A Flexible Regression Model for Count Data

TitleA Flexible Regression Model for Count Data
Publication TypeWorking Paper
Year of Publication2008
AuthorsSellers, K. F., and G. Shmueli
Series TitleWorking Paper RHS 06-060
InstitutionSmith School of Business, University of Maryland

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.


R code is available at http://www9.georgetown.edu/faculty/kfs7/research/

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