A note on conditional Akaike information for Poisson regression with random effects

TL;DR

This paper extends the concept of conditional AIC to Poisson regression models with random effects, providing a new model selection criterion supported by simulation studies.

Contribution

It introduces a conditional AIC for Poisson mixed-effects models, expanding existing methods from linear to Poisson models.

Findings

Conditional AIC can be derived for Poisson regression with random effects.

Simulation studies demonstrate the effectiveness of the proposed criterion.

Abstract

A popular model selection approach for generalized linear mixed-effects models is the Akaike information criterion, or AIC. Among others, \cite{vaida05} pointed out the distinction between the marginal and conditional inference depending on the focus of research. The conditional AIC was derived for the linear mixed-effects model which was later generalized by \cite{liang08}. We show that the similar strategy extends to Poisson regression with random effects, where condition AIC can be obtained based on our observations. Simulation studies demonstrate the usage of the criterion.