Estimating Mean and Covariance Structure with Reweighted Least Squares

• In Event: Generalized Linear Models in Political Science

Abstract

Does Reweighted Least Squares (RLS) perform better in small samples than maximum likelihood (ML) test for mean and covariance structure? ML estimations in covariance structure analysis are based on asymptotic normality assumption; however, actual applications of structural equation modeling (SEM) in social science research usually involve small samples. As a result, chi-square tests often incorrectly over-reject null hypothesis: σ=σ(θ), because when sample is small the sample covariance matrix would become ill-conditioned and entails unstable estimates. In SEM, the vector of parameter cannot only contain both variances and covariances; rather, it must contain both means and covariances. Yet, whether RLS also works in mean and covariance structure remains unexamined. This research is an extended examination of reweighted least squares in mean and covariance structure. Specifically, we replace biased covariance matrix in traditional GLS function (Browne, 1974) with the unbiased sample covariance matrix that derives from ML estimation and tests. Moreover, under the assumption of multivariate normality, a Monte Carlo simulation study was carried out to examine the statistical performance as compared with ML methods in different sample sizes. Based on empirical rejection frequency and empirical averages of test statistics, this study shows that RLS performs much better in small samples in both mean and covariance structures.

Author

• Bang Quan Zheng, UCLA