Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects

Focusing on the model selection problems in the family of Poisson mixture models (including the Poisson mixture regression model with random effects and zero-inflated Poisson regression model with random effects), the current paper derives two conditional Akaike information criteria. The criteria are the unbiased estimators of the conditional Akaike information based on the conditional log-likelihood and the conditional Akaike information based on the joint log-likelihood, respectively. The derivation is free from the specific parametric assumptions about the conditional mean of the true data-generating model and applies to different types of estimation methods. Additionally, the derivation is not based on the asymptotic argument. Simulations show that the proposed criteria have promising estimation accuracy. In addition, it is found that the criterion based on the conditional log-likelihood demonstrates good model selection performance under different scenarios. Two sets of real data are used to illustrate the proposed method.