Generalized Quasi-likelihood versus Hierarchical Likelihood Inferences in Generalized Linear Mixed Models for Count Data

摘要

Inferences for the regression parameters and the variance of the random effects in the generalized linear mixed models (GLMMs) set up, is an extremely important statistical issue. It is however known that the most widely used penalized quasi-likelihood (PQL) approach may not produce consistent estimates for the parameters, especially when the true variance of the random effects is large. In the context of Poisson mixed models, in this paper, we examine the consistency performances of two other competitive estimation approaches, namely, the hierarchical likelihood (HL) and the generalized quasi-likelihood (GQL) approaches. An extensive simulation study shows that the HL approach, similar to the PQL approach, appears to produce highly biased and hence inconsistent estimates for the regression parameters, especially when the variance of the random effects is large. The biases of the HL estimates also appears to vary depending on the cluster sizes. As an alternative, the GQL approach appears to produce consistent estimates for all parameters of this model irrespective of the size of the cluster and the magnitude of the variance of the random effects. The GQL and HL estimates are also compared in a real life data analysis.