Efficiency of D-optimal designs for quasi-likelihood estimation in Poisson regression model with random effects

Abstract

Optimum experimental designs are most commonly used to obtain maximum likelihood estimators of parameters. However, obtaining an explicit form of these estimators is not feasible for generalized linear mixed models (GLMMs). Hence as an alternative method to handle this issue, the quasi-likelihood method is applied to Poisson regression models with random effects, a special case of GLMMs. In this paper, we consider this model and compare D-optimal designs for quasi-likelihood estimation and maximum likelihood estimation of fixed effects parameters. The empirical results in a simulated environment suggest that the optimal designs for quasi-likelihood estimation are efficient.

Keywords

• Optimal Design,Poisson Regression,Quasi-Likelihood,relative efficiency,Laplace approximation

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