Quasi-poisson vs. negative binomial regression: How should we model overdispersed count data?

Ecology

Volumn 88, Issue 11, 2007, Pages 2766-2772

  Ver Hoef, Jay M ^a   Boveng, Peter L ^a  

^a NOAA National Marine Mammal Laboratory   (United States)

Author keywords

Covariates; Generalized linear models; Harbor seals; Iteratively weighted least squares; Overdispersion; Quasi models

Indexed keywords

ABUNDANCE; AERIAL SURVEY; ALGORITHM; ESTIMATION METHOD; MODELING; PINNIPED; POISSON RATIO; REGRESSION ANALYSIS;

PHOCA;

ANIMAL; ARTICLE; BINOMIAL DISTRIBUTION; GROWTH, DEVELOPMENT AND AGING; INFORMATION PROCESSING; METHODOLOGY; PHOCA; POISSON DISTRIBUTION; POPULATION DENSITY; POPULATION GROWTH; PROBABILITY; REGRESSION ANALYSIS; SEASON; STATISTICAL ANALYSIS; STATISTICAL MODEL; TIME;

ANIMALS; BINOMIAL DISTRIBUTION; DATA COLLECTION; DATA INTERPRETATION, STATISTICAL; LINEAR MODELS; MODELS, STATISTICAL; PHOCA; POISSON DISTRIBUTION; POPULATION DENSITY; POPULATION GROWTH; PROBABILITY; REGRESSION ANALYSIS; SEASONS; TIME FACTORS;

EID: 38449113722     PISSN: 00129658     EISSN: None     Source Type: Journal    
DOI: 10.1890/07-0043.1     Document Type: Article

References (29)

1. Akaike, H. 1973. Information theory and the extension of the maximum likelihood principle. Pages 267-281 in B. N. Petrov and F. Czaki, editors. Proceedings of the International Symposium on Information Theory. Akademia Kiadoo, Budapest, Hungary.
2. Alexander, N., R. Moyeed, and J. Stander. 2000. Spatial modeling of individual-level parasite counts using the negative binomial distribution. Biostatistics 1:453-463.
3. Boveng, P. L., J. L. Bengtson, D. E. Withrow, J. C. Cesarone, M. A. Simpkins, K. J. Frost, and J. J. Burns. 2003. The abundance of harbor seals in the Gulf of Alaska. Marine Mammal Science 19:111-127.
4. Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference: a practical information theoretic approach. Second edition. Springer-Verlag, Berlin, Germany.
5. Consul, P. C. 1989. Generalized Poisson distribution: properties and applications. Marcel Dekker, New York, New York, USA.
6. Eberhardt, L. L. 1978. Appraising variability in population studies. Journal of Wildlife Management 42:207-238.
7. Efron, B. 1986. Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association 81:709-721.
8. Frost, K. J., L. F. Lowry, and J. M. Ver Hoef. 1999. Monitoring the trend of harbor seals in Prince William Sound, Alaska, after the Exxon Valdez oil spill. Marine Mammal Science 15:494-506.
9. Gardner, W., E. P. Mulvey, and E. C. Shaw. 1995. Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models. Psychological Bulletin 118: 392-404.
10. Gelfand, A. E., and S. R. Dalal. 1990. A note on overdispersed exponential families. Biometrika 77:55-64.
11. Joe, H., and R. Zhu. 2005. Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution. Biometrical Journal 47:219-229.
12. Lambert, D. 1992. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics 34:1-14.
13. Lee, Y., and J. A. Nelder. 2000. The relationship between double-exponential families and extended quasi-likelihood families, with application to modeling Geissler's human sex ratio data. Applied Statistics 49:413-419.
14. Lord, D., S. Washington, and J. Ivan. 2005. Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accident Analysis and Prevention 37:35-46.
15. Mathews, E. A., and G. W. Pendleton. 2006. Declines in harbor seal (Phoca vitulina) numbers in Glacier Bay National Park, Alaska, 1992-2002. Marine Mammal Science 22:167-189.
16. McCullagh, P., and J. A. Nelder. 1989. Generalized linear models. Second edition. Chapman and Hall, New York, New York, USA.
17. O'Hara, R. B. 2005. Species richness estimators: How many species can dance on the head of a pin? Journal of Animal Ecology 74:375-386.
18. Potts, J., and J. Elith. 2006. Comparing species abundance models. Ecological Modelling 199:153-163.
19. Raftery, A. E. 1995. Bayesian model selection in social research (with discussion by Andrew Gelman, Donald B. Rubin, and Robert M. Hauser). Pages 111-195 in P. V. Marsden, editor. Sociological methodology 1995. Blackwell, Cambridge, Massachusetts, USA.
20. Rissanen, J. 1978. Modeling by the shortest data description. Automatica 14:465-471.
21. SAS Institute. 2003. SAS version 9.1. SAS Institute, Cary, North Carolina, USA.
22. Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6:461-464.
23. Sileshi, G. 2006. Selecting the right statistical model for analysis of insect count data by using information theoretic measures. Bulletin of Entomological Research 96:479-488.
24. Small, R. J., G. W. Pendleton, and K. W. Pitcher. 2003. Trends in abundance of Alaska harbor seals, 1983-2002. Marine Mammal Science 19:344-362.
25. Terceiro, M. 2003. The statistical properties of recreational catch rate data for some fish stocks off the northeast US coast. Fishery Bulletin 101:653-672.
26. Vehtari, A., and J. Lampinen. 2003. Expected utility estimation via cross-validation. Pages 701-710 in J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith, and M. West, editors. Bayesian statistics 7. Oxford University Press, Oxford, UK.
27. Ver Hoef, J. M., and K. J. Frost. 2003. A Bayesian hierarchical model for monitoring harbor seal changes in Prince William Sound, Alaska. Environmental and Ecological Statistics 10: 201-219.
28. Wedderburn, R. W. M. 1974. Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61:439-447.
29. White, G. C., and R. E. Bennetts. 1996. Analysis of frequency count data using the negative binomial distribution. Ecology 77:2549-2557.