Model misspecification effects in clustered count data analysis

Clustered count data are usually analysed using Poisson mixed models based on the assumptions of either gamma distributed or log-normal distributed random effects. As it is difficult to anticipate the true mixed model, the researchers tend to make an arbitrary choice between the assumption of gamma or log-normal distribution for the random effects. This arbitrary choice may not affect the estimation of the regression parameters of the model but the efficiency of the estimates of the variance component of the random effects may however be affected to a great extent. This paper addresses this issue by examining the misspecification effects of the distributional assumptions for the random effects in the clustered data.