Multivariate statistical modelling based on generalized linear models:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
2001
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 467 - 504 |
| Beschreibung: | XXVI, 517 S. graph. Darst. |
| ISBN: | 0387951873 |
Internformat
MARC
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| 245 | 1 | 0 | |a Multivariate statistical modelling based on generalized linear models |c Ludwig Fahrmeir ; Gerhard Tutz |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 2001 | |
| 300 | |a XXVI, 517 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. 467 - 504 | ||
| 650 | 7 | |a Analisi multivariata |2 sbt | |
| 650 | 7 | |a Modelli lineari (statistica) |2 sbt | |
| 650 | 4 | |a Multivariate Daten - Verallgemeinertes lineares Modell | |
| 650 | 7 | |a Statistica - metodi |2 sbt | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a Linear models (Statistics) | |
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Datensatz im Suchindex
| _version_ | 1804128931457007616 |
|---|---|
| adam_text | Contents
Preface to the Second Edition v
Preface to the First Edition vii
List of Examples xvii
List of Figures xxi
List of Tables xxv
1. Introduction 1
1.1 Outline and Examples 2
1.2 Remarks on Notation 13
1.3 Notes and Further Reading 14
2. Modelling and Analysis of Cross Sectional Data: A Review
of Univariate Generalized Linear Models 15
2.1 Univariate Generalized Linear Models 16
2.1.1 Data 16
Coding of Covariates 16
Grouped and Ungrouped Data 17
2.1.2 Definition of Univariate Generalized Linear Models .. 18
2.1.3 Models for Continuous Responses 22
Normal Distribution 22
Gamma Distribution 23
Inverse Gaussian Distribution 24
2.1.4 Models for Binary and Binomial Responses 24
Linear Probability Model 25
Probit Model 26
Logit Model 26
Complementary Log Log Model 26
Complementary Log Model 26
Binary Models as Threshold Models of Latent
Linear Models 29
Parameter Interpretation 29
Overdispersion 35
2.1.5 Models for Count Data 36
Log linear Poisson Model 36
x Contents
Linear Poisson Model 36
2.2 Likelihood Inference 38
2.2.1 Maximum Likelihood Estimation 38
Log likelihood, Score Function and Information Matrix 39
Numerical Computation of the MLE by
Iterative Methods 41
Uniqueness and Existence of MLEs* 43
Asymptotic Properties 44
Discussion of Regularity Assumptions* 46.
Additional Scale or Overdispersion Parameter 47
2.2.2 Hypothesis Testing and Goodness of Fit Statistics ... 47
Goodness of Fit Statistics 50
2.3 Some Extensions 55
2.3.1 Quasi likelihood Models 55
Basic Models 55
Variance Functions with Unknown Parameters 58
Nonconstant Dispersion Parameter 59
2.3.2 Bayesian Models 60
2.3.3 Nonlinear and Nonexponential Family Regression
Models* 65
2.4 Notes and Further Reading 67
3. Models for Multicategorical Responses: Multivariate
Extensions of Generalized Linear Models 69
3.1 Multicategorical Response Models . 70
3.1.1 Multinomial Distribution 70
3.1.2 Data 71
3.1.3 The Multivariate Model 72
3.1.4 Multivariate Generalized Linear Models 75
3.2 Models for Nominal Responses 77
3.2.1 The Principle of Maximum Random Utility 77
3.2.2 Modelling of Explanatory Variables: Choice of
Design Matrix 79
3.3 Models for Ordinal Responses 81
3.3.1 Cumulative Models: The Threshold Approach 83
Cumulative Logistic Model or Proportional
Odds Model 83
Grouped Cox Model or Proportional Hazards Model . 86
Extreme Maximal value Distribution Model 86
3.3.2 Extended Versions of Cumulative Models 87
3.3.3 Link Functions and Design Matrices for Cumulative
Models 88
3.3.4 Sequential Models 92
Generalized Sequential Models 95
Link Functions of Sequential Models 98
Contents xi
3.3.5 Strict Stochastic Ordering* 99
3.3.6 Two Step Models 100
Link Function and Design Matrix for
Two Step Models 102
3.3.7 Alternative Approaches 103
3.4 Statistical Inference 105
3.4.1 Maximum Likelihood Estimation 105
Numerical Computation 107
3.4.2 Testing and Goodness of Fit 107
Testing of Linear Hypotheses 107
Goodness of Fit Statistics 107
3.4.3 Power Divergence Family* 109
Asymptotic Properties under Classical Fixed Cells
Assumptions Ill
Sparseness and Increasing Cells Asymptotics 112
3.5 Multivariate Models for Correlated Responses 112
3.5.1 Conditional Models 114
Asymmetric Models 114
Symmetric Models 116
3.5.2 Marginal Models 119
Marginal Models for Correlated Univariate Responses 120
The Generalized Estimating Approach for Statistical
Inference 123
Marginal Models for Correlated
Categorical Responses 129
Likelihood based Inference for Marginal Models 135
3.6 Notes and Further Reading 136
Bayesian Inference 136
4. Selecting and Checking Models 139
4.1 Variable Selection 139
4.1.1 Selection Criteria 140
4.1.2 Selection Procedures 142
All Subsets Selection 142
Stepwise Backward and Forward Selection 143
4.2 Diagnostics 145
4.2.1 Diagnostic Tools for the Classical Linear Model 146
4.2.2 Generalized Hat Matrix 147
4.2.3 Residuals and Goodness of Fit Statistics 151
4.2.4 Case Deletion 156
4.3 General Tests for Misspecification* 161
4.3.1 Estimation under Model Misspecification 162
4.3.2 Hausman type Tests 165
Hausman Tests 165
Information Matrix Test 166
xii Contents
4.3.3 Tests for Nonnested Hypotheses 167
Tests Based on Artificial Nesting 168
Generalized Wald and Score Tests 168
4.4 Notes and Further Reading 170
Bayesian Model Determination 170
Robust Estimates 172
Model Tests Against Smooth Alternatives 172
5. Semi and Nonparametric Approaches to
Regression Analysis 173
5.1 Smoothing Techniques for Continuous Responses 174
5.1.1 Regression Splines and Other Basis Functions 174
Regression Splines 176
Other Basis Functions 178
Regularization 179
5.1.2 Smoothing Splines 181
5.1.3 Local Estimators 183
Simple Neighborhood Smoothers 183
Local Regression 184
Bias Variance Trade off 187
Relation to Other Smoothers 189
5.1.4 Selection of Smoothing Parameters 190
5.2 Smoothing for Non Gaussian Data 193
5.2.1 Basis Function Approach 193
Fisher Scoring for Penalized Likelihood* 194
5.2.2 Penalization and Spline Smoothing 195
Fisher Scoring for Generalized Spline Smoothing* ... 196
Choice of Smoothing Parameter 197
5.2.3 Localizing Generalized Linear Models 198
Local Fitting by Weighted Scoring 201
5.3 Modelling with Multiple Covariates 202
5.3.1 Modelling Approaches 207
Generalized Additive Models 207
Partially Linear Models 208
Varying Coefficient Models 208
Projection Pursuit Regression 209
Basis Function Approach 210
5.3.2 Estimation Concepts 213
Backfitting Algorithm for Generalized
Additive Models 213
Backfitting with Spline Functions 217
Choice of Smoothing Parameter 220
Partial Linear Models 220
5.4 Semiparametric Bayesian Inference for
Generalized Regression 221
Contents xiii
5.4.1 Gaussian Responses 221
Smoothness Priors Approaches 221
Basis Function Approaches 227
Models with Multiple Covariates 228
5.4.2 Non Gaussian Responses 231
Latent Variable Models for Categorical Responses ... 234
5.5 Notes and Further Reading 239
6. Fixed Parameter Models for Time Series and
Longitudinal Data 241
6.1 Time Series 242
6.1.1 Conditional Models 242
Generalized Autoregressive Models 242
Quasi Likelihood Models and Generalized Autore
gression Moving Average Models 246
6.1.2 Statistical Inference for Conditional Models 249
6.1.3 Marginal Models 255
Estimation of Marginal Models 258
6.2 Longitudinal Data 260
6.2.1 Conditional Models 261
Generalized Autoregressive Models, Quasi Likelihood
Models 261
Statistical Inference 262
Transition Models 264
Subject specific Approaches and
Conditional Likelihood 264
6.2.2 Marginal Models 267
Statistical Inference 268
6.2.3 Generalized Additive Models for Longitudinal Data .. 274
6.3 Notes and Further Reading 278
7. Random Effects Models 283
7.1 Linear Random Effects Models for Normal Data 285
7.1.1 Two stage Random Effects Models 285
Random Intercepts 286
Random Slopes 287
Multilevel Models 288
7.1.2 Statistical Inference 289
Known Variance Covariance Components 289
Unknown Variance Covariance Components 289
Derivation of the EM algorithm* 291
7.2 Random Effects in Generalized Linear Models 292
Generalized Linear Models with Random Effects .... 293
Examples 294
7.3 Estimation Based on Posterior Modes 298
xiv Contents
7.3.1 Known Variance Covariance Components 298
7.3.2 Unknown Variance Covariance Components 299
7.3.3 Algorithmic Details* 300
Fisher Scoring for Given Variance Covariance
Components 300
EM Type Algorithm 302
7.4 Estimation by Integration Techniques 303
7.4.1 Maximum Likelihood Estimation of Fixed Parameters 303
Direct Maximization Using Fitting Techniques for
GLMs 305
Nonparametric Maximum Likelihood for Finite Mix¬
tures 308
7.4.2 Posterior Mean Estimation of Random Effects 310
7.4.3 Indirect Maximization Based on the EM Algorithm* . 311
7.4.4 Algorithmic Details for Posterior Mean Estimation* . 315
7.5 Examples 318
7.6 Bayesian Mixed Models 321
Bayesian Generalized Mixed Models 321
Generalized Additive Mixed Models 322
7.7 Marginal Estimation Approach to Random Effects Models .. 325
7.8 Notes and Further Reading 328
8. State Space and Hidden Markov Models 331
8.1 Linear State Space Models and the Kalman Filter 332
8.1.1 Linear State Space Models 332
8.1.2 Statistical Inference 337
Linear Kalman Filtering and Smoothing 338
Kalman Filtering and Smoothing as Posterior Mode
Estimation* 340
Unknown Hyperparameters 342
EM Algorithm for Estimating Hyperparameters* .... 343
8.2 Non Normal and Nonlinear State Space Models 345
8.2.1 Dynamic Generalized Linear Models 345
Categorical Time Series 347
8.2.2 Nonlinear and Nonexponential Family Models* 349
8.3 Non Normal Filtering and Smoothing 350
8.3.1 Posterior Mode Estimation 351
Generalized Extended Kalman Filter and Smoother* . 352
Gauss Newton and Fisher Scoring Filtering and
Smoothing* 354
Estimation of Hyperparameters* 356
Some Applications 356
8.3.2 Markov Chain Monte Carlo and Integration based
Approaches 361
MCMC Inference 362
Contents xv
Integration based Approaches 365
8.4 Longitudinal Data 369
8.4.1 State Space Modelling of Longitudinal Data 369
8.4.2 Inference For Dynamic Generalized Linear
Mixed Models 372
8.5 Spatial and Spatio temporal Data 376
8.6 Notes and Further Reading 383
9. Survival Models 385
9.1 Models for Continuous Time 385
9.1.1 Basic Models 385
Exponential Distribution 386
Weibull Distribution 387
Piecewise Exponential Model 388
9.1.2 Parametric Regression Models 388
Location Scale Models for log T 388
Proportional Hazards Models 389
Linear Transformation Models and Binary
Regression Models 390
9.1.3 Censoring 391
Random Censoring 391
Type I Censoring 392
9.1.4 Estimation 393
Exponential Model 394
Weibull Model 394
Piecewise Exponential Model 395
9.2 Models for Discrete Time 396
9.2.1 Life Table Estimates 397
9.2.2 Parametric Regression Models 400
The Grouped Proportional Hazards Model 400
A Generalized Version: The Model of Aranda Ordaz . 402
The Logistic Model 403
Sequential Model and Parameterization of the
Baseline Hazard 403
9.2.3 Maximum Likelihood Estimation 404
9.2.4 Time varying Covariates 408
Internal Covariates* 411
Maximum Likelihood Estimation* 412
9.3 Discrete Models for Multiple Modes of Failure 414
9.3.1 Basic Models 414
9.3.2 Maximum Likelihood Estimation 417
9.4 Smoothing in Discrete Survival Analysis 420
9.4.1 Smoothing Life Table Estimates 420
9.4.2 Smoothing with Covariates 422
9.4.3 Dynamic Discrete Time Survival Models 423
xvi Contents
Posterior Mode Smoothing 423
Fully Bayesian Inference via MCMC 425
9.5 Remarks and Further Reading 429
A 433
A.I Exponential Families and Generalized Linear Models 433
A.2 Basic Ideas for Asymptotics 437
A.3 EM Algorithm 442
A.4 Numerical Integration 443
A.5 Monte Carlo Methods 449
B. Software for Fitting Generalized Linear Models
and Extensions 455
Bibliography 467
Author Index 505
Subject Index 512
|
| any_adam_object | 1 |
| author | Fahrmeir, Ludwig 1945- Tutz, Gerhard 1950- |
| author_GND | (DE-588)120635682 (DE-588)172422973 |
| author_facet | Fahrmeir, Ludwig 1945- Tutz, Gerhard 1950- |
| author_role | aut aut |
| author_sort | Fahrmeir, Ludwig 1945- |
| author_variant | l f lf g t gt |
| building | Verbundindex |
| bvnumber | BV014069030 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278.F34 2001 |
| callnumber-search | QA278.F34 2001 |
| callnumber-sort | QA 3278 F34 42001 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CM 4100 QH 234 SK 830 SK 840 |
| ctrlnum | (OCoLC)248546775 (DE-599)BVBBV014069030 |
| dewey-full | 519.538 519.5/3821 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.538 519.5/38 21 |
| dewey-search | 519.538 519.5/38 21 |
| dewey-sort | 3519.538 |
| dewey-tens | 510 - Mathematics |
| discipline | Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV014069030 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:57:05Z |
| institution | BVB |
| isbn | 0387951873 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009635597 |
| oclc_num | 248546775 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-739 DE-824 DE-945 DE-91G DE-BY-TUM DE-703 DE-M347 DE-861 DE-29T DE-521 DE-83 DE-11 DE-M382 DE-355 DE-BY-UBR |
| owner_facet | DE-19 DE-BY-UBM DE-739 DE-824 DE-945 DE-91G DE-BY-TUM DE-703 DE-M347 DE-861 DE-29T DE-521 DE-83 DE-11 DE-M382 DE-355 DE-BY-UBR |
| physical | XXVI, 517 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Fahrmeir, Ludwig 1945- Verfasser (DE-588)120635682 aut Multivariate statistical modelling based on generalized linear models Ludwig Fahrmeir ; Gerhard Tutz 2. ed. New York u.a. Springer 2001 XXVI, 517 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 467 - 504 Analisi multivariata sbt Modelli lineari (statistica) sbt Multivariate Daten - Verallgemeinertes lineares Modell Statistica - metodi sbt Multivariate analysis Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd rswk-swf Multivariate Daten (DE-588)4195680-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf Multivariate Daten (DE-588)4195680-1 s Verallgemeinertes lineares Modell (DE-588)4124382-1 s DE-604 Multivariate Analyse (DE-588)4040708-1 s Lineares Modell (DE-588)4134827-8 s 1\p DE-604 Tutz, Gerhard 1950- Verfasser (DE-588)172422973 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009635597&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 |
| spellingShingle | Fahrmeir, Ludwig 1945- Tutz, Gerhard 1950- Multivariate statistical modelling based on generalized linear models Analisi multivariata sbt Modelli lineari (statistica) sbt Multivariate Daten - Verallgemeinertes lineares Modell Statistica - metodi sbt Multivariate analysis Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd Multivariate Daten (DE-588)4195680-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd |
| subject_GND | (DE-588)4134827-8 (DE-588)4195680-1 (DE-588)4040708-1 (DE-588)4124382-1 |
| title | Multivariate statistical modelling based on generalized linear models |
| title_auth | Multivariate statistical modelling based on generalized linear models |
| title_exact_search | Multivariate statistical modelling based on generalized linear models |
| title_full | Multivariate statistical modelling based on generalized linear models Ludwig Fahrmeir ; Gerhard Tutz |
| title_fullStr | Multivariate statistical modelling based on generalized linear models Ludwig Fahrmeir ; Gerhard Tutz |
| title_full_unstemmed | Multivariate statistical modelling based on generalized linear models Ludwig Fahrmeir ; Gerhard Tutz |
| title_short | Multivariate statistical modelling based on generalized linear models |
| title_sort | multivariate statistical modelling based on generalized linear models |
| topic | Analisi multivariata sbt Modelli lineari (statistica) sbt Multivariate Daten - Verallgemeinertes lineares Modell Statistica - metodi sbt Multivariate analysis Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd Multivariate Daten (DE-588)4195680-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd |
| topic_facet | Analisi multivariata Modelli lineari (statistica) Multivariate Daten - Verallgemeinertes lineares Modell Statistica - metodi Multivariate analysis Linear models (Statistics) Lineares Modell Multivariate Daten Multivariate Analyse Verallgemeinertes lineares Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009635597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fahrmeirludwig multivariatestatisticalmodellingbasedongeneralizedlinearmodels AT tutzgerhard multivariatestatisticalmodellingbasedongeneralizedlinearmodels |