Likelihood inference in generalized linear mixed models with two components of dispersion using data cloning

Abstract

This paper studies generalized linear mixed models (GLMMs) with two components of dispersion. The frequentist analysis of linear mixed model (LMM), and particularly of GLMM, is computationally difficult. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of LMM and GLMM computationally convenient. The recent introduction of the method of data cloning has made frequentist analysis of mixed models also equally computationally convenient. We use data cloning to conduct frequentist analysis of GLMMs with two components of dispersion based on maximum likelihood estimation (MLE). The resultant estimators of the model parameters are efficient. We discuss the performance of the MLE using the well known salamander mating data, and also through simulation studies.