The generalized linear model and extensions: a review and some biological and environmental applications

The generalized linear model (GLM) encompasses many discrete and continuous models and it is particularly useful for analyzing discrete data. However, in many real life applications, the full distributional assumption of the GLM cannot be justified. Further, the GLM cannot accommodate over‐dispersion in the data. Since the inception of the GLM by Nelder and Wedderburn (1972) a number of its extensions have been proposed in the literature for robust analysis of discrete data. The purpose of this paper is to critically review these extensions. Applications to over‐dispersed Poisson and binomial models are shown. Some simulations are conducted to compare, in terms of bias and efficiency, the estimates of mean and the dispersion parameters by different methods. Applications to some biological and environmental data are given. Copyright © 2007 John Wiley & Sons, Ltd.