A Marginalized Model for Zero-Inflated, Overdispersed, and Correlated Count Data

Iddi and Molenberghs (2012) merged the attractive features of the so-called combined model of Molenberghs {\em et al\/} (2010) and the marginalized model of Heagerty (1999) for hierarchical non-Gaussian data with overdispersion. In this model, the fixed-effect parameters retain their marginal interpretation. Lee et al (2011) also developed an extension of Heagerty (1999) to handle zero-inflation from count data, using the hurdle model. To bring together all of these features, a marginalized, zero-inflated, overdispersed model for correlated count data is proposed. Using two empirical sets of data, it is shown that the proposed model leads to important improvements in model fit.