Quasi-Poisson vs. Negative Binomial Regression
How Should We Model Overdispersed Count Data?
Bibliographic Data
| ID | 23318629 |
|---|---|
| Authors | Jay M Ver Hoef (0000-0003-4302-6895, NOAA National Marine Fisheries Service, corresponding author), Peter L Boveng (0000-0003-2732-4833, NOAA National Marine Fisheries Service) |
| Year | 2007 |
| Volume | 88 |
| Issue | 11 |
| Pages | 2766-2772 |
| Publication date | 2007-11-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Ecology (JOURNAL) |
| Journal identifiers | ISSN: 0012-9658 • E-ISSN: 1939-9170 |
| Publisher | Wiley (PUBLISHER • GB) |
| DOI | 10.1890/07-0043.1 |
| PMID | 18051645 |
| OpenAlex | W2121024352 |
| Language | EN |
| Citations received | 104 |
| References cited | 22 |
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.
Count data · Covariate · Econometrics · Generalized linear model · Negative binomial distribution · Overdispersion · Poisson distribution · Poisson regression · Population · Quasi-likelihood · Regression analysis · Statistics · Variance (accounting) · Variance function · Weighting · Zero-inflated model · Avian ecology and behavior · Marine animal studies overview · Mathematics · Water Quality and Resources Studies
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| Unique citing works | 104 |
|---|---|
| Citations per year | 6,12 |
| Citation span | 2009 - 2026 (18) |
| Citation velocity | current |
| Highly cited | Yes |
| Citation types | Neutral: 98 |