Statistical Modelling 4 (2004), 161180
Marginal models for zero inflated clustered data
Daniel B. Hall and Zhengang Zhang
Department of Statistics,
University of Georgia,
Athens, GA 30602-1952,
USA.
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.
Keywords:
extended generalized estimating equations; finite mixture;
generalized linear model; longitudinal data; mixture of experts;
repeated measures
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