Generalized linear mixed-effects models with a finite-support random-effects distribution: A Maximum-penalized-likelihood approach

We discuss a method for simultaneously estimating the fixed parameters of a generalized linear mixed-effects model and the random-effects distribution of which no parametric assumption is made. In addition, classifying subjects into clusters according to the random regression coefficients is a natural by-product of the proposed method. An alternative approach to maximum-likelihood method, maximum-penalized-likelihood method, is used to avoid estimating ''too many'' clusters. Consistency and asymptotic normality properties of the estimators are presented. We also provide robust variance estimators of the fixed parameters estimators which remain consistent even in presence of misspecification. The methodology is illustrated by an application to a weight loss study.