Generalized Additive Models 论文

摘要

This chapter discusses the innovations of additional flexible methods for modeling an individual term in an additive model. It focuses on how we fit additive models. A general and efficient algorithm for fitting a generalized additive model consists of a hierarchy of three modules: scatterplot smoothers, backfitting algorithm, and local-scoring algorithm. These three steps are a rather natural and intuitive generalization of the usual linear model algorithms, and that is how they were originally conceived. The algorithm for fitting a gam is exactly analogous to the algorithm for glms. The chapter presents the S functions for fitting and understanding generalized additive models. In some cases, especially for generalized linear or additive models, adding residuals to a plot is unhelpful because they can distort the scale dramatically. Any interesting features in the functions get lost because of a few large residuals, even though they may carry a very small weight.