ABSTRACT

All the models considered in the preceding chapters can be thought of as ways of extending ideas from linear regression. Various nonlinear or nonnormal regression models have of course been studied on an individual basis for many years. However, only in 1972 did Nelder and Wedderburn provide a unified and accessible theoretical and computational framework for a class of such models, called generalized linear models (GLMs), which have been of enormous influence in statistics. In this chapter we set out ways in which roughness penalty methods can be applied in the broader context of generalized linear models.