ABSTRACT
Generalized linear models (GLMs) allow for response distributions other than normal, and for a degree of non-linearity in the model structure. The exponential family of distributions includes many distributions that are useful for practical modelling, such as the Poisson, binomial, gamma and normal distributions. The comprehensive reference for GLMs is P. McCullagh and J. A. Nelder, while A. J. Dobson and A. Barnett provides a thorough introduction. A generalized linear mixed model follows from a linear mixed model in the same way as a GLM follows from a linear model. The generalization comes at some cost: model fitting now has to be done itera-tively, and distributional results, used for inference, are now approximate and justified by large sample limiting results, rather than being exact. Estimation and inference with GLMs is based on the theory of maximum likelihood estimation, although the maximization of the likelihood turns out to require an iterative least squares approach.
