1d:T7d8,# Estimation of Reliability for Confirmatory Factor Analyses Based on Dichotomous Data This function estimates a model based reliability using confirmatory factor analysis (Green & Yang, 2009). ```r 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. ## Returns 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. ## Note This function needs the `mvtnorm` package. ## See Also This function is used in `greenyang.reliability`. ## Examples ```r ############################################################################# # 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 <- sirt::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$eps.corrM # compute standardized factor loadings facA <- 1 / sqrt( A^2 + 1 ) resvar <- 1 - facA^2 covM <- outer( sqrt(resvar[,1]), sqrt(resvar[,1] ) ) * corM facloadings <- A *facA # estimate reliability rel1 <- sirt::reliability.nonlinearSEM( facloadings=facloadings, thresh=thresh, resid.cov=covM) rel1$omega.rel ```1e:T49a,M7.49933 0.25C3.49635 0.

reliability.nonlinearSEM function