Flexible regression and smoothing: using GAMLSS in R
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| Format: | Book |
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| Language: | English |
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Boca Raton
CRC Press
2017
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| Series: | The R series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 523-542 |
| Physical Description: | xxii, 549 Seiten Illustrationen, Diagramme |
| ISBN: | 9781138197909 |
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MARC
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| 245 | 1 | 0 | |a Flexible regression and smoothing |b using GAMLSS in R |c Mikis D. Stasinopoulos [und 4 weitere] |
| 264 | 1 | |a Boca Raton |b CRC Press |c 2017 | |
| 300 | |a xxii, 549 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The R series | |
| 500 | |a Literaturverzeichnis: Seite 523-542 | ||
| 650 | 4 | |a Regression analysisxData processing | |
| 650 | 4 | |a Linear models (Statistics) | |
| 650 | 4 | |a Smoothing (Statistics) | |
| 650 | 4 | |a Big data | |
| 650 | 4 | |a R (Computer program language) | |
| 650 | 0 | 7 | |a Regressionsanalyse |0 (DE-588)4129903-6 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Regressionsanalyse |0 (DE-588)4129903-6 |D s |
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| 776 | 0 | 8 | |i Erscheint auch als |n Onlineausgabe, ebook |z 978-1-315-26987-0 |
| 776 | 0 | 8 | |i Erscheint auch als |n Onlineausgabe,adobe reader |z 978-1-351-98038-8 |
| 776 | 0 | 8 | |i Erscheint auch als |n Onlineausgabe, ebup |z 978-1-351-98037-1 |
| 776 | 0 | 8 | |i Erscheint auch als |n Onlineausgabe, mobipocket |z 978-1-351-98036-4 |
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Record in the Search Index
| _version_ | 1804177582696955904 |
|---|---|
| adam_text | Contents
Preface xvii
I Introduction to models and packages 1
1 Why GAMLSS? 3
1.1 Introduction ..................................................... 3
1.2 The 1980s Munich rent data ....................................... 4
1.3 The linear regression model (LM) ................................. 6
1.4 The generalized linear model (GLM) .............................. 10
1.5 The generalized additive model (GAM)............................. 16
1.6 Modelling the scale parameter ................................... 20
1.7 The generalized additive model for location, scale and shape
(GAMLSS)........................................................ 23
1.8 Bibliographic notes ............................................. 27
1.9 Exercises........................................................ 28
2 Introduction to the gamlss packages 31
2.1 Introduction..................................................... 31
2.2 The gamlss packages ............................................. 32
2.3 A simple example using the gamlss packages ...................... 33
2.3.1 Fitting a parametric model................................ 34
2.3.2 Fitting a nonparametric smoothing model................... 40
2.3.2.1 P-splines........................................ 40
2.3.2.2 Cubic splines.................................... 43
2.3.2.3 Loess............................................ 44
2.3.2.4 Neural networks.................................. 44
2.3.3 Extracting fitted values.................................. 46
2.3.4 Modelling both ¡i and a................................... 46
2.3.5 Diagnostic plots.......................................... 48
2.3.6 Fitting different distributions........................... 49
2.3.7 Selection between models.................................. 50
2.4 Bibliographic notes ............................................. 54
2.5 Exercises........................................................ 55
II Algorithms, functions and inference 57
3 The algorithms 59
3.1 Introduction .................................................... 59
ix
X
Contents
3.2 Estimating /3 and 7 for fixed A.................................... 62
3.2.1 The RS algorithm............................................ 63
3.2.1.1 The outer iteration (GAMLSS iteration) ........... 63
3.2.1.2 The inner iteration (GLM or GLIM iteration) ... 64
3.2.1.3 The modified backfitting algorithm................. 68
3.2.2 The CG algorithm............................................ 70
3.2.2.1 The outer iteration................................ 70
3.2.2.2 The inner iteration................................ 70
3.2.2.3 The modified backfitting algorithm ................ 72
3.2.3 Fish species example........................................ 72
3.2.4 Remarks on the GAMLSS algorithms............................ 75
3.3 MAP estimators of ¡3 and 7 for fixed A ............................ 76
3.4 Estimating the hyperparameters A................................... 77
3.4.1 Global estimation........................................... 79
3.4.1.1 Maximum likelihood................................. 79
3.4.1.2 Generalized Akaike information criterion........... 79
3.4.1.3 Validation......................................... 80
3.4.2 Local estimation............................................ 81
3.4.2.1 Maximum likelihood................................. 81
3.4.2.2 Generalized Akaike information criterion........... 82
3.4.2.3 Generalized cross validation....................... 82
3.5 Bibliographic notes .............................................. 82
3.6 Exercises......................................................... 84
4 The gamlssO function 87
4.1 Introduction to the gamlssO function ............................. 87
4.2 The arguments of the gamlssO function............................. 88
4.2.1 The algorithmic control functions ......................... 91
4.2.2 Weighting out observations: the weights and data=subset ()
arguments ................................................. 94
4.3 The refit and update functions.................................... 98
4.3.1 refitO...................................................... 98
4.3.2 update 0.................................................... 99
4.4 The gamlss object .................................................102
4.5 Methods and functions for gamlss objects ..........................108
4.6 Bibliographic notes ...............................................109
4.7 Exercises...........................................................HO
5 Inference and prediction 113
5.1 Introduction.......................................................113
5.1.1 Asymptotic behaviour of a parametric GAMLSS model ... 114
5.1.2 Types of inference in a GAMLSS model........................114
5.1.3 Likelihood-based inference ..................................H6
5.1.4 Bootstrapping..............................................
5.2 Functions to obtain standard errors ..............................
Contents xi
5.2.1 The gen.likelihood() function................................118
5.2.2 The vcovO and rvcov() functions .............................120
5.2.3 The summaryO function........................................123
5.3 Functions to obtain confidence intervals.......................... 126
5.3.1 The conf int() function......................................126
5.3.2 The prof .dev() function.....................................127
5.3.3 The prof .term() function....................................130
5.4 Functions to obtain predictions ....................................135
5.4.1 The predict () function......................................135
5.4.2 The predict All () function..................................143
5.5 Appendix: Some theoretical properties of GLM and GAMLSS . . . 144
5.6 Bibliographic notes ................................................145
5.7 Exercises...........................................................146
III Distributions 151
6 The GAMLSS family of distributions 153
6.1 Introduction........................................................153
6.2 Types of distribution within the GAMLSS family .....................156
6.2.1 Explicit GAMLSS family distributions.........................156
6.2.2 Extending GAMLSS family distributions........................161
6.3 Displaying GAMLSS family distributions..............................168
6.3.1 Using the distribution demos.................................168
6.3.2 Using the pdf.plot () function...............................169
6.4 Amending an existing distribution and constructing a new distri-
bution ..................................................................172
6.4.1 Definition of the link functions.............................173
6.4.2 The fitting information......................................174
6.4.3 The S3 class definition......................................176
6.4.4 Definition of the d, p, q and r functions.................. 176
6.4.5 Example: reparameterizing the N0 distribution................177
6.5 The link functions..................................................179
6.5.1 How to display the available link functions..................179
6.5.2 Changing the default link function...........................180
6.5.3 Defining a link function.....................................180
6.5.4 Creating a link function.....................................181
6.5.5 Using the own link function..................................181
6.6 Bibliographic notes ................................................182
6.7 Exercises...........................................................183
7 Finite mixture distributions 191
7.1 Introduction to finite mixtures.....................................191
7.2 Finite mixtures with no parameters in common .......................193
7.2.1 The likelihood function......................................193
7.2.2 Maximizing the likelihood function using the EM algorithm . 194
xii Contents
7.2.3 Modelling the mixing probabilities........................196
7.2.4 Estimating the total number of components.................197
7.2.5 Zero components...........................................197
7.3 The gamlssMXO function...........................................197
7.4 Example using gamlssMXO: Reading glasses data ...................200
7.5 Finite mixtures with parameters in common .......................207
7.6 ThegamlssNPO function............................................209
7.7 Example using gamlssNPO: Animal brain data ......................211
7.8 Bibliographic notes .............................................217
7.9 Exercises........................................................218
IV Model terms 221
8 Linear parametric additive terms 223
8.1 Introduction to linear and additive terms........................223
8.2 Linear additive terms............................................225
8.2.1 Linear main effects.......................................227
8.2.2 Linear interactions ......................................227
8.3 Polynomials .....................................................231
8.4 Fractional polynomials ..........................................233
8.5 Piecewise polynomials and regression splines ....................235
8.6 B-splines........................................................239
8.7 Free knot models ................................................242
8.8 Example: the CD4 data ...........................................243
8.8.1 Orthogonal polynomials....................................245
8.8.2 Fractional polynomials ...................................247
8.8.3 Piecewise polynomials...................................249
8.8.4 Free knot models........................................250
8.9 Bibliographic notes .............................................253
8.10 Exercises........................................................254
9 Additive smoothing terms 255
9.1 Introduction ....................................................256
9.2 What is a scatterplot smoother?..................................258
9.3 Local regression smoothers.......................................261
9.4 Penalized smoothers: Univariate..................................265
9.4.1 Demos on penalized smoothers..............................269
9.4.2 The pb(), pbo() and psO functions for fitting a P-splines
smoother...................................................270
9.4.3 The pbz() function for fitting smooth curves which can
shrink to a constant.......................................274
9.4.4 The pbmO function for fitting monotonie smooth functions . 275
9.4.5 The pbc() and cyO functions for fitting cyclic smooth func-
tions ...........................................................277
9.4.6 The csO and scsO functions for fitting cubic splines .... 278
Contents
9.4.7 The ri() function for fitting ridge and lasso regression terms 282
9.4.8 The pcat() function for reducing levels of a factor.........287
9.4.9 The gmrfO function for fitting Gaussian Markov random
fields ......................................................293
9.5 Penalized smoothers: Multivariate...................................296
9.5.1 The pvcO function for fitting varying coefficient models . . . 296
9.5.1.1 Continuous z........................................297
9.5.1.2 Categorical z . . ............................298
9.5.2 Interfacing with gam(): The ga() function....................301
9.5.2.1 Additive terms......................................301
9.5.2.2 Smooth surface fitting..............................302
9.6 Other smoothers.....................................................305
9.6.1 Interfacing with nnet (): nn() 305
9.6.2 Interfacing with rpartC): tr()..............................308
9.6.3 Interfacing with loess (): lo().............................310
9.6.4 Interfacing with earth(): maO..............................314
9.7 Bibliographic notes ................................................315
9.8 Exercises...........................................................317
10 Random effects 321
10.1 Introduction........................................................322
10.1.1 Random effects at the observational and at the factor level . 323
10.1.2 Marginal and joint likelihood ...............................324
10.1.3 Functions available for fitting random effects...............324
10.2 Nonparametric random effect models .................................327
10.2.1 Nonparametric random intercept model for ¡x at the factor
level........................................................327
10.2.2 Fitting the nonparametric random intercept model for fx at
the factor level.............................................328
10.2.3 Nonparametric random intercept and slopes model for ¡x . . . 331
10.3 Normal random effect models ........................................334
10.3.1 Summary of the (r + l)st iteration of the EM algorithm . . . 335
10.4 The function gamlssNPO for random effects ..........................336
10.4.1 Fitting a normal random intercept for ¡x.....................337
10.4.2 Fitting nonparametric random effects.........................337
10.4.2.1 Fitting a nonparametric random intercept in the
predictor for ¡x....................................337
10.4.2.2 Fitting nonparametric random intercept and slopes
in the predictor for //.............................337
10.4.2.3 Fitting nonparametric random coefficients in the
predictor for other distribution parameters.........338
10.5 Examples using gamlssNPO ...........................................339
10.5.1 Example: Binary response with normal random intercept . . 339
10.5.2 Example: Binomial response with nonparametric random in-
tercept and slope...................................................341
XIV
Contents
10.6 The function random () 346
10.7 Examples using random () ..................................347
10.7.1 The Hodges data..............................................347
10.7.2 Revisiting the respiratory infection in children.......352
10.8 The function re(), interfacing with lme() ..........................354
10.9 Examples using re () 358
10.9.1 Refitting Hodges data using re () .....................358
10.9.2 Fitting a P-spline smoother using re () ...............359
10.9.3 Leukemia data................................................361
10.10 Bibliographic notes ................................................366
10.11 Exercises...........................................................367
V Model selection and diagnostics 375
11 Model selection techniques 377
11.1 Introduction: Statistical model selection ..........................377
11.2 GAMLSS model selection..............................................380
11.2.1 Component T : Selection of the distribution..............381
11.2.2 Component Q: Selection of the link functions.............381
11.2.3 Component 7՜: Selection of the additive terms in the model . 382
11.2.4 Component C: Selection of the smoothing parameters .... 383
11.2.5 Selection of all components using a validation data set ... . 384
11.2.6 Summary of the GAMLSS functions for model selection . . . 384
11.3 The addtermO and droptermO functions ...............................385
11.4 The stepGAICO function..............................................392
11.4.1 Selecting a model for //.................................393
11.4.2 Selecting a model for a..................................396
11.5 Strategy A: The stepGAICAll .A() function ..........................397
11.6 Strategy B: The stepGAICAll .B() function ..........................399
11.7 K-fold cross validation ............................................401
11.8 Validation and test data ...........................................402
11.8.1 The gamlssVGDO and VGD() functions ....................402
11.8.2 The getTGDO and TGDO functions ...........................404
11.8.3 The stepTGDO function........................................404
11.8.4 The stepTGDAll.AO function...................................406
11.9 The find.hyperO function ...........................................408
11.10 Bibliographic notes ................................................411
11.11 Exercises...........................................................411
12 Diagnostics 417
12.1 Introduction .......................................................417
12.2 Normalized (randomized) quantile residuals .........................418
12.3 The plot () function ...............................................422
12.4 The wp() function...................................................426
12.4.1 Single worm plot.............................................426
Contents
XV
12.4.2 Multiple worm plot ......................................428
12.4.3 Arguments of the wp function...........................432
12.5 The dtopO function .............................................433
12.5.1 Arguments of the dtop function...........................434
12.6 The Q. stats() function ......................................435
12.6.1 Examples.................................................436
12.6.2 Arguments of the Q. stats function.....................439
12.7 The rqres.plot() function ......................................439
12.7.1 Example .................................................439
12.7.2 Arguments of the rqres .plot () function.................440
12.8 Appendix .......................................................441
12.8.1 Proof of probability integral transform: Continuous case . . . 441
12.8.2 Proof of calibration: Calibrating the pdf................441
12.9 Bibliographic notes .......................................... 442
12.10 Exercises......................................................443
VI Applications 447
13 Centile estimation 449
13.1 Introduction....................................................449
13.1.1 Quantile regression......................................451
13.1.2 The LMS method and extensions............................452
13.1.3 Example: The Dutch boys BMI data.........................455
13.2 Fitting centile curves .........................................455
13.2.1 The 1ms () function......................................456
13.2.2 Estimating the smoothing degrees of freedom using a local
GAIC.....................................................458
13.2.3 The find.hyper() function................................459
13.2.4 Residual diagnostics.....................................460
13.2.5 The fittedPlot () function...............................462
13.3 Plotting centile curves ........................................465
13.3.1 centilesO................................................465
13.3.2 calibrationO ............................................468
13.3.3 centiles. f anO........................................ 470
13.3.4 centiles.split() 471
13.3.5 Comparing centile curves: centiles. com()................473
13.3.6 Plot of distribution of y for specific values of ........474
13.4 Predictive centile curves: centiles.pred(), z.scoresO ..........475
13.4.1 Case 1: Centile for y given x and centile percentage.....476
13.4.2 Case 2: Centile for y given x and centile z-score........477
13.4.3 Case 3: z-score given y and x............................478
13.5 Quantile sheets: quant Sheets () 480
13.5.1 Smoothing parameters.....................................481
13.5.2 Residuals................................................481
13.5.3 Fitting the model .......................................482
xvi Contents
13.6 Bibliographic notes ..............................................487
13.7 Exercises.........................................................488
14 Further applications 497
14.1 Introduction .....................................................497
14.2 Count data: The fish species data ................................498
14.3 Binomial data: The hospital stay data.............................508
14.4 Continuous data: Revisiting the 1990s film data ..................513
14.4.1 Preliminary analysis.......................................513
14.4.2 Modelling the data using the normal distribution..........514
14.4.3 Modelling the data using the BCPE distribution..........518
14.5 Epilogue .........................................................519
Bibliography 523
Index 543
|
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| id | DE-604.BV044345733 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:50:22Z |
| institution | BVB |
| isbn | 9781138197909 |
| language | English |
| lccn | 2016051819 |
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| owner_facet | DE-473 DE-BY-UBG DE-19 DE-BY-UBM |
| physical | xxii, 549 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | CRC Press |
| record_format | marc |
| series2 | The R series |
| spelling | Flexible regression and smoothing using GAMLSS in R Mikis D. Stasinopoulos [und 4 weitere] Boca Raton CRC Press 2017 xxii, 549 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier The R series Literaturverzeichnis: Seite 523-542 Regression analysisxData processing Linear models (Statistics) Smoothing (Statistics) Big data R (Computer program language) Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf R Programm (DE-588)4705956-4 s Regressionsanalyse (DE-588)4129903-6 s DE-604 Stasinopoulos, Mikis D. Sonstige (DE-588)1200420330 oth Erscheint auch als Onlineausgabe, ebook 978-1-315-26987-0 Erscheint auch als Onlineausgabe,adobe reader 978-1-351-98038-8 Erscheint auch als Onlineausgabe, ebup 978-1-351-98037-1 Erscheint auch als Onlineausgabe, mobipocket 978-1-351-98036-4 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029748673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Flexible regression and smoothing using GAMLSS in R Regression analysisxData processing Linear models (Statistics) Smoothing (Statistics) Big data R (Computer program language) Regressionsanalyse (DE-588)4129903-6 gnd R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4705956-4 |
| title | Flexible regression and smoothing using GAMLSS in R |
| title_auth | Flexible regression and smoothing using GAMLSS in R |
| title_exact_search | Flexible regression and smoothing using GAMLSS in R |
| title_full | Flexible regression and smoothing using GAMLSS in R Mikis D. Stasinopoulos [und 4 weitere] |
| title_fullStr | Flexible regression and smoothing using GAMLSS in R Mikis D. Stasinopoulos [und 4 weitere] |
| title_full_unstemmed | Flexible regression and smoothing using GAMLSS in R Mikis D. Stasinopoulos [und 4 weitere] |
| title_short | Flexible regression and smoothing |
| title_sort | flexible regression and smoothing using gamlss in r |
| title_sub | using GAMLSS in R |
| topic | Regression analysisxData processing Linear models (Statistics) Smoothing (Statistics) Big data R (Computer program language) Regressionsanalyse (DE-588)4129903-6 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Regression analysisxData processing Linear models (Statistics) Smoothing (Statistics) Big data R (Computer program language) Regressionsanalyse R Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029748673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT stasinopoulosmikisd flexibleregressionandsmoothingusinggamlssinr |