Generalized Linear Models

Abstract

In all examples in previous chapters it was assumed that the errors of observation were either normally distributed or, in Chapter 4, could be made approximately so by transformation. This chapter extends the class of models for the forward search to include generalized linear models. We give examples in which the errors of observation have the gamma distribution. For this continuous distribution the results are similar to those for the normal distribution. We also give examples of discrete data from the Poisson distribution and from the binomial. Interest again is in the relationship between the distribution of the response and the values of one or more explanatory variables. The distribution which is most unlike the normal is that for binary data, that is, binomial observations with one trial at each combination of factors.