Relative Performance of Categorical Diagonally Weighted Least Squares and Robust Maximum Likelihood Estimation

Abstract

Robust maximum likelihood (ML) and categorical diagonally weighted least squares (cat-DWLS) estimation have both been proposed for use with categorized and nonnormally distributed data. This study compares results from the 2 methods in terms of parameter estimate and standard error bias, power, and Type I error control, with unadjusted ML and WLS estimation methods included for purposes of comparison. Conditions manipulated include model misspecification, level of asymmetry, level and categorization, sample size, and type and size of the model. Results indicate that cat-DWLS estimation method results in the least parameter estimate and standard error bias under the majority of conditions studied. Cat-DWLS parameter estimates and standard errors were generally the least affected by model misspecification of the estimation methods studied. Robust ML also performed well, yielding relatively unbiased parameter estimates and standard errors. However, both cat-DWLS and robust ML resulted in low power under conditions of high data asymmetry, small sample sizes, and mild model misspecification. For more optimal conditions, power for these estimators was adequate.

Keywords:

• DWLS
• WLS
• Robust Maximum Likelihood
• categorical data

Notes

¹Although, strictly speaking, the terms skewness and kurtosis are not germane to categorical data, they are used in this article to convey a sense of the levels of asymmetry that were introduced.

²The term population is used to refer to values to which parameters were set for the generating model. Sample values did, of course, vary somewhat from the generating values.

FIGURE 1 Small confirmatory factor analysis model: Standardized population values are shown for factor covariances; standardized population values for factor loadings are .7 for primary loadings and .3 for secondary loadings.

³Information on bias in individual parameter estimates was also calculated and is available from the author by request.