Quasi-Poisson vs. negative binomial regression: how should we model overdispersed count data?
Abstract
Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of a negative binomial model is a quadratic function of the mean. These variance relationships affect the weights in the iteratively weighted least-squares algorithm of fitting models to data. Because the variance is a function of the mean, large and small counts get weighted differently in quasi-Poisson and negative binomial regression. We provide an example using harbor seal counts from aerial surveys. These counts are affected by date, time of day, and time relative to low tide. We present results on a data set that showed a dramatic difference on estimating abundance of harbor seals when using quasi-Poisson vs. negative binomial regression. This difference is described and explained in light of the different weighting used in each regression method. A general understanding of weighting can help ecologists choose between these two methods.
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Quasi-Poisson regression was chosen to address violations of the equidispersion assumption, providing adjusted SEs when variance exceeds the mean.
“Quasi-Poisson regression was chosen to address violations of the equidispersion assumption, because it provides adjusted SEs when the variance exceeds the mean.14”
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- Authors
- Ver Hoef, J. M., & Boveng, P. L.
- Affiliations
- NOAA National Marine Fisheries Service (US)
- ORCID
- Boveng, Peter L.
- Venue
- Ecology
- Publisher
- Wiley
- Published
- 2007-11
- Volume
- 88
- Issue
- 11
- Pages
- 2766-2772
- ISSN
- 0012-9658 (ISSN-L)
- OpenAlex
- W2121024352
- Cited by
- 1,238
- References
- 1
- Citations by year
- 2026: 100 · 2025: 94 · 2024: 100 · 2023: 82 · 2022: 118 · 2021: 119 · 2020: 96 · 2019: 70 · 2018: 91 · 2017: 65 · 2016: 69 · 2015: 58 · 2014: 50 · 2013: 41 · 2012: 31
- FWCI
- 10.10
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Ecology (publishedVersion)
- PubMed (publishedVersion)
- Lincoln (University of Nebraska) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- quasi-Poisson regression, negative binomial regression, overdispersed count data, variance weighting, abundance estimation, Phoca vitulina
- MeSH terms
- Animals, Data Collection, Data Interpretation, Statistical, Population Density, Population Growth, Probability, Regression Analysis, Seasons, Time Factors, Models, Statistical, Binomial Distribution, Poisson Distribution, Linear Models, Phoca
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