Source: Ann. Appl. Stat. Volume 4, Number 2
(2010), 943-961.
Poisson regression is a popular tool for modeling count data and
is applied in a vast array of applications from the social to
the physical sciences and beyond. Real data, however, are often
over- or under-dispersed and, thus, not conducive to Poisson
regression. We propose a regression model based on the
Conway–Maxwell-Poisson (COM-Poisson) distribution to address
this problem. The COM-Poisson regression generalizes the
well-known Poisson and logistic regression models, and is
suitable for fitting count data with a wide range of dispersion
levels. With a GLM approach that takes advantage of exponential
family properties, we discuss model estimation, inference,
diagnostics, and interpretation, and present a test for
determining the need for a COM-Poisson regression over a
standard Poisson regression. We compare the COM-Poisson to
several alternatives and illustrate its advantages and
usefulness using three data sets with varying dispersion.
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