|Title||A Flexible Regression Model for Count Data|
|Publication Type||Journal Article|
|Year of Publication||2010|
|Authors||Sellers, K. F., and G. Shmueli|
|Journal||Annals of Applied Statistics|
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 tting 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 three datasets with varying dispersion.
Attached are both the paper and the supplementary materials (two separate files). R code is available in the COMPoissonReg R package at http://cran.r-project.org/web/packages/COMPoissonReg/index.html