『Generalized Additive Models: An Introduction with R』

Simon Wood

(2006年2月27日刊行,Chapman & Hall/CRC[Texts in Statistical Science Series 67], ISBN:1584884746



【目次】

LINEAR MODELS

A simple linear model
Linear models in general
The theory of linear models
The geometry of linear modelling
Practical linear models
Practical modelling with factors
General linear model specification in R
Further linear modelling theory
Exercises

GENERALIZED LINEAR MODELS

The theory of GLMs
Geometry of GLMs
GLMs with R
Likelihood
Exercises

INTRODUCING GAMS

Introduction
Univariate smooth functions
Additive models
Generalized additive models
Summary
Exercises

SOME GAM THEORY

Smoothing bases
Setting up GAMs as penalized GLMs
Justifying P-IRLS
Degrees of freedom and residual variance estimation
Smoothing Parameter Estimation Criteria
Numerical GCV/UBRE: performance iteration
Numerical GCV/UBRE optimization by outer iteration
Distributional results
Confidence interval performance
Further GAM theory
Other approaches to GAMs
Exercises

GAMs IN PRACTICE: mgcv

Cherry trees again
Brain imaging example
Air pollution in Chicago example
Mackerel egg survey example
Portuguese larks example
Other packages
Exercises

MIXED MODELS and GAMMs

Mixed models for balanced data
Linear mixed models in general
Linear mixed models in R
Generalized linear mixed models
GLMMs with R
Generalized additive mixed models
GAMMs with R
Exercises

APPENDICES

A Some matrix algebra
B Solutions to exercises
Bibliography
Index