Sample Size Requirements of the Robust Weighted Least Squares Estimator

The present study investigated sample size requirements of maximum likelihood (ML) and robust weighted least squares (robust WLS) estimation for ordinal data with confirmatory factor analysis (CFA) models with 3-10 indicators per factor, primary loadings between .4 and .9, and four different levels of categorization (2, 3, 5, and 7). Additionally, the utility of the H-measure of construct reliability (an index combining the number of indicators and the magnitude of loadings) in predicting sample size requirements was examined. Results indicated that a higher number of indicators per factors and higher factor loadings increased the rates of proper convergence and solution propriety. However, the H-measure could only partly account for the results. Moreover, it was demonstrated that robust WLS was mostly superior to ML, suggesting that there is little reason to prefer ML over robust WLS when the data are ordinal. Sample size recommendations for the robust WLS estimator are provided.