Import the dataset
library(readxl)
config2data <- read_excel("2_16_configural 2_data.xlsx")
View(config2data)Call the lavaan package
library(lavaan)## This is lavaan 0.6-7## lavaan is BETA software! Please report any bugs.Specify the factor structure
config.model <- '
sa =~ NA*au7 + au2 + au10 +au12 #free up the estimation of au7
sa ~~ 1*sa #fix the variance of sa1 to 1
au12 ~~ au10 #correlate the two variables
'Specify the configural model, using the argument group= to specify the grouping variable
fit <- cfa(config.model, data = config2data, group = "gender")Take a look at the model summary with model fit statistics
summary(fit, fit.measures=T)## lavaan 0.6-7 ended normally after 48 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 26
##
## Number of observations per group:
## 1 43
## 2 238
##
## Model Test User Model:
##
## Test statistic 2.451
## Degrees of freedom 2
## P-value (Chi-square) 0.294
## Test statistic for each group:
## 1 1.874
## 2 0.576
##
## Model Test Baseline Model:
##
## Test statistic 396.446
## Degrees of freedom 12
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999
## Tucker-Lewis Index (TLI) 0.993
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1783.240
## Loglikelihood unrestricted model (H1) -1782.014
##
## Akaike (AIC) 3618.479
## Bayesian (BIC) 3713.077
## Sample-size adjusted Bayesian (BIC) 3630.632
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.040
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.177
## P-value RMSEA <= 0.05 0.412
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.007
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## sa =~
## au7 1.465 0.233 6.286 0.000
## au2 1.190 0.212 5.627 0.000
## au10 1.312 0.225 5.834 0.000
## au12 1.393 0.203 6.876 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .au10 ~~
## .au12 0.438 0.259 1.690 0.091
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .au7 3.535 0.268 13.195 0.000
## .au2 3.000 0.237 12.650 0.000
## .au10 3.349 0.248 13.501 0.000
## .au12 3.302 0.238 13.853 0.000
## sa 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## sa 1.000
## .au7 0.939 0.325 2.888 0.004
## .au2 1.002 0.274 3.662 0.000
## .au10 0.924 0.320 2.892 0.004
## .au12 0.502 0.254 1.972 0.049
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## sa =~
## au7 0.965 0.108 8.918 0.000
## au2 0.908 0.108 8.397 0.000
## au10 0.769 0.102 7.545 0.000
## au12 0.765 0.103 7.458 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .au10 ~~
## .au12 0.611 0.125 4.889 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .au7 3.529 0.091 38.942 0.000
## .au2 3.336 0.093 35.976 0.000
## .au10 2.987 0.086 34.654 0.000
## .au12 2.790 0.087 32.190 0.000
## sa 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## sa 1.000
## .au7 1.023 0.171 5.995 0.000
## .au2 1.222 0.169 7.238 0.000
## .au10 1.178 0.147 8.025 0.000
## .au12 1.202 0.149 8.093 0.000If we want to look at specific data-model fit measures, we can use the function fitmeasures()
fitmeasures(fit, c("chisq","df","pvalue","cfi","tli","rmsea","rmsea.ci.lower","rmsea.ci.upper","AIC","srmr"))## chisq df pvalue cfi tli
## 2.451 2.000 0.294 0.999 0.993
## rmsea rmsea.ci.lower rmsea.ci.upper aic srmr
## 0.040 0.000 0.177 3618.479 0.007There is an easier way to check all the four invariance model statistics:
library(semTools)## ## ################################################################################# This is semTools 0.5-4## All users of R (or SEM) are invited to submit functions or ideas for functions.## ###############################################################################measurementInvariance(model = config.model, data = config2data, group = "gender")## Warning: The measurementInvariance function is deprecated, and it will cease to
## be included in future versions of semTools. See help('semTools-deprecated) for
## details.## Warning in lavaan::lavTestLRT(...): lavaan WARNING: method = "satorra.bentler.2001"
## but no robust test statistics were used;
## switching to the standard chi-square difference test##
## Measurement invariance models:
##
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.intercepts
## Model 4 : fit.means
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit.configural 2 3618.5 3713.1 2.4506
## fit.loadings 6 3622.2 3702.2 14.1246 11.6740 4 0.019947 *
## fit.intercepts 9 3630.2 3699.3 28.1854 14.0608 3 0.002824 **
## fit.means 10 3628.3 3693.8 28.2565 0.0711 1 0.789674
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Fit measures:
##
## cfi rmsea cfi.delta rmsea.delta
## fit.configural 0.999 0.040 NA NA
## fit.loadings 0.979 0.098 0.020 0.058
## fit.intercepts 0.950 0.123 0.029 0.025
## fit.means 0.953 0.114 0.002 0.009predict, used for regression of observed outcome to observed predictors
=~ indicator, used for latent variable to observed indicator in factor analysis measurement models
~~ covariance
~1 intercept or mean (e.g., q01 ~ 1 estimates the mean of variable q01)
1* fixes parameter or loading to one
NA* frees parameter or loading (useful to override default marker method)
a* labels the parameter ‘a’, used for model constraints