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June 2010 A flexible regression model for count data
Kimberly F. Sellers, Galit Shmueli
Ann. Appl. Stat. 4(2): 943-961 (June 2010). DOI: 10.1214/09-AOAS306


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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Kimberly F. Sellers. Galit Shmueli. "A flexible regression model for count data." Ann. Appl. Stat. 4 (2) 943 - 961, June 2010.


Published: June 2010
First available in Project Euclid: 3 August 2010

zbMATH: 1194.62091
MathSciNet: MR2758428
Digital Object Identifier: 10.1214/09-AOAS306

Keywords: Conway–Maxwell-Poisson (COM-Poisson) distribution , dispersion , generalized linear models (GLM) , generalized Poisson

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.4 • No. 2 • June 2010
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