『Generalized Additive Models : An Introduction with R』

Simon N. Wood

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



【目次】
Preface xv


1. LINEAR MODELS 1

1.1 A simple linear model
1.2 Linear models in general
1.3 The theory of linear models
1.4 The geometry of linear modelling
1.5 Practical linear models
1.6 Practical modelling with factors
1.7 General linear model specification in R
1.8 Further linear modelling theory
1.9 Exercises

2. GENERALIZED LINEAR MODELS 59

2.1 The theory of GLMs
2.2 Geometry of GLMs
2.3 GLMs with R
2.4 Likelihood
2.5 Exercises

3. INTRODUCING GAMS 121

3.1 Introduction
3.2 Univariate smooth functions
3.3 Additive models
3.4 Generalized additive models
3.5 Summary
3.6 Exercises

4. SOME GAM THEORY 145

4.1 Smoothing bases
4.2 Setting up GAMs as penalized GLMs
4.3 Justifying P-IRLS
4.4 Degrees of freedom and residual variance estimation
4.5 Smoothing Parameter Estimation Criteria
4.6 Numerical GCV/UBRE: performance iteration
4.7 Numerical GCV/UBRE optimization by outer iteration
4.8 Distributional results
4.9 Confidence interval performance
4.10 Further GAM theory
4.11 Other approaches to GAMs
4.12 Exercises

5. GAMs IN PRACTICE: mgcv 221

5.1 Cherry trees again
5.2 Brain imaging example
5.3 Air pollution in Chicago example
5.4 Mackerel egg survey example
5.5 Portuguese larks example
5.6 Other packages
5.7 Exercises

6. MIXED MODELS and GAMMs 277

6.1 Mixed models for balanced data
6.2 Linear mixed models in general
6.3 Linear mixed models in R
6.4 Generalized linear mixed models
6.5 GLMMs with R
6.6 Generalized additive mixed models
6.7 GAMMs with R
6.8 Exercises

A : Some matrix algebra 331

B : Solutions to exercises 341



Bibliography 379
Index 385