Statistical Modelling 5 (2005), 1–19
Random effect models for repeated measures of zero-inflated count data
Yongyi Min
Statistical Division,
The United Nations,
2 UN Plaza,
DC2-1404, NY 10017
USA
eMail:
min3@un.org
Alan Agresti
Department of Statistics,
University of Florida,
Gainesville, Florida,
USA
Abstract:
For count responses, the situation of excess zeros (relative to what
standard models allow) often occurs in biomedical and sociological
applications. Modeling repeated measures of zero-inflated count data
presents special challenges. This is because in addition to the problem
of extra zeros, the correlation between measurements upon the same
subject at different occasions needs to be taken into account. This
article discusses random effect models for repeated measurements on
this type of response variable. A useful model is the hurdle model
with random effects, which separately handles the zero observations
and the positive counts. In maximum likelihood model fitting, we
consider both a normal distribution and a nonparametric approach
for the random effects. A special case of the hurdle model can be
used to test for zero inflation. Random effects can also be introduced
in a zero-inflated Poisson or negative binomial model, but such a model
may encounter fitting problems if there is zero deflation at any settings
of the explanatory variables. A simple alternative approach adapts the
cumulative logit model with random effects, which has a single set of
parameters for describing effects. We illustrate the proposed methods with
examples.
Keywords:
CUMULATIVE LOGIT MODEL; GENERALIZED LINEAR MIXED MODEL; HURDLE MODEL;
NEGATIVE BINOMIAL MODEL; NONPARAMETRIC MIXTURE MODEL;
ZERO-INFLATED POISSON MODEL
Downloads:
Example
data and SAS code in zipped archive
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