The Performance of ML, DWLS, and ULS Estimation With Robust Corrections in Structural Equation Models With Ordinal Variables

• Published in: Psychological methods Vol. 21; no. 3; pp. 369 - 387
• Main Author: Li, Cheng-Hsien
• Format: Journal Article
• Language: English
• Published: United States American Psychological Association 01-09-2016
• Subjects: Humans; Least Squares; Least-Squares Analysis; Likelihood Functions; Maximum Likelihood; Models, Theoretical; Monte Carlo Method; Sample Size; Statistical Estimation; unweighted least squares; ordinal data; diagonally weighted least squares; maximum likelihood; robust statistics
• ISSN: 1082-989X; 1939-1463
• DOI: 10.1037/met0000093

Three estimation methods with robust corrections-maximum likelihood (ML) using the sample covariance matrix, unweighted least squares (ULS) using a polychoric correlation matrix, and diagonally weighted least squares (DWLS) using a polychoric correlation matrix-have been proposed in the literature, and are considered to be superior to normal theory-based maximum likelihood when observed variables in latent variable models are ordinal. A Monte Carlo simulation study was carried out to compare the performance of ML, DWLS, and ULS in estimating model parameters, and their robust corrections to standard errors, and chi-square statistics in a structural equation model with ordinal observed variables. Eighty-four conditions, characterized by different ordinal observed distribution shapes, numbers of response categories, and sample sizes were investigated. Results reveal that (a) DWLS and ULS yield more accurate factor loading estimates than ML across all conditions; (b) DWLS and ULS produce more accurate interfactor correlation estimates than ML in almost every condition; (c) structural coefficient estimates from DWLS and ULS outperform ML estimates in nearly all asymmetric data conditions; (d) robust standard errors of parameter estimates obtained with robust ML are more accurate than those produced by DWLS and ULS across most conditions; and (e) regarding robust chi-square statistics, robust ML is inferior to DWLS and ULS in controlling for Type I error in almost every condition, unless a large sample is used (N = 1,000). Finally, implications of the findings are discussed, as are the limitations of this study as well as potential directions for future research.