Chapter 18

Generalized Additive Models

Up to this point, continuous explanatory variables have been added to models as linear functions, linearized parametric transformations, or through various link functions. In all cases, an explicit or implicit assumption was made about the parametric form of the function to be fitted to the data (whether quadratic, logarithmic, exponential, logistic, reciprocal or whatever). In many cases, however, you have one or more continuous explanatory variables, but you have no a priori reason to choose one particular parametric form over another for describing the shape of the relationship between the response variable and the explanatory variable(s). Generalized additive models (GAMs) are useful in such cases because they allow you to capture the shape of a relationship between y and x without prejudging the issue by choosing a particular parametric form.

Generalized additive models (implemented in R by the gam function) extend the range of application of generalized linear models (glm) by allowing non-parametric smoothers in addition to parametric forms, and these can be associated with a range of link functions. All of the error families allowed with glm are available with gam (binomial, poisson, Gamma, etc.). Indeed, gam has many of the attributes of both glm and lm, and the output can be modified using update. You can use all of the familiar methods such as print, plot, summary, anova, predict and fitted after a GAM has been fitted to data. The ...

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