Abstract

Count data are very common in many practical fields such as medical studies, biology, epidemiology, and actuarial sciences. To analyze such data, Poisson regression is considered in the context of a generalized linear model. However, in a real data set, count responses may be clustered and hierarchical indicating the clustering effects. A hierarchical Poisson mixed model is a further improvement for analyzing such data by incorporating clustering effects, where random effects distribution is usually assumed to be normal. However, random effects distribution may be a member of the conjugate family i.e. a gamma distribution for count responses. In this study, we explored the performance of conjugate random effects distribution in the generalized linear mixed model framework by using both simulation studies and a real-life data set extracted from the latest Bangladesh Demographic and Health Survey (BDHS) 2017–18.