Generalized linear models:
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Boca Raton [u.a.]
Chapman and Hall
1989
|
Ausgabe: | 2. ed. |
Schriftenreihe: | Monographs on statistics and applied probability
37 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Literaturverz. S. 479 - 499 |
Beschreibung: | XIX, 511 S. graph. Darst. |
ISBN: | 0412317605 9780412317606 |
Internformat
MARC
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Datensatz im Suchindex
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adam_text | Contents
Preface to the first edition xvi
Preface xviii
1 Introduction 1
1.1 Background 1
1.1.1 The problem of looking at data 3
1.1.2 Theory as pattern 4
1.1.3 Model fitting 5
1.1.4 What is a good model? 7
1.2 The origins of generalized linear models 8
1.2.1 Terminology 8
1.2.2 Classical linear models 9
1.2.3 R.A. Fisher and the design of experiments 10
1.2.4 Dilution assay 11
1.2.5 Probit analysis 13
1.2.6 Logit models for proportions 14
1.2.7 Log linear models for counts 14
1.2.8 Inverse polynomials 16
1.2.9 Survival data 16
1.3 Scope of the rest of the book 17
1.4 Bibliographic notes 19
1.5 Further results and exercises 1 19
2 An outline of generalized linear models 21
2.1 Processes in model fitting 21
2.1.1 Model selection 21
2.1.2 Estimation 23
2.1.3 Prediction 25
vii
viii CONTENTS
2.2 The components of a generalized linear model 26
2.2.1 The generalization 27
2.2.2 Likelihood functions 28
2.2.3 Link functions 30
2.2.4 Sufficient statistics and canonical links 32
2.3 Measuring the goodness of fit 33
2.3.1 The discrepancy of a fit 33
2.3.2 The analysis of deviance 35
2.4 Residuals 37
2.4.1 Pearson residual 37
2.4.2 Anscombe residual 38
2.4.3 Deviance residual 39
2.5 An algorithm for fitting generalized linear models 40
2.5.1 Justification of the fitting procedure 41
2.6 Bibliographic notes 43
2.7 Further results and exercises 2 44
3 Models for continuous data with constant variance 48
3.1 Introduction 48
3.2 Error structure 49
3.3 Systematic component (linear predictor) 51
3.3.1 Continuous covariates 51
3.3.2 Qualitative covariates 52
3.3.3 Dummy variates 54
3.3.4 Mixed terms 55
3.4 Model formulae for linear predictors 56
3.4.1 Individual terms 56
3.4.2 The dot operator 56
3.4.3 The + operator 57
3.4.4 The crossing (*) and nesting (/) operators 58
3.4.5 Operators for the removal of terms 59
3.4.6 Exponential operator 60
3.5 Aliasing 61
3.5.1 Intrinsic aliasing with factors 63
3.5.2 Aliasing in a two way cross classification 65
3.5.3 Extrinsic aliasing 68
3.5.4 Functional relations among covariates 69
3.6 Estimation 70
3.6.1 The maximum likelihood equations 70
3.6.2 Geometrical interpretation 71
CONTENTS ix
3.6.3 Information 72
3.6.4 A model with two covariates 74
3.6.5 The information surface 77
3.6.6 Stability 78
3.7 Tables as data 79
3.7.1 Empty cells 79
3.7.2 Fused cells 81
3.8 Algorithms for least squares 81
3.8.1 Methods based on the information matrix 82
3.8.2 Direct decomposition methods 85
3.8.3 Extension to generalized linear models 88
3.9 Selection of covariates 89
3.10 Bibliographic notes 93
3.11 Further results and exercises 3 93
4 Binary data 98
4.1 Introduction 98
4.1.1 Binary responses 98
4.1.2 Covariate classes 99
4.1.3 Contingency tables 100
4.2 Binomial distribution 101
4.2.1 Genesis 101
4.2.2 Moments and cumulants 102
4.2.3 Normal limit 103
4.2.4 Poisson limit 105
4.2.5 Transformations 105
4.3 Models for binary responses 107
4.3.1 Link functions 107
4.3.2 Parameter interpretation 110
4.3.3 Retrospective sampling 111
4.4 Likelihood functions for binary data 114
4.4.1 Log likelihood for binomial data 114
4.4.2 Parameter estimation 115
4.4.3 Deviance function 118
4.4.4 Bias and precision of estimates 119
4.4.5 Sparseness 120
4.4.6 Extrapolation 122
4.5 Over dispersion 124
4.5.1 Genesis 124
4.5.2 Parameter estimation 126
x CONTENTS
4.6 Example 128
4.6.1 Habitat preferences of lizards 128
4.7 Bibliographic notes 135
4.8 Further results and exercises 4 135
5 Models for polytomous data 149
5.1 Introduction 149
5.2 Measurement scales 150
5.2.1 General points 150
5.2.2 Models for ordinal scales 151
5.2.3 Models for interval scales 155
5.2.4 Models for nominal scales 159
5.2.5 Nested or hierarchical response scales 160
5.3 The multinomial distribution 164
5.3.1 Genesis 164
5.3.2 Moments and cumulants 165
5.3.3 Generalized inverse matrices 168
5.3.4 Quadratic forms 169
5.3.5 Marginal and conditional distributions 170
5.4 Likelihood functions 171
5.4.1 Log likelihood for multinomial responses 171
5.4.2 Parameter estimation 172
5.4.3 Deviance function 174
5.5 Over dispersion 174
5.6 Examples 175
5.6.1 A cheese tasting experiment 175
5.6.2 Pneumoconiosis among coalminers 178
5.7 Bibliographic notes 182
5.8 Further results and exercises 5 184
6 Log linear models 193
6.1 Introduction 193
6.2 Likelihood functions 194
6.2.1 Poisson distribution 194
6.2.2 The Poisson log likelihood function 197
6.2.3 Over dispersion 198
6.2.4 Asymptotic theory 200
6.3 Examples 200
6.3.1 A biological assay of tuberculins 200
6.3.2 A study of wave damage to cargo ships 204
CONTENTS xi
6.4 Log linear models and multinomial response models 209
6.4.1 Comparison of two or more Poisson means 209
6.4.2 Multinomial response models 211
6.4.3 Summary 213
6.5 Multiple responses 214
6.5.1 Introduction 214
6.5.2 Independence and conditional independence 215
6.5.3 Canonical correlation models 217
6.5.4 Multivariate regression models 219
6.5.5 Multivariate model formulae 222
6.5.6 Log linear regression models 223
6.5.7 Likelihood equations 225
6.6 Example 229
6.6.1 Respiratory ailments of coalminers 229
6.6.2 Parameter interpretation 233
6.7 Bibliographic notes 235
6.8 Further results and exercises 6 236
7 Conditional likelihoods* 245
7.1 Introduction 245
7.2 Marginal and conditional likelihoods 246
7.2.1 Marginal likelihood 246
7.2.2 Conditional likelihood 248
7.2.3 Exponential family models 252
7.2.4 Profile likelihood 254
7.3 Hypergeometric distributions 255
7.3.1 Central hypergeometric distribution 255
7.3.2 Non central hypergeometric distribution 257
7.3.3 Multivariate hypergeometric distribution 260
7.3.4 Multivariate non central distribution 261
7.4 Some applications involving binary data 262
7.4.1 Comparison of two binomial probabilities 262
7.4.2 Combination of information from 2x2 tables 265
7.4.3 Ille et Vilaine study of oesophageal cancer 267
7.5 Some applications involving polytomous data 270
7.5.1 Matched pairs: nominal response 270
7.5.2 Ordinal responses 273
7.5.3 Example 276
7.6 Bibliographic notes 277
7.7 Further results and exercises 7 279
xii CONTENTS
8 Models with constant coefficient of variation 285
8.1 Introduction 285
8.2 The gamma distribution 287
8.3 Models with gamma distributed observations 289
8.3.1 The variance function 289
8.3.2 The deviance 290
8.3.3 The canonical link 291
8.3.4 Multiplicative models: log link 292
8.3.5 Linear models: identity link 294
8.3.6 Estimation of the dispersion parameter 295
8.4 Examples 296
8.4.1 Car insurance claims 296
8.4.2 Clotting times of blood 300
8.4.3 Modelling rainfall data using
two generalized linear models 302
8.4.4 Developmental rate of Drosophila melanogaster 306
8.5 Bibliographic notes 313
8.6 Further results and exercises 8 314
9 Quasi likelihood functions 323
9.1 Introduction 323
9.2 Independent observations 324
9.2.1 Covariance functions 324
9.2.2 Construction of the quasi likelihood function 325
9.2.3 Parameter estimation 327
9.2.4 Example: incidence of leaf blotch on barley 328
9.3 Dependent observations 332
9.3.1 Quasi likelihood estimating equations 332
9.3.2 Quasi likelihood function 333
9.3.3 Example: estimation of probabilities from
marginal frequencies 336
9.4 Optimal estimating functions 339
9.4.1 Introduction 339
9.4.2 Combination of estimating functions 340
9.4.3 Example: estimation for megalithic stone rings 343
9.5 Optimality criteria 347
9.6 Extended quasi likelihood 349
9.7 Bibliographic notes 352
9.8 Further results and exercises 9 352
CONTENTS xiii
10 Joint modelling of mean and dispersion 357
10.1 Introduction 357
10.2 Model specification 358
10.3 Interaction between mean and dispersion effects 359
10.4 Extended quasi likelihood as a criterion 360
10.5 Adjustments of the estimating equations 361
10.5.1 Adjustment for kurtosis 361
10.5.2 Adjustment for degrees of freedom 362
10.5.3 Summary of estimating equations for
the dispersion model 363
10.6 Joint optimum estimating equations 364
10.7 Example: the production of leaf springs for trucks 365
10.8 Bibliographic notes 370
10.9 Further results and exercises 10 371
11 Models with additional non linear parameters 372
11.1 Introduction 372
11.2 Parameters in the variance function 373
11.3 Parameters in the link function 375
11.3.1 One link parameter 375
11.3.2 More than one link parameter 377
11.3.3 Transformation of data vs
transformation of fitted values 378
11.4 Non linear parameters in the covariates 379
11.5 Examples 381
11.5.1 The effects of fertilizers on coastal
Bermuda grass 381
11.5.2 Assay of an insecticide with a synergist 384
11.5.3 Mixtures of drugs 386
11.6 Bibliographic notes 389
11.7 Further results and exercises 11 389
12 Model checking 391
12.1 Introduction 391
12.2 Techniques in model checking 392
12.3 Score tests for extra parameters 393
12.4 Smoothing as an aid to informal checks 394
12.5 The raw materials of model checking 396
xiv CONTENTS
12.6 Checks for systematic departure from model 398
12.6.1 Informal checks using residuals 398
12.6.2 Checking the variance function 400
12.6.3 Checking the link function 401
12.6.4 Checking the scales of covariates 401
12.6.5 Checks for compound discrepancies 403
12.7 Checks for isolated departures from the model 403
12.7.1 Measure of leverage 405
12.7.2 Measure of consistency 406
12.7.3 Measure of influence 406
12.7A Informal assessment of extreme values 407
12.7.5 Extreme points and checks for
systematic discrepancies 408
12.8 Examples 409
12.8.1 Carrot damage in an insecticide experiment 409
12.8.2 Minitab tree data 410
12.8.3 Insurance claims (continued) 413
12.9 A strategy for model checking? 414
12.10 Bibliographic notes 415
12.11 Further results and exercises 12 416
13 Models for survival data 419
13.1 Introduction 419
13.1.1 Survival functions and hazard functions 419
13.2 Proportional hazards models 421
13.3 Estimation with a specified survival distribution 422
13.3.1 The exponential distribution 423
13.3.2 The Weibull distribution 423
13.3.3 The extreme value distribution 424
13.4 Example: remission times for leukaemia 425
13.5 Cox s proportional hazards model 426
13.5.1 Partial likelihood 426
13.5.2 The treatment of ties 427
13.5.3 Numerical methods 429
13.6 Bibliographic notes 430
13.7 Further results and exercises 13 430
14 Components of dispersion 432
14.1 Introduction 432
14.2 Linear models 433
CONTENTS xv
14.3 Non linear models 434
14.4 Parameter estimation 437
14.5 Example: A salamander mating experiment 439
14.5.1 Introduction 439
14.5.2 Experimental procedure 441
14.5.3 A linear logistic model with random effects 444
14.5.4 Estimation of the dispersion parameters 448
14.6 Bibliographic notes 450
14.7 Further results and exercises 14 452
15 Further topics 455
15.1 Introduction 455
15.2 Bias adjustment 455
15.2.1 Models with canonical link 455
15.2.2 Non canonical models 457
15.2.3 Example: Lizard data (continued) 458
15.3 Computation of Bartlett adjustments 459
15.3.1 General theory 459
15.3.2 Computation of the adjustment 460
15.3.3 Example: exponential regression model 463
15.4 Generalized additive models 465
15.4.1 Algorithms for fitting 465
15.4.2 Smoothing methods 466
15.4.3 Conclusions 467
15.5 Bibliographic notes 467
15.6 Further results and exercises 15 467
Appendices 469
A Elementary likelihood theory 469
B Edgeworth series 474
C Likelihood ratio statistics 476
References 479
Index of data sets 500
Author index 501
Subject index 506
|
any_adam_object | 1 |
author | McCullagh, Peter 1952- Nelder, John A. 1924-2010 |
author_GND | (DE-588)129749575 (DE-588)1070718866 |
author_facet | McCullagh, Peter 1952- Nelder, John A. 1924-2010 |
author_role | aut aut |
author_sort | McCullagh, Peter 1952- |
author_variant | p m pm j a n ja jan |
building | Verbundindex |
bvnumber | BV004626116 |
classification_rvk | QH 230 QH 231 SK 840 |
classification_tum | MAT 628f |
ctrlnum | (OCoLC)263152293 (DE-599)BVBBV004626116 |
discipline | Mathematik Wirtschaftswissenschaften |
edition | 2. ed. |
format | Book |
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id | DE-604.BV004626116 |
illustrated | Illustrated |
indexdate | 2024-07-09T16:15:13Z |
institution | BVB |
isbn | 0412317605 9780412317606 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002841793 |
oclc_num | 263152293 |
open_access_boolean | |
owner | DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-29 DE-19 DE-BY-UBM DE-83 DE-11 DE-188 DE-523 DE-2070s |
owner_facet | DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-29 DE-19 DE-BY-UBM DE-83 DE-11 DE-188 DE-523 DE-2070s |
physical | XIX, 511 S. graph. Darst. |
publishDate | 1989 |
publishDateSearch | 1989 |
publishDateSort | 1989 |
publisher | Chapman and Hall |
record_format | marc |
series | Monographs on statistics and applied probability |
series2 | Monographs on statistics and applied probability |
spelling | McCullagh, Peter 1952- Verfasser (DE-588)129749575 aut Generalized linear models P. McCullagh and J. A. Nelder 2. ed. Boca Raton [u.a.] Chapman and Hall 1989 XIX, 511 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 37 Literaturverz. S. 479 - 499 Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Lineares Modell (DE-588)4134827-8 gnd rswk-swf Lineares Modell (DE-588)4134827-8 s Statistik (DE-588)4056995-0 s DE-604 Verallgemeinertes lineares Modell (DE-588)4124382-1 s 1\p DE-604 2\p DE-604 Nelder, John A. 1924-2010 Verfasser (DE-588)1070718866 aut Monographs on statistics and applied probability 37 (DE-604)BV002494005 37 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002841793&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 |
spellingShingle | McCullagh, Peter 1952- Nelder, John A. 1924-2010 Generalized linear models Monographs on statistics and applied probability Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Statistik (DE-588)4056995-0 gnd Lineares Modell (DE-588)4134827-8 gnd |
subject_GND | (DE-588)4124382-1 (DE-588)4056995-0 (DE-588)4134827-8 |
title | Generalized linear models |
title_auth | Generalized linear models |
title_exact_search | Generalized linear models |
title_full | Generalized linear models P. McCullagh and J. A. Nelder |
title_fullStr | Generalized linear models P. McCullagh and J. A. Nelder |
title_full_unstemmed | Generalized linear models P. McCullagh and J. A. Nelder |
title_short | Generalized linear models |
title_sort | generalized linear models |
topic | Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Statistik (DE-588)4056995-0 gnd Lineares Modell (DE-588)4134827-8 gnd |
topic_facet | Verallgemeinertes lineares Modell Statistik Lineares Modell |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002841793&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV002494005 |
work_keys_str_mv | AT mccullaghpeter generalizedlinearmodels AT nelderjohna generalizedlinearmodels |