On approximate likelihood inference in a poisson mixed model

Abstract

AbstractA two‐step estimation approach is proposed for the fixed‐effect parameters, random effects and their variance σ2 of a Poisson mixed model. In the first step, it is proposed to construct a small σ2‐based approximate likelihood function of the data and utilize this function to estimate the fixed‐effect parameters and σ2. In the second step, the random effects are estimated by minimizing their posterior mean squared error. Methods of Waclawiw and Liang (1993) based on so‐called Stein‐type estimating functions and of Breslow and Clayton (1993) based on penalized quasilikelihood are compared with the proposed likelihood method. The results of a simulation study on the performance of all three approaches are reported.