Testing Mean and Covariance Structures with Reweighted Least Squares. Issue 2 (4th March 2022)

• Record Type: Journal Article
• Authors: Zheng, Bang Quan; Bentler, Peter M.
• Is Part Of: Structural equation modeling. Volume 29:Issue 2(2022)
• Page Start: 259
• Page End: 266
• Publication Date: 2022-03-04
• Subjects: Mean and covariance structure -- reweighted least squares -- goodness-of-fit test -- structural equation models -- small sample size; Multivariate analysis -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 519.535
• DOI: 10.1080/10705511.2021.1977649
• Languages: English
• ISSNs: 1070-5511

Abstract

ABSTRACT: Chi-square tests based on maximum likelihood (ML) estimation of covariance structures often incorrectly over-reject the null hypothesis: Σ = Σ θ when the sample size is small. Reweighted least squares (RLS) avoids this problem. In some models, the vector of parameter must contain means, variances, and covariances, yet whether RLS also works in mean and covariance structures remains unexamined. This research extends RLS to mean and covariance structures, evaluating a generalized least squares function with ML parameter estimates. A Monte Carlo simulation study was carried out to examine the statistical performance of ML vs RLS with multivariate normal data. Based on empirical rejection frequencies and empirical averages of test statistics, this study shows that RLS performs much better than ML in mean and covariance structure models when sample sizes are small, whereas it does not perform better than ML to reject misspecified models.