A Flexible Regression Model for Count Data

By Kimberly F. Sellers, Galit Shmueli. 2010

294 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability, Transportation

View Paper: https://www.semanticscholar.org/paper/3da83127d9f97d2529a3d168a0650cd587f6fc47

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Wagner Hugo Bonat
2. Bent Jørgensen
3. Darcy Steeg Morris
4. John P. Hinde
5. Clarice G. B. Dem'etrio
6. A. Huang
7. Casper W. Berg
8. Martin Mächler

In Statistics and Probability

1. Casper W. Berg
2. Wagner Hugo Bonat
3. Anders Nielsen
4. Célestin C. Kokonendji
5. Benjamin M. Bolker
6. John P. Hinde
7. Clarice G. B. Dem'etrio
8. Bent Jørgensen

In Transportation

1. Darcy Steeg Morris
2. A. Huang
3. Kimberly F. Sellers
4. Clarice G. B. Dem'etrio

Citations in the corpus

• Extended Poisson–Tweedie: Properties and regression models for count data (2016, methodology): “In the COM-Poisson case, we took 0 = 8 and 1 = 4, and for the Gamma-count case, we fixed 0 = 2 and 1 = 1.”
• Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts (2016, background): “Sellers & Shmueli (2010) argue that GP models are less attractive than CMP models because GP models achieve underdispersion via a somewhat unnatural truncation of the support of the distribution.”
• Underdispersion models: Models that are “under the radar” (2017, methodology): “…models including regressions (Mamode-Khan and Jowaheer 2013; ChooWosaba and Datta 2017; Morris et al. 2017; Lord, Guikema, and Geedipally 2008; Sellers and Shmueli 2010; Choo-Wosoba et al. 2015; Sellers and Raim 2016), multivariate distributions (Sellers, Morris, and Balakrishnan 2016),…”
• glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling (2017, methodology): “Depending on the dispersion, the upper tail of the Conway-Maxwell-Poisson distribution can be either longer or shorter than that of the Poisson (Sellers and Shmueli, 2010).”