ABSTRACT
The multiple regression model described in Chapter 6 and the generalized linear model featured in Chapter 8 can accommodate nonlinear functions of the explanatory variables, for example, quadratic or cubic terms, if these are thought to be necessary to provide an adequate fit. In this chapter, however, we consider some alternative and generally more flexible statistical methods for modelling nonlinear relationships between a response variable and one or more explanatory variables. The main component of these methods, known as
generalized additive models
(GAMs), is the fitting of a “smooth” relationship between the response and each explanatory variable by means of a
scatterplot smoother
(see Chapter 4 and Section 9.2). GAMs are useful where:
• The relationship between the variables is expected to be of complex form not easily fitted by standard linear or nonlinear models.
