Generalized Additive Models

Abstract

The multiple linear regression model discussed in Chapter 8 and the generalized linear model covered in Chapters 9 and 10 accommodate nonlinear relationships between the response variable (or the link function of its mean) and one or more of the explanatory variables by using polynomial terms or parametric transformations. (The predictor remains linear in the parameters, of course; nonlinear models are nonlinear in their parameters and are the subject of Chapter 14.) In this chapter, however, we consider some more flexible models in which the relationship between the response variable and one or more of the explanatory variables is modeled by using some type of scatterplot smoother (these were introduced informally in earlier chapters—see, for example, Chapter 4); their use here allows the data to suggest the form of the relationship involved, and indirectly to suggest whether the data might be better modeled by a linear or generalized linear model which included polynomial terms of a particular degree for some, or all, of the explanatory variables.