Generalized additive models: an introduction with R
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
Chapman & Hall/CRC
2006
|
| Schriftenreihe: | Texts in statistical science
[67] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xvii, 392 Seiten Illustrationen, Diagramme |
| ISBN: | 1584884746 9781584884743 |
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| 245 | 1 | 0 | |a Generalized additive models |b an introduction with R |c Simon N. Wood |
| 264 | 1 | |a Boca Raton |b Chapman & Hall/CRC |c 2006 | |
| 300 | |a xvii, 392 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Texts in statistical science |v [67] | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Lineaire modellen |2 gtt | |
| 650 | 4 | |a Modelos matemáticos | |
| 650 | 7 | |a Modèle additif généralisé |2 rasuqam | |
| 650 | 7 | |a Modèle linéaire |2 rasuqam | |
| 650 | 7 | |a R (Langage de programmation) |2 rasuqam | |
| 650 | 4 | |a R (Lenguaje de programación) | |
| 650 | 7 | |a R (computerprogramma) |2 gtt | |
| 650 | 7 | |a Random walks (statistiek) |2 gtt | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Random walks (Mathematics) | |
| 650 | 4 | |a Linear models (Statistics) | |
| 650 | 4 | |a R (Computer program language) |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804135402887446528 |
|---|---|
| adam_text | CONTENTS PREFACE XV 1 LINEAR MODELS 1 1.1 A SIMPLE LINEAR MODEL 2 SIMPLE
LEAST SQUARES ESTIMATION 3 1.1.1 SAMPLING PROPERTIES OF /? 3 1.1.2 SO
HOW OLD IS THE UNIVERSE? 5 1.1.3 ADDING A DISTRIBUTIONAL ASSUMPTION 7
TESTING HYPOTHESES ABOUT (3 7 CONFIDENCE INTERVALS 9 1.2 LINEAR MODELS
IN GENERAL 10 1.3 THE THEORY OF LINEAR MODELS 12 1.3.1 LEAST SQUARES
ESTIMATION OF (3 12 1.3.2 THE DISTRIBUTION OF 0 13 1.3.3 {FA -&)/&$. ~T
N - P 14 1.3.4 F-RATIO RESULTS 15 1.3.5 THE INFLUENCE MATRIX 16 1.3.6
THE RESIDUALS, I, AND FITTED VALUES, (I 16 1.3.7 RESULTS IN TERMS OF X
17 1.3.8 THE GAUSS MARKOV THEOREM: WHAT S SPECIAL ABOUT LEAST SQUARES?
17 1 4 THE GEOMETRY OF LINEAR MODELLING 18 1.4.1 LEAST SQUARES 19 1.4.2
FITTING BY ORTHOGONAL DECOMPOSITIONS 20 VLL VIII CONTENTS 1.4.3
COMPARISON OF NESTED MODELS 21 1.5 PRACTICAL LINEAR MODELLING 22 1.5.1
MODEL FITTING AND MODEL CHECKING 23 1.5.2 MODEL SUMMARY 28 1.5.3 MODEL
SELECTION 30 1.5.4 ANOTHER MODEL SELECTION EXAMPLE 31 A FOLLOW-UP 35
1.5.5 CONFIDENCE INTERVALS 36 1.5.6 PREDICTION 36 1.6 PRACTICAL
MODELLING WITH FACTORS 37 1.6.1 IDENTIFIABILITY 38 1.6.2 MULTIPLE
FACTORS 39 1.6.3 INTERACTIONS OF FACTORS 40 1.6.4 USING FACTOR
VARIABLES IN R 41 1.7 GENERAL LINEAR MODEL SPECIFICATION IN R 44 1.8
FURTHER LINEAR MODELLING THEORY 45 1.8.1 CONSTRAINTS I: GENERAL LINEAR
CONSTRAINTS 46 1.8.2 CONSTRAINTS II: CONTRASTS AND FACTOR VARIABLES 46
1.8.3 LIKELIHOOD 48 1.8.4 NON-INDEPENDENT DATA WITH VARIABLE VARIANCE 49
1.8.5 AIC AND MALLOW S STATISTIC 51 1.8.6 NON-LINEAR LEAST SQUARES 53
1.8.7 FURTHER READING 55 1.9 EXERCISES 55 2 GENERALIZED LINEAR MODELS 59
2. 1 THE THEORY OF GLMS 60 2.1.1 THE EXPONENTIAL FAMILY OF DISTRIBUTIONS
62 2.1.2 FITTING GENERALIZED LINEAR MODELS 63 2.1.3 THE IRLS OBJECTIVE
IS A QUADRATIC APPROXIMATION TO THE LOG-LIKELIHOOD 66 CONTENTS IX 2.1.4
AICFORGLMS 68 2.1.5 LARGE SAMPLE DISTRIBUTION OF 0 69 2.1.6 COMPARING
MODELS BY HYPOTHESIS TESTING 69 DEVIANCE 70 MODEL COMPARISON WITH
UNKNOWN 4 71 2.1.7 $ AND PEARSON S STATISTIC 71 2.1.8 CANONICAL LINK
FUNCTIONS 72 2.1.9 RESIDUALS 73 PEARSON RESIDUALS 73 DEVIANCE RESIDUALS
73 2.1.10 QUASI-LIKELIHOOD 74 2.2 GEOMETRY OF GLMS 76 2.2.1 THE GEOMETRY
OF IRLS 77 2.2.2 GEOMETRY AND IRLS CONVERGENCE 78 2.3 GLMS WITH R 81
2.3.1 BINOMIAL MODELS AND HEART DISEASE 81 2.3.2 A POISSON REGRESSION
EPIDEMIC MODEL 87 2.3.3 LOG-LINEAR MODELS FOR CATEGORICAL DATA 93 2.3.4
SOLE EGGS IN THE BRISTOL CHANNEL 97 2.4 LIKELIHOOD 102 2.4.1 INVARIANCE
102 2.4.2 PROPERTIES OF THE EXPECTED LOG-LIKELIHOOD 103 2.4.3
CONSISTENCY 106 2.4.4 LARGE SAMPLE DISTRIBUTION OF 0 107 2.4.5 THE
GENERALIZED LIKELIHOOD RATIO TEST (GLRT) 108 2.4.6 DERIVATION OF 2 A ~
XR U N D E R H O 109 2.4.7 AIC IN GENERAL 111 2.4.8 QUASI-LIKELIHOOD
RESULTS 113 2.5 EXERCISES 115 X CONTENTS 3 INTRODUCING GAMS 121 3.1
INTRODUCTION 121 3.2 UNIVARIATE SMOOTH FUNCTIONS 122 3.2.1 REPRESENTING
A SMOOTH FUNCTION: REGRESSION SPLINES 122 A VERY SIMPLE EXAMPLE: A
POLYNOMIAL BASIS 122 ANOTHER EXAMPLE: A CUBIC SPLINE BASIS 124 USING THE
CUBIC SPLINE BASIS 126 3.2.2 CONTROLLING THE DEGREE OF SMOOTHING WITH
PENALIZED REGRES- SION SPLINES 128 3.2.3 CHOOSING THE SMOOTHING
PARAMETER, A: CROSS VALIDATION 130 3.3 ADDITIVE MODELS 133 3.3.1
PENALIZED REGRESSION SPLINE REPRESENTATION OF AN ADDITIVE MODEL 134
3.3.2 FITTING ADDITIVE MODELS BY PENALIZED LEAST SQUARES 135 3.4
GENERALIZED ADDITIVE MODELS 137 3.5 SUMMARY 139 3.6 EXERCISES 140 4 SOME
GAM THEORY 145 4.1 SMOOTHING BASES 146 4.1.1 WHY SPLINES? 146 NATURAL
CUBIC SPLINES ARE SMOOTHEST INTERPOLATORS 146 CUBIC SMOOTHING SPLINES
148 4.1.2 CUBIC REGRESSION SPLINES 149 4.1.3 A CYCLIC CUBIC REGRESSION
SPLINE 151 4.1.4 P-SPLINES 152 4.1.5 THIN PLATE REGRESSION SPLINES 154
THIN PLATE SPLINES 154 THIN PLATE REGRESSION SPLINES 157 PROPERTIES OF
THIN PLATE REGRESSION SPLINES 158 KNOT-BASED APPROXIMATION 160 4.1.6
SHRINKAGE SMOOTHERS 160 CONTENTS XI 4.1.7 CHOOSING THE BASIS DIMENSION
161 4.1.8 TENSOR PRODUCT SMOOTHS 162 TENSOR PRODUCT BASES 162 TENSOR
PRODUCT PENALTIES 165 4.2 SETTING UP GAMS AS PENALIZED GLMS 167 4.2.1
VARIABLE COEFFICIENT MODELS 168 4.3 JUSTIFYING P-IRLS 169 4.4 DEGREES OF
FREEDOM AND RESIDUAL VARIANCE ESTIMATION 170 4.4.1 RESIDUAL VARIANCE OR
SCALE PARAMETER ESTIMATION 171 4.5 SMOOTHING PARAMETER SELECTION
CRITERIA 172 4.5.1 KNOWN SCALE PARAMETER: UBRE 172 4.5.2 UNKNOWN SCALE
PARAMETER: CROSS VALIDATION 173 PROBLEMS WITH ORDINARY CROSS VALIDATION
174 4.5.3 GENERALIZED CROSS VALIDATION 175 4.5.4 GCV/UBRE/AIC IN THE
GENERALIZED CASE 177 APPROACHES TO GAM GCV/UBRE MINIMIZATION 179 4.6
NUMERICAL GCV/UBRE: PERFORMANCE ITERATION 181 4.6.1 MINIMIZING THE GCV
OR UBRE SCORE 181 STABLE AND EFFICIENT EVALUATION OF THE SCORES AND
DERIVATIVES 183 THE WEIGHTED CONSTRAINED CASE 185 4.7 NUMERICAL GCV/UBRE
OPTIMIZATION BY OUTER ITERATION 186 4.7.1 DIFFERENTIATING THE GCV/UBRE
FUNCTION 187 4.8 DISTRIBUTIONAL RESULTS 189 4.8.1 BAYESIAN MODEL, AND
POSTERIOR DISTRIBUTION OF THE PARAMETERS, FOR AN ADDITIVE MODEL 190
4.8.2 STRUCTURE OF THE PRIOR 191 4.8.3 POSTERIOR DISTRIBUTION FOR A GAM
192 4.8.4 BAYESIAN CONFIDENCE INTERVALS FOR NON-LINEAR FUNCTIONS OF
PARAMETERS 194 4.8.5 P-VALUES 194 4.9 CONFIDENCE INTERVAL PERFORMANCE
196 XII CONTENTS 4.9.1 SINGLE SMOOTHS 196 4.9.2 GAMS AND THEIR
COMPONENTS 200 4.9.3 UNCONDITIONAL BAYESIAN CONFIDENCE INTERVALS 202
4.10 FURTHER GAM THEORY 204 4.10.1 COMPARING GAMS BY HYPOTHESIS TESTING
204 4.10.2 ANOVA DECOMPOSITIONS AND NESTING 206 4.10.3 THE GEOMETRY OF
PENALIZED REGRESSION 208 4.10.4 THE NATURAL PARAMETERIZATION OF A
PENALIZED SMOOTHER 210 4.11 OTHER APPROACHES TO GAMS 212 4.11.1
BACKFILLING GAMS 213 4.11.2 GENERALIZED SMOOTHING SPLINES 215 4.12
EXERCISES 217 5 GAMS IN PRACTICE: MGCV 221 5.1 CHERRY TREES AGAIN 221
5.1.1 FINER CONTROL OF GAM 223 5.1.2 SMOOTHS OF SEVERAL VARIABLES 225
5.1.3 PARAMETRIC MODEL TERMS 228 5.2 BRAIN IMAGING EXAMPLE 230 5.2.1
PRELIMINARY MODELLING 232 5.2.2 WOULD AN ADDITIVE STRUCTURE BE BETTER?
236 5.2.3 ISOTROPIC OR TENSOR PRODUCT SMOOTHS? 237 5.2.4 DETECTING
SYMMETRY (WITH BY VARIABLES) 239 5.2.5 COMPARING TWO SURFACES 241 5.2.6
PREDICTION WITH PREDICT. GAM 243 PREDICTION WITH LPMATRIX 245 5.2.7
VARIANCES OF NON-LINEAR FUNCTIONS OF THE FITTED MODEL 246 5.3 AIR
POLLUTION IN CHICAGO EXAMPLE 247 5.4 MACKEREL EGG SURVEY EXAMPLE 254
5.4.1 MODEL DEVELOPMENT 254 5.4.2 MODEL PREDICTIONS 260 CONTENTS 5.5
PORTUGUESE LARKS EXAMPLE 262 5.6 OTHER PACKAGES 265 5.6.1 PACKAGE GAM
265 5.6.2 PACKAGE GSS 267 5.7 EXERCISES 270 6 MIXED MODELS AND GAMMS 277
6.1 MIXED MODELS FOR BALANCED DATA 277 6.1.1 A MOTIVATING EXAMPLE 277
THE WRONG APPROACH: A FIXED EFFECTS LINEAR MODEL 278 THE RIGHT APPROACH:
A MIXED EFFECTS MODEL 280 6.1.2 GENERAL PRINCIPLES 281 6.1.3 A SINGLE
RANDOM FACTOR 282 6.1.4 A MODEL WITH TWO FACTORS 286 6.1.5 DISCUSSION
290 6.2 LINEAR MIXED MODELS IN GENERAL 291 6.2.1 ESTIMATION OF LINEAR
MIXED MODELS 292 6.2.2 DIRECTLY MAXIMIZING A MIXED MODEL LIKELIHOOD IN R
293 6.2.3 INFERENCE WITH LINEAR MIXED MODELS 295 FIXED EFFECTS 295
INFERENCE ABOUT THE RANDOM EFFECTS 296 6.2.4 PREDICTING THE RANDOM
EFFECTS 297 6.2.5 REML 298 THE EXPLICIT FORM OF THE REML CRITERION 299
6.2.6 A LINK WITH PENALIZED REGRESSION 300 6.2.7 THE EM ALGORITHM 302
6.3 LINEAR MIXED MODELS IN R 303 6.3.1 TREE GROWTH: AN EXAMPLE USING IME
304 6.3.2 SEVERAL LEVELS OF NESTING 309 6.4 GENERALIZED LINEAR MIXED
MODELS 310 6.5 GLMMSWITHR 312 XIV CONTENTS 6.6 GENERALIZED ADDITIVE
MIXED MODELS 316 6.6.1 SMOOTHS AS MIXED MODEL COMPONENTS 316 6.6.2
INFERENCE WITH GAMMS 318 6.7 GAMMS WITH R 319 6.7.1 A GAMM FOR SOLE EGGS
319 6.7.2 THE TEMPERATURE IN CAIRO 321 6.8 EXERCISES 325 A SOME MATRIX
ALGEBRA 331 A.I BASIC COMPUTATIONAL EFFICIENCY 331 A.2 COVARIANCE
MATRICES 332 A.3 DIFFERENTIATING A MATRIX INVERSE 332 A.4 KRONECKER
PRODUCT 333 A.5 ORTHOGONAL MATRICES AND HOUSEHOLDER MATRICES 333 A.6 QR
DECOMPOSITION 334 A.7 CHOLESKI DECOMPOSITION 334 A.8 EIGEN-DECOMPOSITION
335 A.9 SINGULAR VALUE DECOMPOSITION 336 A. 10 PIVOTING 337 A. 11
LANCZOS ITERATION 337 B SOLUTIONS TO EXERCISES 341 B.I CHAPTER! 341 B.2
CHAPTER 2 346 B.3 CHAPTER 3 351 B.4 CHAPTER 4 353 B.5 CHAPTER 5 360 B.6
CHAPTER 6 369 BIBLIOGRAPHY 379 INDEX 385 PPN: 251820610 TITEL:
GENERALIZED ADDITIVE MODELS : AN INTRODUCTION WITH R / SIMON N. WOOD. -
BOCA RATON [U.A.] : CHAPMAN & HALL/CRC, 2006 ISBN: 1-58488-474-6;
978-1-58488-474-3 BIBLIOGRAPHISCHER DATENSATZ IM SWB-VERBUND
|
| adam_txt |
CONTENTS PREFACE XV 1 LINEAR MODELS 1 1.1 A SIMPLE LINEAR MODEL 2 SIMPLE
LEAST SQUARES ESTIMATION 3 1.1.1 SAMPLING PROPERTIES OF /? 3 1.1.2 SO
HOW OLD IS THE UNIVERSE? 5 1.1.3 ADDING A DISTRIBUTIONAL ASSUMPTION 7
TESTING HYPOTHESES ABOUT (3 7 CONFIDENCE INTERVALS 9 1.2 LINEAR MODELS
IN GENERAL 10 1.3 THE THEORY OF LINEAR MODELS 12 1.3.1 LEAST SQUARES
ESTIMATION OF (3 12 1.3.2 THE DISTRIBUTION OF 0 13 1.3.3 {FA -&)/&$. ~T
N - P 14 1.3.4 F-RATIO RESULTS 15 1.3.5 THE INFLUENCE MATRIX 16 1.3.6
THE RESIDUALS, I, AND FITTED VALUES, (I 16 1.3.7 RESULTS IN TERMS OF X
17 1.3.8 THE GAUSS MARKOV THEOREM: WHAT'S SPECIAL ABOUT LEAST SQUARES?
17 1 4 THE GEOMETRY OF LINEAR MODELLING 18 1.4.1 LEAST SQUARES 19 1.4.2
FITTING BY ORTHOGONAL DECOMPOSITIONS 20 VLL VIII CONTENTS 1.4.3
COMPARISON OF NESTED MODELS 21 1.5 PRACTICAL LINEAR MODELLING 22 1.5.1
MODEL FITTING AND MODEL CHECKING 23 1.5.2 MODEL SUMMARY 28 1.5.3 MODEL
SELECTION 30 1.5.4 ANOTHER MODEL SELECTION EXAMPLE 31 A FOLLOW-UP 35
1.5.5 CONFIDENCE INTERVALS 36 1.5.6 PREDICTION 36 1.6 PRACTICAL
MODELLING WITH FACTORS 37 1.6.1 IDENTIFIABILITY 38 1.6.2 MULTIPLE
FACTORS 39 1.6.3 'INTERACTIONS' OF FACTORS 40 1.6.4 USING FACTOR
VARIABLES IN R 41 1.7 GENERAL LINEAR MODEL SPECIFICATION IN R 44 1.8
FURTHER LINEAR MODELLING THEORY 45 1.8.1 CONSTRAINTS I: GENERAL LINEAR
CONSTRAINTS 46 1.8.2 CONSTRAINTS II: 'CONTRASTS'AND FACTOR VARIABLES 46
1.8.3 LIKELIHOOD 48 1.8.4 NON-INDEPENDENT DATA WITH VARIABLE VARIANCE 49
1.8.5 AIC AND MALLOW'S STATISTIC 51 1.8.6 NON-LINEAR LEAST SQUARES 53
1.8.7 FURTHER READING 55 1.9 EXERCISES 55 2 GENERALIZED LINEAR MODELS 59
2. 1 THE THEORY OF GLMS 60 2.1.1 THE EXPONENTIAL FAMILY OF DISTRIBUTIONS
62 2.1.2 FITTING GENERALIZED LINEAR MODELS 63 2.1.3 THE IRLS OBJECTIVE
IS A QUADRATIC APPROXIMATION TO THE LOG-LIKELIHOOD 66 CONTENTS IX 2.1.4
AICFORGLMS 68 2.1.5 LARGE SAMPLE DISTRIBUTION OF 0 69 2.1.6 COMPARING
MODELS BY HYPOTHESIS TESTING 69 DEVIANCE 70 MODEL COMPARISON WITH
UNKNOWN 4 71 2.1.7 $ AND PEARSON'S STATISTIC 71 2.1.8 CANONICAL LINK
FUNCTIONS 72 2.1.9 RESIDUALS 73 PEARSON RESIDUALS 73 DEVIANCE RESIDUALS
73 2.1.10 QUASI-LIKELIHOOD 74 2.2 GEOMETRY OF GLMS 76 2.2.1 THE GEOMETRY
OF IRLS 77 2.2.2 GEOMETRY AND IRLS CONVERGENCE 78 2.3 GLMS WITH R 81
2.3.1 BINOMIAL MODELS AND HEART DISEASE 81 2.3.2 A POISSON REGRESSION
EPIDEMIC MODEL 87 2.3.3 LOG-LINEAR MODELS FOR CATEGORICAL DATA 93 2.3.4
SOLE EGGS IN THE BRISTOL CHANNEL 97 2.4 LIKELIHOOD 102 2.4.1 INVARIANCE
102 2.4.2 PROPERTIES OF THE EXPECTED LOG-LIKELIHOOD 103 2.4.3
CONSISTENCY 106 2.4.4 LARGE SAMPLE DISTRIBUTION OF 0 107 2.4.5 THE
GENERALIZED LIKELIHOOD RATIO TEST (GLRT) 108 2.4.6 DERIVATION OF 2 A ~
XR U N D E R H O 109 2.4.7 AIC IN GENERAL 111 2.4.8 QUASI-LIKELIHOOD
RESULTS 113 2.5 EXERCISES 115 X CONTENTS 3 INTRODUCING GAMS 121 3.1
INTRODUCTION 121 3.2 UNIVARIATE SMOOTH FUNCTIONS 122 3.2.1 REPRESENTING
A SMOOTH FUNCTION: REGRESSION SPLINES 122 A VERY SIMPLE EXAMPLE: A
POLYNOMIAL BASIS 122 ANOTHER EXAMPLE: A CUBIC SPLINE BASIS 124 USING THE
CUBIC SPLINE BASIS 126 3.2.2 CONTROLLING THE DEGREE OF SMOOTHING WITH
PENALIZED REGRES- SION SPLINES 128 3.2.3 CHOOSING THE SMOOTHING
PARAMETER, A: CROSS VALIDATION 130 3.3 ADDITIVE MODELS 133 3.3.1
PENALIZED REGRESSION SPLINE REPRESENTATION OF AN ADDITIVE MODEL 134
3.3.2 FITTING ADDITIVE MODELS BY PENALIZED LEAST SQUARES 135 3.4
GENERALIZED ADDITIVE MODELS 137 3.5 SUMMARY 139 3.6 EXERCISES 140 4 SOME
GAM THEORY 145 4.1 SMOOTHING BASES 146 4.1.1 WHY SPLINES? 146 NATURAL
CUBIC SPLINES ARE SMOOTHEST INTERPOLATORS 146 CUBIC SMOOTHING SPLINES
148 4.1.2 CUBIC REGRESSION SPLINES 149 4.1.3 A CYCLIC CUBIC REGRESSION
SPLINE 151 4.1.4 P-SPLINES 152 4.1.5 THIN PLATE REGRESSION SPLINES 154
THIN PLATE SPLINES 154 THIN PLATE REGRESSION SPLINES 157 PROPERTIES OF
THIN PLATE REGRESSION SPLINES 158 KNOT-BASED APPROXIMATION 160 4.1.6
SHRINKAGE SMOOTHERS 160 CONTENTS XI 4.1.7 CHOOSING THE BASIS DIMENSION
161 4.1.8 TENSOR PRODUCT SMOOTHS 162 TENSOR PRODUCT BASES 162 TENSOR
PRODUCT PENALTIES 165 4.2 SETTING UP GAMS AS PENALIZED GLMS 167 4.2.1
VARIABLE COEFFICIENT MODELS 168 4.3 JUSTIFYING P-IRLS 169 4.4 DEGREES OF
FREEDOM AND RESIDUAL VARIANCE ESTIMATION 170 4.4.1 RESIDUAL VARIANCE OR
SCALE PARAMETER ESTIMATION 171 4.5 SMOOTHING PARAMETER SELECTION
CRITERIA 172 4.5.1 KNOWN SCALE PARAMETER: UBRE 172 4.5.2 UNKNOWN SCALE
PARAMETER: CROSS VALIDATION 173 PROBLEMS WITH ORDINARY CROSS VALIDATION
174 4.5.3 GENERALIZED CROSS VALIDATION 175 4.5.4 GCV/UBRE/AIC IN THE
GENERALIZED CASE 177 APPROACHES TO GAM GCV/UBRE MINIMIZATION 179 4.6
NUMERICAL GCV/UBRE: PERFORMANCE ITERATION 181 4.6.1 MINIMIZING THE GCV
OR UBRE SCORE 181 STABLE AND EFFICIENT EVALUATION OF THE SCORES AND
DERIVATIVES 183 THE WEIGHTED CONSTRAINED CASE 185 4.7 NUMERICAL GCV/UBRE
OPTIMIZATION BY OUTER ITERATION 186 4.7.1 DIFFERENTIATING THE GCV/UBRE
FUNCTION 187 4.8 DISTRIBUTIONAL RESULTS 189 4.8.1 BAYESIAN MODEL, AND
POSTERIOR DISTRIBUTION OF THE PARAMETERS, FOR AN ADDITIVE MODEL 190
4.8.2 STRUCTURE OF THE PRIOR 191 4.8.3 POSTERIOR DISTRIBUTION FOR A GAM
192 4.8.4 BAYESIAN CONFIDENCE INTERVALS FOR NON-LINEAR FUNCTIONS OF
PARAMETERS 194 4.8.5 P-VALUES 194 4.9 CONFIDENCE INTERVAL PERFORMANCE
196 XII CONTENTS 4.9.1 SINGLE SMOOTHS 196 4.9.2 GAMS AND THEIR
COMPONENTS 200 4.9.3 UNCONDITIONAL BAYESIAN CONFIDENCE INTERVALS 202
4.10 FURTHER GAM THEORY 204 4.10.1 COMPARING GAMS BY HYPOTHESIS TESTING
204 4.10.2 ANOVA DECOMPOSITIONS AND NESTING 206 4.10.3 THE GEOMETRY OF
PENALIZED REGRESSION 208 4.10.4 THE "NATURAL" PARAMETERIZATION OF A
PENALIZED SMOOTHER 210 4.11 OTHER APPROACHES TO GAMS 212 4.11.1
BACKFILLING GAMS 213 4.11.2 GENERALIZED SMOOTHING SPLINES 215 4.12
EXERCISES 217 5 GAMS IN PRACTICE: MGCV 221 5.1 CHERRY TREES AGAIN 221
5.1.1 FINER CONTROL OF GAM 223 5.1.2 SMOOTHS OF SEVERAL VARIABLES 225
5.1.3 PARAMETRIC MODEL TERMS 228 5.2 BRAIN IMAGING EXAMPLE 230 5.2.1
PRELIMINARY MODELLING 232 5.2.2 WOULD AN ADDITIVE STRUCTURE BE BETTER?
236 5.2.3 ISOTROPIC OR TENSOR PRODUCT SMOOTHS? 237 5.2.4 DETECTING
SYMMETRY (WITH BY VARIABLES) 239 5.2.5 COMPARING TWO SURFACES 241 5.2.6
PREDICTION WITH PREDICT. GAM 243 PREDICTION WITH LPMATRIX 245 5.2.7
VARIANCES OF NON-LINEAR FUNCTIONS OF THE FITTED MODEL 246 5.3 AIR
POLLUTION IN CHICAGO EXAMPLE 247 5.4 MACKEREL EGG SURVEY EXAMPLE 254
5.4.1 MODEL DEVELOPMENT 254 5.4.2 MODEL PREDICTIONS 260 CONTENTS 5.5
PORTUGUESE LARKS EXAMPLE 262 5.6 OTHER PACKAGES 265 5.6.1 PACKAGE GAM
265 5.6.2 PACKAGE GSS 267 5.7 EXERCISES 270 6 MIXED MODELS AND GAMMS 277
6.1 MIXED MODELS FOR BALANCED DATA 277 6.1.1 A MOTIVATING EXAMPLE 277
THE WRONG APPROACH: A FIXED EFFECTS LINEAR MODEL 278 THE RIGHT APPROACH:
A MIXED EFFECTS MODEL 280 6.1.2 GENERAL PRINCIPLES 281 6.1.3 A SINGLE
RANDOM FACTOR 282 6.1.4 A MODEL WITH TWO FACTORS 286 6.1.5 DISCUSSION
290 6.2 LINEAR MIXED MODELS IN GENERAL 291 6.2.1 ESTIMATION OF LINEAR
MIXED MODELS 292 6.2.2 DIRECTLY MAXIMIZING A MIXED MODEL LIKELIHOOD IN R
293 6.2.3 INFERENCE WITH LINEAR MIXED MODELS 295 FIXED EFFECTS 295
INFERENCE ABOUT THE RANDOM EFFECTS 296 6.2.4 PREDICTING THE RANDOM
EFFECTS 297 6.2.5 REML 298 THE EXPLICIT FORM OF THE REML CRITERION 299
6.2.6 A LINK WITH PENALIZED REGRESSION 300 6.2.7 THE EM ALGORITHM 302
6.3 LINEAR MIXED MODELS IN R 303 6.3.1 TREE GROWTH: AN EXAMPLE USING IME
304 6.3.2 SEVERAL LEVELS OF NESTING 309 6.4 GENERALIZED LINEAR MIXED
MODELS 310 6.5 GLMMSWITHR 312 XIV CONTENTS 6.6 GENERALIZED ADDITIVE
MIXED MODELS 316 6.6.1 SMOOTHS AS MIXED MODEL COMPONENTS 316 6.6.2
INFERENCE WITH GAMMS 318 6.7 GAMMS WITH R 319 6.7.1 A GAMM FOR SOLE EGGS
319 6.7.2 THE TEMPERATURE IN CAIRO 321 6.8 EXERCISES 325 A SOME MATRIX
ALGEBRA 331 A.I BASIC COMPUTATIONAL EFFICIENCY 331 A.2 COVARIANCE
MATRICES 332 A.3 DIFFERENTIATING A MATRIX INVERSE 332 A.4 KRONECKER
PRODUCT 333 A.5 ORTHOGONAL MATRICES AND HOUSEHOLDER MATRICES 333 A.6 QR
DECOMPOSITION 334 A.7 CHOLESKI DECOMPOSITION 334 A.8 EIGEN-DECOMPOSITION
335 A.9 SINGULAR VALUE DECOMPOSITION 336 A. 10 PIVOTING 337 A. 11
LANCZOS ITERATION 337 B SOLUTIONS TO EXERCISES 341 B.I CHAPTER! 341 B.2
CHAPTER 2 346 B.3 CHAPTER 3 351 B.4 CHAPTER 4 353 B.5 CHAPTER 5 360 B.6
CHAPTER 6 369 BIBLIOGRAPHY 379 INDEX 385 PPN: 251820610 TITEL:
GENERALIZED ADDITIVE MODELS : AN INTRODUCTION WITH R / SIMON N. WOOD. -
BOCA RATON [U.A.] : CHAPMAN & HALL/CRC, 2006 ISBN: 1-58488-474-6;
978-1-58488-474-3 BIBLIOGRAPHISCHER DATENSATZ IM SWB-VERBUND |
| any_adam_object | 1 |
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| author | Wood, Simon N. |
| author_GND | (DE-588)1070265071 |
| author_facet | Wood, Simon N. |
| author_role | aut |
| author_sort | Wood, Simon N. |
| author_variant | s n w sn snw |
| building | Verbundindex |
| bvnumber | BV021614809 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.73 |
| callnumber-search | QA274.73 |
| callnumber-sort | QA 3274.73 |
| callnumber-subject | QA - Mathematics |
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| classification_tum | DAT 368f MAT 627f |
| ctrlnum | (OCoLC)64084887 (DE-599)BVBBV021614809 |
| dewey-full | 519.2/82 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/82 |
| dewey-search | 519.2/82 |
| dewey-sort | 3519.2 282 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Psychologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Informatik Psychologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV021614809 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:51:53Z |
| indexdate | 2024-07-09T20:39:57Z |
| institution | BVB |
| isbn | 1584884746 9781584884743 |
| language | English |
| lccn | 2006040209 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014829960 |
| oclc_num | 64084887 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-824 DE-473 DE-BY-UBG DE-Grf2 DE-706 DE-703 DE-634 DE-11 DE-29 DE-384 |
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| physical | xvii, 392 Seiten Illustrationen, Diagramme |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Texts in statistical science |
| series2 | Texts in statistical science |
| spelling | Wood, Simon N. Verfasser (DE-588)1070265071 aut Generalized additive models an introduction with R Simon N. Wood Boca Raton Chapman & Hall/CRC 2006 xvii, 392 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Texts in statistical science [67] Includes bibliographical references and index Lineaire modellen gtt Modelos matemáticos Modèle additif généralisé rasuqam Modèle linéaire rasuqam R (Langage de programmation) rasuqam R (Lenguaje de programación) R (computerprogramma) gtt Random walks (statistiek) gtt Mathematisches Modell Random walks (Mathematics) Linear models (Statistics) R (Computer program language) Mathematical models Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Lineares Regressionsmodell (DE-588)4127971-2 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Irrfahrtsproblem (DE-588)4162442-7 s Verallgemeinertes lineares Modell (DE-588)4124382-1 s R Programm (DE-588)4705956-4 s 1\p DE-604 Lineares Regressionsmodell (DE-588)4127971-2 s 2\p DE-604 Stochastischer Prozess (DE-588)4057630-9 s 3\p DE-604 Texts in statistical science [67] (DE-604)BV022819715 67 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014829960&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wood, Simon N. Generalized additive models an introduction with R Texts in statistical science Lineaire modellen gtt Modelos matemáticos Modèle additif généralisé rasuqam Modèle linéaire rasuqam R (Langage de programmation) rasuqam R (Lenguaje de programación) R (computerprogramma) gtt Random walks (statistiek) gtt Mathematisches Modell Random walks (Mathematics) Linear models (Statistics) R (Computer program language) Mathematical models Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4124382-1 (DE-588)4162442-7 (DE-588)4057630-9 (DE-588)4127971-2 (DE-588)4129903-6 (DE-588)4705956-4 |
| title | Generalized additive models an introduction with R |
| title_auth | Generalized additive models an introduction with R |
| title_exact_search | Generalized additive models an introduction with R |
| title_exact_search_txtP | Generalized additive models an introduction with R |
| title_full | Generalized additive models an introduction with R Simon N. Wood |
| title_fullStr | Generalized additive models an introduction with R Simon N. Wood |
| title_full_unstemmed | Generalized additive models an introduction with R Simon N. Wood |
| title_short | Generalized additive models |
| title_sort | generalized additive models an introduction with r |
| title_sub | an introduction with R |
| topic | Lineaire modellen gtt Modelos matemáticos Modèle additif généralisé rasuqam Modèle linéaire rasuqam R (Langage de programmation) rasuqam R (Lenguaje de programación) R (computerprogramma) gtt Random walks (statistiek) gtt Mathematisches Modell Random walks (Mathematics) Linear models (Statistics) R (Computer program language) Mathematical models Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd Regressionsanalyse (DE-588)4129903-6 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Lineaire modellen Modelos matemáticos Modèle additif généralisé Modèle linéaire R (Langage de programmation) R (Lenguaje de programación) R (computerprogramma) Random walks (statistiek) Mathematisches Modell Random walks (Mathematics) Linear models (Statistics) R (Computer program language) Mathematical models Verallgemeinertes lineares Modell Irrfahrtsproblem Stochastischer Prozess Lineares Regressionsmodell Regressionsanalyse R Programm |
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