Modeling multivariate, overdispersed binomial data with additive and multiplicative random effects

Abstract

Often, when modeling longitudinal binomial data, one needs to take into consideration both clustering and overdispersion. When the primary interest is in accommodating both phenomena, we can use separate sets of random effects that capture the within-cluster association and the extra variability due to overdispersion. In this paper, we propose a series of hierarchical Bayesian generalized linear mixed models that deal simultaneously with both phenomena. The proposed models are applied to a sample of multivariate data on hepatitis C virus (HCV) and human immunodeficiency virus (HIV) infection prevalence in injecting drug users in Italy from 1998 to 2007.