A Numerical Study of PQL Estimation Biases in Generalized Linear Mixed Models Under Heterogeneity of Random Effects

Abstract

The penalized quasi-likelihood (PQL) approach is the most common estimation procedure for the generalized linear mixed model (GLMM). However, it has been noticed that the PQL tends to underestimate variance components as well as regression coefficients in the previous literature. In this article, we numerically show that the biases of variance component estimates by PQL are systematically related to the biases of regression coefficient estimates by PQL, and also show that the biases of variance component estimates by PQL increase as random effects become more heterogeneous.

Keywords:

• Generalized linear mixed models
• Heterogeneity
• Penalized quasi-likelihood estimator
• Variance components

Mathematics Subject Classification:

• 62J12
• 62P10