Fitting Mixed Poisson Regression Models Using Quasi‐Likelihood Methods

Abstract

Abstract This paper is to investigate the use of the quasi‐likelihood, extended quasi‐likelihood, and pseudo‐likelihood approach to estimating and testing the mean parameters with respect to two variance models, M1: φ μ θ (1+μphis;) and M2: φ μ θ (1+τ). Simulation was conducted to compare the bias and standard deviation, and type I error of the Wald tests, based on the model‐based and robust variance estimates, using the three semi‐parametric approaches under four mixed Poisson models, two variance structures, and two sample sizes. All methods perform reasonably well in terms of bias. Type I error of the Wald test, based on either the model‐based or robust estimate, tends to be larger than the nominal level when over‐dispersion is moderate. The extended quasi‐likelihood method with the variance model M1 performs more consistently in terms of the efficiency and controlling the type I error than with the model M2, and better than the pseudo‐likelihood approach with either the M1 or M2 model. The model‐based estimate seems to perform better than the robust estimate when the sample size is small.