CONICET | Buscador de Institutos y Recursos Humanos

Generalized linear models are widely used by ornithologists for modelling the relationship between a response variable and a set of predictor variables. In many cases, the response variable is a count that takes nonnegative integer values. For this type of data, the most commonly used model is Poisson regression. However, the Poisson distribution cannot account for underdispersion (less variation than theoretically expected) usually encountered in response variables as clutch size or brood size. The Conway-Maxwell-Poisson (COM-Poisson) distribution is a two-parameter extension of the Poisson model that generalizes discrete distributions as Poisson, binomial and negative binomial. Remarkably, it is a flexible distribution that can account for both overdispersion and underdispersion. Using simulated and real data from Imperial Shags (Phalacrocorax atriceps), I evaluate the performance of Poisson and COM-Poisson models in the context of generalized linear models applied to clutch size and brood size. To illustrate the relationship between predictor and response variables, I used date of egg laying as predictor variable. Both clutch size and brood size exhibited severe underdispersion. Predicted values derived from Poisson and COM-Poisson models were similar. Standard errors derived from COM-Poisson models were comparatively smaller than those from Poisson, and differences increased as underdispersion increases. Thus, Poisson model showed unappropriated to model clutch size and brood size in Imperial Shags. This study shows the flexibility and utility of the COM-Poisson distribution applied to generalized linear models. Also, I show how generalized linear models with COM-Poisson distribution can be implemented in R (a free software environment for statistical computing) using CompGLM, compoisson and COMPoissonReg packages.