Bayesian inference for generalized linear mixed models: A comparison of different statistical software procedures

Bayesian inference for generalized linear mixed models (GLMM) is appealing, but its widespread use has been hampered by the lack of a fast implementation tool and difficulty in specifying prior distributions. In this paper, we conduct an extensive simulation study to evaluate performance INLA estimation hierarchical Poisson regression with overdispersion comparison JAGS Stan while assuming variety specifications variance components. Further, analysed influence different factors such as small number observations per cluster, values cluster from misspecified model. A shown that approximation strategy employed accurate general all software leads similar results most cases considered. Estimation components, however, difficult when their true value methods specifications. The estimates obtained tend be biased downward or upward depending on assumed priors.