Estimation in Generalized Linear Models with Heterogeneous Random Effects

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