Some Results on the Behavior of Alternate Covariance Structure Estimation Procedures in the Presence of Non-Normal Data

Abstract

The authors report some results on the behavior of alternative covariance structure estimation procedures in the presence of non-normal data. They conducted Monté Carlo simulation experiments with a factorial design involving three levels of skewness, three level of kurtosis, and three different sample sizes. For normal data, among all the elliptical estimation techniques, elliptical reweighted least squares (ERLS) was equivalent in performance to ML. However, as expected, for non-normal data parameter estimates were unbiased for ML and the elliptical estimation techniques, whereas the bias in standard errors was substantial for GLS and ML. Among elliptical estimation techniques, ERLS was superior in performance. On the basis of the simulation results, the authors recommend that researchers use ERLS for both normal and non-normal data.