reliability.nonlinearSEM: Estimation of Reliability for Confirmatory Factor Analyses Based on Dichotomous Data

Description

This function estimates a model based reliability using confirmatory factor analysis (Green & Yang, 2009).

Usage

reliability.nonlinearSEM(facloadings, thresh, resid.cov = NULL , cor.factors = NULL)

Arguments

facloadings

Matrix of factor loadings

thresh

Vector of thresholds

resid.cov

Matrix of residual covariances

cor.factors

Optional matrix of covariances (correlations) between factors. The default is a diagonal matrix with variances of 1.

Value

A list. The reliability is the list element omega.rel

References

Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74, 155-167.

Examples

Run this code

#############################################################################
# EXAMPLE 1: Reading data set
#############################################################################
data(data.read)
dat <- data.read
I <- ncol(dat)

# define item clusters
itemcluster <- rep( 1:3 , each=4)
error.corr <- diag(1,ncol(dat))
for ( ii in 1:3){
    ind.ii <- which( itemcluster == ii )
    error.corr[ ind.ii , ind.ii ] <- ii
        }
# estimate the model with error correlations
mod1 <- rasch.pml3( dat , error.corr = error.corr)
summary(mod1)

# extract item parameters
thresh <- - matrix( mod1$item$a * mod1$item$b , I , 1 )
A <- matrix( mod1$item$a * mod1$item$sigma , I , 1 )
# extract estimated correlation matrix
corM <- mod1$eps.corrM
# compute standardized factor loadings
facA <- 1 / sqrt( A^2 + 1 )
resvar <- 1 - facA^2 
covM <- outer( sqrt(resvar[,1]) , sqrt(resvar[,1] ) ) * corM
facloadings <- A *facA

# estimate reliability
rel1 <- reliability.nonlinearSEM( facloadings =facloadings , thresh =thresh , 
           resid.cov=covM)
rel1$omega.rel