Poisson-Lognormal Mixed Model Based Estimation in Clustered Longitudinal Count Data Analysis

Abstract

Poisson mixed models are useful for accommodating the overdispersion and correlations often observed among count data. These models are generated from the well-known independent Poisson model by adding normally distributed random effects to the linear predictor, and they are known as Poisson-log-normal mixed models. Unfortunately, a full likelihood analysis for such Poisson mixed models is hampered by the need for numerical integration. In this paper, generalised estimating equations procedure is discussed for the estimation of the parameters of the Poisson-log-normal mixed model under a longitudinal set-up.

Keywords: count clustered data, higher order structural moments, mixed effects, multivariate repeated measures, normal based higher order longitudinal moments.