Generalized Additive Models: 43 (Chapman & Hall/CRC Monographs on Statistics and Applied Probability) - Hardcover

Hastie, T.J.; Tibshirani, R.J.

Hardcover

ISBN 10: 0412343908 ISBN 13: 9780412343902

Publisher: Chapman and Hall/CRC, 1990

Synopsis

This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and allow analysts to uncover structure in the data that might otherwise have been missed. While McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear methodology to cover analysis of a range of data types, Generalized Additive Models enhances this methodology even further by incorporating the flexibility of nonparametric regression. Clear prose, exercises in each chapter, and case studies enhance this popular text.

About this title

Review

"That the authors succeed in conveying their message is largely due to the extremely clear and effective organization of the text. General concepts are introduced, illustrated with relatively simple applications, and then re-examined at a more theoretical level." -Journal of the Royal Statistical Society, Series C "This book aims to 'provide an up-to-date survey of current research in additive modelling, ' with the 'emphasis on practical rather than theoretical.' With that in mind, the book does extremely well." -Statistics in Medicine "Generalized Additive Models is a good starting point for researchers wishing to initiate themselves in the vast and burgeoning area of large-sample nonparametric model fitting." -Journal of the American Statistical Association "Overall, my impressions of this book are very favorable, and I consider it a book worth owning... The material is presented clearly and attractively. I recommend it to anyone interested in or needing to use extensions to the general linear model." -Technometrics ..". a complete introduction to the topic in a single monograph... a very readable book that provides the reader with great insight into a vast array of data analysis techniques... an excellent text for a course on smoothing-based analysis techniques... highly recommended to any reader interested in an introduction to many of the recent developments in data analysis." -Siam Review

Synopsis

A new array of power tools for data analysis is described in this book, based on non-parametric 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 range of types of data. "Generalized Additive Models" enhances this methodology further by incorporating the flexibility of non-parametric regression. Despite the additional flexibility, these models still retain the interpretability so important in multipredictor regression analysis by modelling the regression surfaces as a sum of smoooth 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 loglinear 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 described.

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 1990
• ISBN 10: 0412343908
• ISBN 13: 9780412343902
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 352
• Editor: Cox D.R., Reid N., Isham Valerie, Louis Thomas A., Tong Howell, Keiding Niels, Tibshirani R.J.