This paper presents an approach to posterior simulation and model comparison for generalized linear models with multiple random effects. Alternative MCMC approaches for posterior simulation and alternative parameterizations are considered and compared in the context of panel data and multiple random effects. A straightforward approach for the calculation of Bayes factors from the MCMC output is developed. This approach relies on the computation of the marginal likelihood of each contending model. Estimation of modal estimates based on Monte Carlo versions of the E-M algorithm is also discussed. The methods are illustrated with several real data applications involving count data and the Poisson link function.