A Flexible Regression Model for Count Data

36 Pages Posted: 1 May 2008 Last revised: 25 Jul 2011

See all articles by Kimberly F. Sellers

Kimberly F. Sellers

Georgetown University - Department of Mathematics and Statistics

Galit Shmueli

Institute of Service Science, National Tsing Hua University, Taiwan

Date Written: December 4, 2008

Abstract

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 (CMP) distribution to address this problem. The CMP 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 CMP regression over a standard Poisson regression. We compare the CMP to several alternatives and illustrate its advantages and usefulness using four datasets with varying dispersion.

Keywords: Conway-Maxwell Poisson distribution, dispersion, generalized linear models

Suggested Citation

Sellers, Kimberly F. and Shmueli, Galit, A Flexible Regression Model for Count Data (December 4, 2008). Robert H. Smith School Research Paper No. RHS 06-060. Available at SSRN: https://ssrn.com/abstract=1127359 or http://dx.doi.org/10.2139/ssrn.1127359

Kimberly F. Sellers

Georgetown University - Department of Mathematics and Statistics ( email )

United States
202-687-8829 (Phone)

HOME PAGE: http://www9.georgetown.edu/faculty/kfs7

Galit Shmueli (Contact Author)

Institute of Service Science, National Tsing Hua University, Taiwan ( email )

Hsinchu, 30013
Taiwan

HOME PAGE: http://www.iss.nthu.edu.tw

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