ABSTRACT
Generalized linear models (GLMs) are a natural extension of the NLM that permit a wide range of non-Normal responses to be modeled as ¯exibly as in the Normal case. The most common examples are Binomial and Poisson data, with these often being modeled using logistic and log-linear regression, respectively. As discussed in Chapter 3 for the NLM, all the location parameters in a GLM are also ˜xed constants. GLMs were introduced by Nelder and Wedderburn (1972), with McCullagh and Nelder (1989) being the standard reference book on the subject. However, more recent books have been written that are much more accessible to the applied statistician, for example, Myers et al. (2002), Dobson (2002), or Faraway (2006). Chapter 16 of Gelman et al. (2004) covers GLMs from a Bayesian perspective. There are three components to a GLM:
1. The linear predictor, η = X β 2. The link function, g(μ) = η 3. The error distribution, specifying the distribution of the response, y,
given the explanatory variables, X, with mean E(y | X) = μ. This error distribution can also depend upon a further dispersion parameter, φ.
