@article {VerHoef2007QuasiPoisson,
	title = {Quasi-Poisson vs. negative binomial regression: how should we model overdispersed count data?},
	journal = {Ecology},
	volume = {88},
	number = {11},
	year = {2007},
	month = {November},
	pages = {2766{\textendash}2772},
	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.},
	keywords = {distribution, ecology, overdispersion, poisson, statistics},
	issn = {0012-9658},
	url = {http://www.biomedexperts.com/Abstract.bme/18051645},
	author = {Ver Hoef, Jay M. and Boveng, Peter L.}
}
@article {Potts2006Comparing,
	title = {Comparing species abundance models},
	journal = {Predicting Species Distributions - Results from a Second Workshop on Advances in Predictive Species Distribution Models, held in Riederalp, Switzerland, 2004},
	volume = {199},
	number = {2},
	year = {2006},
	month = {November},
	pages = {153{\textendash}163},
	abstract = {Five regression models (Poisson, negative binomial, quasi-Poisson, the hurdle model and the zero-inflated Poisson) were used to assess the relationship between the abundance of a vulnerable plant species, Leionema ralstonii, and the environment. The methods differed in their capacity to deal with common properties of ecological data. They were assessed theoretically, and their predictive performance was evaluated with correlation, calibration and error statistics calculated within a bootstrap evaluation procedure that simulated performance for independent data.The hurdle model performed best, with the highest correlations between the observed and predicted abundances. This model was also well calibrated, giving the closest agreement between observed and predicted abundances. The negative binomial was the worst performing model. It had weaker correlations than the other models and resulted in a strong, inconsistent bias in predictions. The standard Poisson model which accommodates neither zero-inflation nor over-dispersion gave accurate estimates of regional population abundance, but at the individual population level they were inconsistent and biased.The strong performance of the hurdle model, coupled with theoretical properties that suit it for these data and for the ecology of this species, suggest that it is a useful alternative to other modelling methods. The gains in performance have practical advantages where predictions are used by conservation planners to understand population dynamics or to assess the relative risks of alternative management scenarios.},
	keywords = {distribution, ecology, modelling, poisson},
	doi = {10.1016/j.ecolmodel.2006.05.025},
	url = {http://dx.doi.org/10.1016/j.ecolmodel.2006.05.025},
	author = {Potts, Joanne M. and Elith, Jane}
}
