Sample Size Requirements of the Robust Weighted Least Squares Estimator

Abstract

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. Confirmatory factor analysis (CFA), as a special case of structural equation models, is a powerful technique to model and test relationships between manifest variables and latent constructs. Estimation of CFA models usually proceeds using normal-theory estimators with the most commonly used being maximum likelihood (ML). Nor- mal-theory estimation methods assume continuous and multivariate normally distributed observed variables; how- ever, many measures in the social and behavioral sciences are characterized by a dichotomous or an ordinal level of measurement. Although the items of a test or a question- naire are conceived to be measures of a theoretically contin- uous construct, the observed responses are discrete realizations of a small number of categories and, thus, lack the scale and distributional properties assumed by normal- theory estimators.