Generalized Additive Models

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Abstract
In the previous chapters we introduced a number of new functions for fitting linear models. In particular, glm() fits linear models in a variety of settings such as ordinary regression or logistic regression for binary data. The data and formula arguments provide a flexible language for specifying the variables and their form in a model, and the family argument supplies information on the error structure and the link function. The output of glm() can be fed into a number of auxiliary functions for summarizing the estimated coefficients and evaluating and examining the fits. In particular, residual and partial residual plots are used to identify discrepant observations and to identify nonlinearities. This chapter describes some tools for identifying nonlinearities in a more direct way by incorporating them into the model. This practice is not new, of course, if by nonlinearities we mean polynomial terms and parametric transformations. We use a more adaptive approach; the techniques described here allow us to model the terms nonparametrically using a scatterplot smoother, and in so doing let the data suggest the nonlinearities. The gam functions share many of the features of glm() and lm(), with some added flexibility. The output of gam(), being graphical in nature, tends to complement rather than overlap with glm().

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