Marginal models for zero inflated clustered data

Abstract

Over the last decade or so, there has been increasing interest in ‘zero inflated’ (ZI) regression models to account for ‘excess’ zeros in data. Examples include ZI poisson (ZIP), ZI binomial (ZIB), ZI negative binomial and ZI tobit models. Recently, extensions of these models to the clustered data case have begun to appear. For example, Hall considered ZIP and ZIB models with cluster specific random effects. In this paper, we consider an alternative expectation maximization approach on the basis of marginal models and generalized estimating equation (GEE) methodology. In the usual EM algorithm for fitting ZI models, the M step is replaced by the solution of a GEE to take into account within cluster correlation. The details of this approach, including formulas for an asymptotic variance-covariance matrix of parameter estimates, are given for several of the most important ZI regression model classes. Alternatively, GEEs can be applied directly by computing the first two marginal moments of the observed response. We illustrate these two marginal modeling approaches with examples, and compare them via a small simulation study.