ABSTRACT
Generalized linear models∗ (Nelder and Wedderburn, 1972) allow for response distributions other than normal, and for a degree of non-linearity in the model structure.
A GLM has the basic structure
g(µi) = Xiβ,
where µi ≡ E(Yi), g is a smooth monotonic ‘link function’, Xi is the ith row of a model matrix, X, and β is a vector of unknown parameters. In addition, a GLM
usually makes the distributional assumptions that the Yi are independent and
Yi ∼ some exponential family distribution. The exponential family of distributions includes many distributions that are useful
for practical modelling, such as the Poisson, Binomial, Gamma and Normal distri-
butions. The comprehensive reference for GLMs is McCullagh and Nelder (1989),
while Dobson (2001) provides a thorough introduction.
