Annals of Applied Statistics

A flexible regression model for count data

Kimberly F. Sellers and Galit Shmueli

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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 (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.

Article information

Source
Ann. Appl. Stat., Volume 4, Number 2 (2010), 943-961.

Dates
First available in Project Euclid: 3 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1280842147

Digital Object Identifier
doi:10.1214/09-AOAS306

Mathematical Reviews number (MathSciNet)
MR2758428

Zentralblatt MATH identifier
1194.62091

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

Citation

Sellers, Kimberly F.; Shmueli, Galit. A flexible regression model for count data. Ann. Appl. Stat. 4 (2010), no. 2, 943--961. doi:10.1214/09-AOAS306. https://projecteuclid.org/euclid.aoas/1280842147


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Supplemental materials

  • Supplementary materials: Supplementary Material for "A Flexible Regression Model for Count Data". Materials include details of the iterative reweighted least squares estimation, the Fisher information matrix components associated with the COM-Poisson coefficients, the full airfreight data set and diagnostics under various regression models for the airfreight and crash data, and additional logistic regression examples.
    Digital Object Identifier: doi:10.1214/09-AOAS306SUPP
    Supplemental PDF (165 KB)

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