Performance of some estimators in covariance structure models with nonnormal data

Maximum likelihood (ML) and generalized least squares (GLS) methods are frequently used in CSM. ML and GLS estimators assume that data are multivariate normally distributed. However, the assumption of multivariate normality is often violated in practice and Monte Carlo studies (e.g., Harlow, 1985) have shown that normal theory estimators are often not robust for non-normal distributions. Three approaches to dealing with the problem of non-normal data in CSM have been to (a) develop estimators (e.g., ADF) based on less restrictive distributional assumptions, (b) correct the relevant statistics obtained from normal theory estimators, and (c) investigate conditions where normal theory methods are robust. A simulation was conducted to examine the performance of the three approaches at a sample size of 500 for 6-variable, 15-variable, and 16-variable confirmatory factor analysis (CFA) models for multivariate and/or moderately non-normal data. For multivariate normal data, ML, GLS, and ADF estimators did fairly well with respect to the parameter estimates, standard errors, and goodness of fit statistics for the 6-variable CFA model at a sample size of 500. In contrast, the ADF goodness of fit statistic completely broke down for the larger models (15 or 16-variables) at a sample size of 500. However, ML and GLS goodness of fit statistics performed well for the 15 and 16-variable models and multivariate normal data. For moderately non-normal data, the ADF estimator outperformed ML and GLS estimators for the 6 variable model and a sample size of 500. In addition, corrected ML and GLS (ROBUST) standard errors outperformed uncorrected ML and GLS standard errors for moderately non-normal data