Marginal Models for Zero-inflated Clustered Data

• Activity Number: 111
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Daniel B. Hall*+ and Zhengang Zhang
• Companies: University of Georgia and University of Georgia
• Keywords: longitudinal data ; repeated measures ; mixture models ; EM

Abstract

Over the last decade there has been increasing interest in mixture models to account for "excess" zeros in data. These models, often called zero-inflated (ZI) regression models, mix a degenerate distribution with point mass of one at 0 with a regression model based on a standard distribution. Examples include ZI-Poisson, ZI-Binomial, ZI-Negative Binomial, and ZI-Tobit models. Recently, extensions of these models to the clustered data case have begun to appear. For example, Hall (2000) considered ZI-Poisson and ZI-Binomial models with cluster-specific random effects. We consider an alternative approach based on 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 are given for several of the most important ZI 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.