  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.
