel(CANEAWASI.cor, n.obs = nCANEA)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1fa.parallel(CANEAWRIT.cor, n.obs = nCANEA)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1Exploratory Factor Analyses
FATOT1 <- fa(CANEA.cor, n.obs = nCANEA, nfactors = 1)
FATOT2 <- fa(CANEA.cor, n.obs = nCANEA, nfactors = 2)## Loading required namespace: GPArotationFAWASI1 <- fa(CANEAWASI.cor, n.obs = nCANEA, nfactors = 1)
FAWASI2 <- fa(CANEAWASI.cor, n.obs = nCANEA, nfactors = 2)
FAWRIT1 <- fa(CANEAWRIT.cor, n.obs = nCANEA, nfactors = 1)
FAWRIT2 <- fa(CANEAWRIT.cor, n.obs = nCANEA, nfactors = 2)
print(FATOT1$loadings)##
## Loadings:
## MR1
## VocWA 0.844
## BD 0.732
## SIM 0.834
## MR 0.776
## VA 0.785
## VocWR 0.829
## MAT 0.774
## DIA 0.713
##
## MR1
## SS loadings 4.957
## Proportion Var 0.620print(FATOT2$loadings)##
## Loadings:
## MR1 MR2
## VocWA 0.956
## BD 0.777
## SIM 0.767 0.113
## MR 0.796
## VA 0.662 0.162
## VocWR 0.920
## MAT 0.739
## DIA 0.839
##
## MR1 MR2
## SS loadings 2.801 2.529
## Proportion Var 0.350 0.316
## Cumulative Var 0.350 0.666print(FAWASI1$loadings)##
## Loadings:
## MR1
## VocWA 0.853
## BD 0.724
## SIM 0.840
## MR 0.768
##
## MR1
## SS loadings 2.547
## Proportion Var 0.637print(FAWASI2$loadings)##
## Loadings:
## MR1 MR2
## VocWA 1.009
## BD 0.836
## SIM 0.620 0.249
## MR 0.743
##
## MR1 MR2
## SS loadings 1.412 1.314
## Proportion Var 0.353 0.328
## Cumulative Var 0.353 0.681print(FAWRIT1$loadings)##
## Loadings:
## MR1
## VA 0.825
## VocWR 0.789
## MAT 0.800
## DIA 0.687
##
## MR1
## SS loadings 2.415
## Proportion Var 0.604print(FAWRIT2$loadings)##
## Loadings:
## MR1 MR2
## VA 1.006
## VocWR 0.485 0.341
## MAT 0.255 0.597
## DIA 0.858
##
## MR1 MR2
## SS loadings 1.315 1.209
## Proportion Var 0.329 0.302
## Cumulative Var 0.329 0.631Assessment of Loading Stability
EFATOCANEA <- c(0.844, 0.732, 0.834, 0.776, 0.785, 0.829, 0.774, 0.713)
EFATOCANEAPsy <- c(0.844, 0.732, 0.834, 0.776); EFATOCANEAWRIT <- c(0.785, 0.829, 0.774, 0.713)
EFASECANEAO <- c(0.853, 0.724, 0.840, 0.768, 0.825, 0.789, 0.800, 0.687)
EFASECANEAOPsy <- c(0.853, 0.724, 0.840, 0.768); EFASECANEAOWRIT <- c(0.825, 0.789, 0.800, 0.687)
cor(EFATOCANEA, EFASECANEAO, method = "pearson"); cor(EFATOCANEA, EFASECANEAO, method = "spearman"); CONGO(EFATOCANEA, EFASECANEAO)## [1] 0.8921335## [1] 0.8809524## [1] 0.9995165cor(EFATOCANEAPsy, EFASECANEAOPsy, method = "pearson"); cor(EFATOCANEAPsy, EFASECANEAOPsy, method = "spearman"); CONGO(EFATOCANEAPsy, EFASECANEAOPsy)## [1] 0.9986834## [1] 1## [1] 0.9999519cor(EFATOCANEAWRIT, EFASECANEAOWRIT, method = "pearson"); cor(EFATOCANEAWRIT, EFASECANEAOWRIT, method = "spearman"); CONGO(EFATOCANEAWRIT, EFASECANEAOWRIT)## [1] 0.7674648## [1] 0.4## [1] 0.9990572Confirmatory Factor Analyses
Solo Models
WASISO.model <- '
gWASI =~ VocWA + BD + SIM + MR'
WASISO.fit <- cfa(WASISO.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T)
summary(WASISO.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 18 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 8
##
## Number of observations 152
##
## Model Test User Model:
##
## Test statistic 19.354
## Degrees of freedom 2
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 330.132
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.946
## Tucker-Lewis Index (TLI) 0.839
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -705.319
## Loglikelihood unrestricted model (H1) -695.642
##
## Akaike (AIC) 1426.638
## Bayesian (BIC) 1450.829
## Sample-size adjusted Bayesian (BIC) 1425.510
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.239
## 90 Percent confidence interval - lower 0.149
## 90 Percent confidence interval - upper 0.341
## P-value RMSEA <= 0.05 0.001
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.052
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gWASI =~
## VocWA 0.880 0.067 13.148 0.000 0.880 0.883
## BD 0.683 0.074 9.211 0.000 0.683 0.685
## SIM 0.868 0.067 12.895 0.000 0.868 0.871
## MR 0.723 0.073 9.953 0.000 0.723 0.725
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VocWA 0.219 0.046 4.740 0.000 0.219 0.221
## .BD 0.527 0.068 7.801 0.000 0.527 0.531
## .SIM 0.239 0.047 5.098 0.000 0.239 0.241
## .MR 0.471 0.062 7.553 0.000 0.471 0.474
## gWASI 1.000 1.000 1.000WASISODU.model <- ' #Unidentified alone
Gc =~ VocWA + SIM
Gf =~ BD + MR
gWASI =~ Gf + Gc'
WASISODU.fit <- cfa(WASISODU.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T)## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.summary(WASISODU.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 24 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 10
##
## Number of observations 152
##
## Model Test User Model:
##
## Test statistic 0.192
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 330.132
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -695.738
## Loglikelihood unrestricted model (H1) -695.642
##
## Akaike (AIC) 1411.476
## Bayesian (BIC) 1441.715
## Sample-size adjusted Bayesian (BIC) 1410.065
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value RMSEA <= 0.05 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.003
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Gc =~
## VocWA 0.375 NA 0.895 0.898
## SIM 0.368 NA 0.877 0.880
## Gf =~
## BD 0.328 NA 0.776 0.779
## MR 0.351 NA 0.832 0.835
## gWASI =~
## Gf 2.146 NA 0.906 0.906
## Gc 2.163 NA 0.908 0.908
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VocWA 0.193 NA 0.193 0.194
## .SIM 0.224 NA 0.224 0.225
## .BD 0.391 NA 0.391 0.393
## .MR 0.301 NA 0.301 0.303
## .Gc 1.000 0.176 0.176
## .Gf 1.000 0.178 0.178
## gWASI 1.000 1.000 1.000WRITSO.model <- '
gWRIT =~ VocWR + VA + MAT + DIA'
WRITSO.fit <- cfa(WRITSO.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T)
summary(WRITSO.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 15 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 8
##
## Number of observations 152
##
## Model Test User Model:
##
## Test statistic 13.702
## Degrees of freedom 2
## P-value (Chi-square) 0.001
##
## Model Test Baseline Model:
##
## Test statistic 282.957
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.958
## Tucker-Lewis Index (TLI) 0.873
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -726.080
## Loglikelihood unrestricted model (H1) -719.229
##
## Akaike (AIC) 1468.160
## Bayesian (BIC) 1492.351
## Sample-size adjusted Bayesian (BIC) 1467.031
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.196
## 90 Percent confidence interval - lower 0.107
## 90 Percent confidence interval - upper 0.300
## P-value RMSEA <= 0.05 0.005
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.039
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gWRIT =~
## VocWR 0.799 0.071 11.210 0.000 0.799 0.802
## VA 0.838 0.070 11.972 0.000 0.838 0.841
## MAT 0.777 0.072 10.784 0.000 0.777 0.780
## DIA 0.672 0.076 8.874 0.000 0.672 0.674
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VocWR 0.355 0.058 6.162 0.000 0.355 0.357
## .VA 0.292 0.055 5.325 0.000 0.292 0.294
## .MAT 0.390 0.060 6.540 0.000 0.390 0.392
## .DIA 0.542 0.071 7.580 0.000 0.542 0.545
## gWRIT 1.000 1.000 1.000WRITSODU.model <- ' #Unidentified alone
Gc =~ VocWR + VA
Gf =~ MAT + DIA
gWRIT =~ Gf + Gc'
WRITSODU.fit <- cfa(WRITSODU.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T)## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.summary(WRITSODU.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 10
##
## Number of observations 152
##
## Model Test User Model:
##
## Test statistic 2.467
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 282.957
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.991
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -720.463
## Loglikelihood unrestricted model (H1) -719.229
##
## Akaike (AIC) 1460.926
## Bayesian (BIC) 1491.165
## Sample-size adjusted Bayesian (BIC) 1459.515
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value RMSEA <= 0.05 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.014
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Gc =~
## VocWR 0.311 NA 0.810 0.813
## VA 0.334 NA 0.871 0.874
## Gf =~
## MAT 0.339 NA 0.860 0.863
## DIA 0.282 NA 0.716 0.718
## gWRIT =~
## Gf 2.332 NA 0.919 0.919
## Gc 2.404 NA 0.923 0.923
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VocWR 0.338 NA 0.338 0.340
## .VA 0.235 NA 0.235 0.236
## .MAT 0.253 NA 0.253 0.255
## .DIA 0.481 NA 0.481 0.484
## .Gc 1.000 0.147 0.147
## .Gf 1.000 0.155 0.155
## gWRIT 1.000 1.000 1.000Joint Models
CANEANO.model <- '
gWASI =~ VocWA + BD + SIM + MR
gWRIT =~ VocWR + VA + MAT + DIA
gWASI ~~ 0*gWRIT'
CANEA.model <- '
gWASI =~ VocWA + BD + SIM + MR
gWRIT =~ VocWR + VA + MAT + DIA
gWASI ~~ gWRIT'
CANEAID.model <- '
gWASI =~ VocWA + BD + SIM + MR
gWRIT =~ VocWR + VA + MAT + DIA
gWASI ~~ 1*gWRIT'
CANEANO.fit <- cfa(CANEANO.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T)
CANEA.fit <- cfa(CANEA.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T)
CANEAID.fit <- cfa(CANEAID.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T)
round(cbind("No Relationship" = fitMeasures(CANEANO.fit, FITM),
"Free Relationship" = fitMeasures(CANEA.fit, FITM),
"Identical" = fitMeasures(CANEAID.fit, FITM)), 3)## No Relationship Free Relationship Identical
## chisq 338.081 121.397 121.483
## df 20.000 19.000 20.000
## npar 16.000 17.000 16.000
## cfi 0.643 0.885 0.886
## rmsea 0.323 0.188 0.183
## rmsea.ci.lower 0.294 0.157 0.152
## rmsea.ci.upper 0.354 0.221 0.215
## aic 2894.799 2680.114 2678.200
## bic 2943.181 2731.520 2726.582summary(CANEA.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 25 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 17
##
## Number of observations 152
##
## Model Test User Model:
##
## Test statistic 121.397
## Degrees of freedom 19
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 918.115
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.885
## Tucker-Lewis Index (TLI) 0.830
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1323.057
## Loglikelihood unrestricted model (H1) -1262.359
##
## Akaike (AIC) 2680.114
## Bayesian (BIC) 2731.520
## Sample-size adjusted Bayesian (BIC) 2677.715
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.188
## 90 Percent confidence interval - lower 0.157
## 90 Percent confidence interval - upper 0.221
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.069
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gWASI =~
## VocWA 0.876 0.065 13.545 0.000 0.876 0.879
## BD 0.697 0.072 9.673 0.000 0.697 0.700
## SIM 0.853 0.066 12.983 0.000 0.853 0.856
## MR 0.739 0.071 10.484 0.000 0.739 0.742
## gWRIT =~
## VocWR 0.859 0.066 13.081 0.000 0.859 0.862
## VA 0.797 0.068 11.664 0.000 0.797 0.800
## MAT 0.735 0.071 10.385 0.000 0.735 0.738
## DIA 0.674 0.073 9.244 0.000 0.674 0.677
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gWASI ~~
## gWRIT 0.995 0.018 56.164 0.000 0.995 0.995
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VocWA 0.226 0.035 6.497 0.000 0.226 0.227
## .BD 0.507 0.062 8.131 0.000 0.507 0.511
## .SIM 0.265 0.038 6.959 0.000 0.265 0.267
## .MR 0.447 0.056 7.964 0.000 0.447 0.450
## .VocWR 0.255 0.038 6.659 0.000 0.255 0.257
## .VA 0.358 0.048 7.536 0.000 0.358 0.360
## .MAT 0.453 0.057 7.947 0.000 0.453 0.456
## .DIA 0.539 0.066 8.182 0.000 0.539 0.542
## gWASI 1.000 1.000 1.000
## gWRIT 1.000 1.000 1.000CANEANO.model <- '
GcWA =~ VocWA + SIM
GfWA =~ BD + MR
gWASI =~ GfWA + GcWA
GcWR =~ VocWR + VA
GfWR =~ MAT + DIA
gWRIT =~ GfWR + GcWR
gWASI ~~ 0*gWRIT'
CANEA.model <- '
GcWA =~ VocWA + SIM
GfWA =~ BD + MR
gWASI =~ GfWA + GcWA
GcWR =~ VocWR + VA
GfWR =~ MAT + DIA
gWRIT =~ GfWR + GcWR
gWASI ~~ gWRIT'
CANEAID.model <- '
GcWA =~ VocWA + SIM
GfWA =~ BD + MR
gWASI =~ GfWA + GcWA
GcWR =~ VocWR + VA
GfWR =~ MAT + DIA
gWRIT =~ GfWR + GcWR
gWASI ~~ 1*gWRIT'
CANEANO.fit <- cfa(CANEANO.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"CANEA.fit <- cfa(CANEA.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T); "\n"## 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.## [1] "\n"CANEAID.fit <- cfa(CANEAID.model, sample.cov = CANEA.cor, sample.nobs = nCANEA, std.lv = T, orthogonal = T)
round(cbind("No Relationship" = fitMeasures(CANEANO.fit, FITM),
"Free Relationship" = fitMeasures(CANEA.fit, FITM),
"Identical" = fitMeasures(CANEAID.fit, FITM)), 3)## No Relationship Free Relationship Identical
## chisq 307.684 89.114 91.461
## df 16.000 15.000 16.000
## npar 20.000 21.000 20.000
## cfi 0.672 0.917 0.915
## rmsea 0.346 0.180 0.176
## rmsea.ci.lower 0.313 0.145 0.142
## rmsea.ci.upper 0.381 0.217 0.212
## aic 2872.402 2655.831 2656.178
## bic 2932.879 2719.332 2716.656summary(CANEA.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 58 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 21
##
## Number of observations 152
##
## Model Test User Model:
##
## Test statistic 89.114
## Degrees of freedom 15
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 918.115
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.917
## Tucker-Lewis Index (TLI) 0.845
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1306.915
## Loglikelihood unrestricted model (H1) -1262.359
##
## Akaike (AIC) 2655.831
## Bayesian (BIC) 2719.332
## Sample-size adjusted Bayesian (BIC) 2652.868
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.180
## 90 Percent confidence interval - lower 0.145
## 90 Percent confidence interval - upper 0.217
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.060
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GcWA =~
## VocWA 0.303 0.066 4.582 0.000 0.902 0.905
## SIM 0.292 0.064 4.602 0.000 0.870 0.873
## GfWA =~
## BD 0.380 0.061 6.239 0.000 0.778 0.781
## MR 0.405 0.065 6.197 0.000 0.830 0.832
## gWASI =~
## GfWA 1.787 0.331 5.404 0.000 0.873 0.873
## GcWA 2.803 0.679 4.130 0.000 0.942 0.942
## GcWR =~
## VocWR 0.252 0.086 2.919 0.004 0.882 0.884
## VA 0.229 0.078 2.938 0.003 0.800 0.803
## GfWR =~
## MAT 0.390 0.070 5.606 0.000 0.816 0.819
## DIA 0.361 0.064 5.645 0.000 0.755 0.757
## gWRIT =~
## GfWR 1.836 0.368 4.988 0.000 0.878 0.878
## GcWR 3.347 1.212 2.762 0.006 0.958 0.958
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gWASI ~~
## gWRIT 1.053 0.028 37.538 0.000 1.053 1.053
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VocWA 0.179 0.035 5.138 0.000 0.179 0.181
## .SIM 0.237 0.038 6.274 0.000 0.237 0.238
## .BD 0.387 0.061 6.367 0.000 0.387 0.390
## .MR 0.305 0.059 5.195 0.000 0.305 0.307
## .VocWR 0.216 0.042 5.148 0.000 0.216 0.218
## .VA 0.353 0.049 7.178 0.000 0.353 0.356
## .MAT 0.328 0.062 5.293 0.000 0.328 0.330
## .DIA 0.424 0.064 6.592 0.000 0.424 0.427
## .GcWA 1.000 0.113 0.113
## .GfWA 1.000 0.238 0.238
## gWASI 1.000 1.000 1.000
## .GcWR 1.000 0.082 0.082
## .GfWR 1.000 0.229 0.229
## gWRIT 1.000 1.000 1.000Conclusion
The latent factor correlations from Canivez et al. (2009) were perfect. The batteries were extremely unidimensional and could only legitimately be interpreted as g measures.
References
Canivez, G. L., Konold, T. R., Collins, J. M., & Wilson, G. (2009). Construct validity of the Wechsler Abbreviated Scale of Intelligence and Wide Range Intelligence Test: Convergent and structural validity. School Psychology Quarterly, 24(4), 252–265. https://doi.org/10.1037/a0018030