Generalized additive models.

This book describes a new array of power tools for data analysis, based on nonparametric regression or smoothing techniques. These methods relax the usual linear assumption in many standard models allowing the analyst to uncover structure in the data that might otherwise have been missed. McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear model methodology to cover the analysis of a diversity of types of data. Generalized Additive Models enhances this methodology further by incorporating the flexibility of nonparametric regression. Despite the additional flexibility, these models still retain the interpretability so important in multi-predictor regression analysis by modelling the regression surfaces as a sum of smooth terms. The early chapters give an overview of a variety of popular smoothing techniques, such as smoothing, splines, kernel and near-neighbour smoothers, and cover the general properties of smoothers in some detail. The next few chapters describe additive models, which allow one to build up a regression surface as a sum of lower dimensional terms. At one extreme these could all be linear, in which case the standard linear methodology is applicable; at the other extreme, many or all terms might be smooth functions of one or more variables. Typically the interesting models lie somewhere in between the two extremes. Additive models can be used in all of the settings in which generalized linear models have been so useful, such as logistic and log-linear models, models for censored survival data, and quasi-likelihood models. Many topics associated with generalized additive models are described, including the effective number of parameters for smoothing, confidence band estimation, resistant fitting and diagnostics, transformation models (including ACE) and the modelling of interactions. The last chapter features two case studies, and each chapter has many exercises, making the book useful as a course textbook. Some computer programs for fitting generalized additive models are also discussed. (Author/publisher)