Generalised Linear Models

Abstract

In previous chapters, we have studied the model

$$y = A\beta + \epsilon, $$

where the mean Ey = Aβ depends linearly on the parameters β, the errors are normal (Gaussian), and the errors are additive. We have also seen (Chapter 7) that in some situations, a transformation of the problem may help to correct some departure from our standard model assumptions. For example, in §7.3 on variance-stabilising transformations, we transformed our data from y to some function g(y), to make the variance constant (at least approximately). We did not there address the effect on the error structure of so doing. Of course, $g(y) = g(A\beta + \epsilon )$ as above will not have an additive Gaussian error structure any more, even approximately, in general.