Second-order Least Squares Estimation in Generalized Linear Mixed Models

Abstract

Generalized linear mixed models are widely used in the analysis of longitudinal or repeated measures data. The mainstream method for inference in statistics is likelihood-based approach, which is difficult to compute and relies on the normality assumption. We propose the second-order least squares method which are based on the first two marginal moments of the response variable, and allow the random effects to have any parametric distribution (not necessarily normal). We also propose a simulation-based estimator for the situation where the closed forms of the moments are not available. The proposed estimators are not only computationally attractive but also strongly root-n consistent. In addition, they are robust against data contaminations or outliers. Some simulation results and real data applications will be presented.