Regression: models, methods and applications
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| Main Authors: | , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
[2013]
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Aus dem Vorwort: "This book is partly based on a preceding German version that has been translated and considerably extended." |
| Physical Description: | xiv, 698 Seiten Illustrationen, Diagramme |
| ISBN: | 9783642343322 9783642433764 |
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MARC
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| 245 | 1 | 0 | |a Regression |b models, methods and applications |c Ludwig Fahrmeir, Thomas Kneib, Stefan Lang, Brian Marx |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c [2013] | |
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Record in the Search Index
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IMAGE 1
1 INTRODUCTION 1
1.1 EXAMPLES O F APPLICATIONS 4
1.2 FIRST STEPS 11
1.2.1 UNIVARIATE DISTRIBUTIONS OF THE VARIABLES 11
1.2.2 GRAPHICAL ASSOCIATION ANALYSIS 13
1.3 NOTATIONAL REMARKS 19
2 REGRESSION MODELS 21
2.1 INTRODUCTION 21
2.2 LINEAR REGRESSION MODELS 22
2.2.1 SIMPLE LINEAR REGRESSION MODEL 22
2.2.2 MULTIPLE LINEAR REGRESSION 26
2.3 REGRESSION WITH BINARY RESPONSE VARIABLES: THE LOGIT MODEL 33 2.4
MIXED MODELS 38
2.5 SIMPLE NONPARAMETRIC REGRESSION 44
2.6 ADDITIVE MODELS 49
2.7 GENERALIZED ADDITIVE MODELS 52
2.8 GEOADDITIVE REGRESSION 55
2.9 BEYOND MEAN REGRESSION 61
2.9.1 REGRESSION MODELS FOR LOCATION, SCALE, AND SHAPE 62
2.9.2 QUANTILE REGRESSION 66
2.10 MODELS IN A NUTSHELL 68
2.10.1 LINEAR MODELS (LMS, CHAPS. 3 AND 4) 68
2.10.2 LOGIT MODEL (CHAP. 5) 68
2.10.3 POISSON REGRESSION (CHAP. 5) 68
2.10.4 GENERALIZED LINEAR MODELS (GLMS, CHAPS. 5 AND 6) 69 2.10.5 LINEAR
MIXED MODELS (LMMS, CHAP. 7) 69
2.10.6 ADDITIVE MODELS AND EXTENSIONS (AMS, CHAPS. 8 AND 9) 70
2.10.7 GENERALIZED ADDITIVE (MIXED) MODELS (GA(M)MS, CHAP. 9) 7 0
2.10.8 STRUCTURED ADDITIVE REGRESSION (STAR, CHAP. 9) 71
2.10.9 QUANTILE REGRESSION (CHAP. 10) 71
IX
HTTP://D-NB.INFO/1026184177
IMAGE 2
TABLE O F CONTENTS
3 THE CLASSICAL LINEAR MODEL 73
3.1 MODEL DEFINITION 73
3.1.1 MODEL PARAMETERS, ESTIMATION, AND RESIDUALS 77
3.1.2 DISCUSSION OF MODEL ASSUMPTIONS 78
3.1.3 MODELING THE EFFECTS OF COVARIATES 86
3.2 PARAMETER ESTIMATION 104
3.2.1 ESTIMATION O F REGRESSION COEFFICIENTS 104
3.2.2 ESTIMATION O F THE ERROR VARIANCE 108
3.2.3 PROPERTIES O F THE ESTIMATORS 110
3.3 HYPOTHESIS TESTING AND CONFIDENCE INTERVALS 125
3.3.1 EXACT F-TEST 128
3.3.2 CONFIDENCE REGIONS AND PREDICTION INTERVALS 136
3.4 MODEL CHOICE AND VARIABLE SELECTION 139
3.4.1 BIAS, VARIANCE AND PREDICTION QUALITY 142
3.4.2 MODEL CHOICE CRITERIA 146
3.4.3 PRACTICAL USE O F MODEL CHOICE CRITERIA 150
3.4.4 MODEL DIAGNOSIS 155
3.5 BIBLIOGRAPHIC NOTES AND PROOFS 168
3.5.1 BIBLIOGRAPHIC NOTES 168
3.5.2 PROOFS 168
4 EXTENSIONS O F THE CLASSICAL LINEAR MODEL 177
4.1 THE GENERAL LINEAR MODEL 177
4.1.1 MODEL DEFINITION 177
4.1.2 WEIGHTED LEAST SQUARES 178
4.1.3 HETEROSCEDASTIC ERRORS 182
4.1.4 AUTOCORRELATED ERRORS 191
4.2 REGULARIZATION TECHNIQUES 201
4.2.1 STATISTICAL REGULARIZATION 202
4.2.2 RIDGE REGRESSION 203
4.2.3 LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR 208
4.2.4 GEOMETRIC PROPERTIES O F REGULARIZED ESTIMATES 211
4.2.5 PARTIAL REGULARIZATION 216
4.3 BOOSTING LINEAR REGRESSION MODELS 217
4.3.1 BASIC PRINCIPLES 217
4.3.2 COMPONENTWISE BOOSTING 218
4.3.3 GENERIC COMPONENTWISE BOOSTING 222
4.4 BAYESIAN LINEAR MODELS 225
4.4.1 STANDARD CONJUGATE ANALYSIS 227
4.4.2 REGULARIZATION PRIORS 237
4.4.3 CLASSICAL BAYESIAN MODEL CHOICE (AND BEYOND) 243
4.4.4 SPIKE AND SLAB PRIORS 253
4.5 BIBLIOGRAPHIC NOTES AND PROOFS 257
4.5.1 BIBLIOGRAPHIC NOTES 257
4.5.2 PROOFS 258
IMAGE 3
TABLE O F CONTENTS XI
5 GENERALIZED LINEAR MODELS 269
5.1 BINARY REGRESSION 270
5.1.1 BINARY REGRESSION MODELS 270
5.1.2 MAXIMUM LIKELIHOOD ESTIMATION 279
5.1.3 TESTING LINEAR HYPOTHESES 285
5.1.4 CRITERIA FOR MODEL FIT AND MODEL CHOICE 287
5.1.5 ESTIMATION OF THE OVERDISPERSION PARAMETER 292
5.2 COUNT DATA REGRESSION.! 293
5.2.1 MODELS FOR COUNT DATA 293
5.2.2 ESTIMATION AND TESTING: LIKELIHOOD INFERENCE 295
5.2.3 CRITERIA FOR MODEL FIT AND MODEL CHOICE 297
5.2.4 ESTIMATION O F THE OVERDISPERSION PARAMETER 297
5.3 MODELS FOR NONNEGATIVE CONTINUOUS RESPONSE VARIABLES 298
5.4 GENERALIZED LINEAR MODELS 301
5.4.1 GENERAL MODEL DEFINITION 301
5.4.2 LIKELIHOOD INFERENCE 306
5.5 QUASI-LIKELIHOOD MODELS 309
5.6 BAYESIAN GENERALIZED LINEAR MODELS 311
5.6.1 POSTERIOR MODE ESTIMATION 313
5.6.2 FULLY BAYESIAN INFERENCE VIA M C M C SIMULATION TECHNIQUES 314
5.6.3 MCMC-BASED INFERENCE USING DATA AUGMENTATION 316 5.7 BOOSTING
GENERALIZED LINEAR MODELS 319
5.8 BIBLIOGRAPHIC NOTES AND PROOFS 320
5.8.1 BIBLIOGRAPHIC NOTES 320
5.8.2 PROOFS 321
6 CATEGORICAL REGRESSION MODELS 325
6.1 INTRODUCTION 325
6.2 MODELS FOR UNORDERED CATEGORIES 329
6.3 ORDINAL MODELS 334
6.3.1 THE CUMULATIVE MODEL 334
6.3.2 THE SEQUENTIAL MODEL 337
6.4 ESTIMATION AND TESTING: LIKELIHOOD INFERENCE 343
6.5 BIBLIOGRAPHIC NOTES 347
7 MIXED MODELS 349
7.1 LINEAR MIXED MODELS FOR LONGITUDINAL AND CLUSTERED DATA 350
7.1.1 RANDOM INTERCEPT MODELS 350
7.1.2 RANDOM COEFFICIENT OR SLOPE MODELS 357
7.1.3 GENERAL MODEL DEFINITION AND MATRIX NOTATION 361
7.1.4 CONDITIONAL AND MARGINAL FORMULATION 365
7.1.5 STOCHASTIC COVARIATES 366
7.2 GENERAL LINEAR MIXED MODELS 368
IMAGE 4
TABLE O F CONTENTS
7.3 LIKELIHOOD INFERENCE IN LMMS 371
7.3.1 KNOWN VARIANCE-COVARIANCE PARAMETERS 371
7.3.2 UNKNOWN VARIANCE-COVARIANCE PARAMETERS 372
7.3.3 VARIABILITY O F FIXED AND RANDOM EFFECTS ESTIMATORS 378 7.3.4
TESTING HYPOTHESES 380
7.4 BAYESIAN LINEAR MIXED MODELS 383
7.4.1 ESTIMATION FOR KNOWN COVARIANCE STRUCTURE 384
7.4.2 ESTIMATION FOR UNKNOWN COVARIANCE STRUCTURE 385
7.5 GENERALIZED LINEAR MIXED MODELS 389
7.5.1 GLMMS FOR LONGITUDINAL AND CLUSTERED DATA 389
7.5.2 CONDITIONAL AND MARGINAL MODELS 392
7.5.3 GLMMS IN GENERAL FORM 394
7.6 LIKELIHOOD AND BAYESIAN INFERENCE IN GLMMS 394
7.6.1 PENALIZED LIKELIHOOD AND EMPIRICAL BAYES ESTIMATION. 395 7.6.2
FULLY BAYESIAN INFERENCE USING MCMC 397
7.7 PRACTICAL APPLICATION OF MIXED MODELS 401
7.7.1 GENERAL GUIDELINES AND RECOMMENDATIONS 401
7.7.2 CASE STUDY ON SALES O F ORANGE JUICE 403
7.8 BIBLIOGRAPHIC NOTES AND PROOFS 409
7.8.1 BIBLIOGRAPHIC NOTES 409
7.8.2 PROOFS 410
8 NONPARAMETRIC REGRESSION 413
8.1 UNIVARIATE SMOOTHING 415
8.1.1 POLYNOMIAL SPLINES 415
8.1.2 PENALIZED SPLINES (P-SPLINES) 431
8.1.3 GENERAL PENALIZATION APPROACHES 446
8.1.4 SMOOTHING SPLINES 448
8.1.5 RANDOM WALKS 452
8.1.6 KRIGING 453
8.1.7 LOCAL SMOOTHING PROCEDURES 460
8.1.8 GENERAL SCATTER PLOT SMOOTHING 468
8.1.9 CHOOSING THE SMOOTHING PARAMETER 478
8.1.10 ADAPTIVE SMOOTHING APPROACHES 490
8.2 BIVARIATE AND SPATIAL SMOOTHING 500
8.2.1 TENSOR PRODUCT P-SPLINES 503
8.2.2 RADIAL BASIS FUNCTIONS AND THIN PLATE SPLINES 512
8.2.3 KRIGING: SPATIAL SMOOTHING WITH CONTINUOUS LOCATION VARIABLES 515
8.2.4 MARKOV RANDOM FIELDS 521
8.2.5 SUMMARY O F ROUGHNESS PENALTY APPROACHES 527
8.2.6 LOCAL AND ADAPTIVE SMOOTHING 529
8.3 HIGHER-DIMENSIONAL SMOOTHING 530
8.4 BIBLIOGRAPHIC NOTES 531
IMAGE 5
TABLE O F CONTENTS XIII
9 STRUCTURED ADDITIVE REGRESSION 535
9.1 ADDITIVE MODELS 536
9.2 GEOADDITIVE REGRESSION 540
9.3 MODELS WITH INTERACTIONS 543
9.3.1 MODELS WITH VARYING COEFFICIENT TERMS 544
9.3.2 INTERACTIONS BETWEEN TWO CONTINUOUS COVARIATES 547
9.4 MODELS WITH RANDOM EFFECTS 549
9.5 STRUCTURED ADDITIVE REGRESSION 553
9.6 INFERENCE 561
9.6.1 PENALIZED LEAST SQUARES OR LIKELIHOOD ESTIMATION 561
9.6.2 INFERENCE BASED ON MIXED MODEL REPRESENTATION 566
9.6.3 BAYESIAN INFERENCE BASED ON MCMC 568
9.7 BOOSTING STAR MODELS 573
9.8 CASE STUDY: MALNUTRITION IN ZAMBIA 576
9.8.1 GENERAL GUIDELINES 576
9.8.2 DESCRIPTIVE ANALYSIS 580
9.8.3 MODELING VARIANTS 583
9.8.4 ESTIMATION RESULTS AND MODEL EVALUATION 584
9.8.5 AUTOMATIC FUNCTION SELECTION 589
9.9 BIBLIOGRAPHIC NOTES 594
10 QUANTILE REGRESSION 597
10.1 QUANTILES 599
10.2 LINEAR QUANTILE REGRESSION 601
10.2.1 CLASSICAL QUANTILE REGRESSION 601
10.2.2 BAYESIAN QUANTILE REGRESSION 609
10.3 ADDITIVE QUANTILE REGRESSION 612
10.4 BIBLIOGRAPHIC NOTES AND PROOFS 616
10.4.1 BIBLIOGRAPHIC NOTES 616
10.4.2 PROOFS 618
A MATRIX ALGEBRA 621
A.L DEFINITION AND ELEMENTARY MATRIX OPERATIONS 621
A.2 RANK O F A MATRIX 626
A.3 BLOCK MATRICES AND THE MATRIX INVERSION LEMMA 628
A.4 DETERMINANT AND TRACE O F A MATRIX 629
A.5 GENERALIZED INVERSE 631
A.6 EIGENVALUES AND EIGENVECTORS 631
A.7 QUADRATIC FORMS 633
A.8 DIFFERENTIATION O F MATRIX FUNCTIONS 635
B PROBABILITY CALCULUS AND STATISTICAL INFERENCE 639
B.L SOME UNIVARIATE DISTRIBUTIONS 639
B.2 RANDOM VECTORS 645
IMAGE 6
XIV TABLE O F CONTENTS
B.3 MULTIVARIATE NORMAL DISTRIBUTION 648
B.3.1 DEFINITION AND PROPERTIES 648
B.3.2 THE SINGULAR MULTIVARIATE NORMAL DISTRIBUTION 650
B.3.3 DISTRIBUTIONS O F QUADRATIC FORMS 651
B.3.4 MULTIVARIATE T-DISTRIBUTION 651
B.3.5 NORMAL-INVERSE GAMMA DISTRIBUTION 652
B.4 LIKELIHOOD INFERENCE 653
B.4.1 MAXIMUM LIKELIHOOD ESTIMATION 653
B.4.2 NUMERICAL COMPUTATION OF THE MLE 660
B.4.3 ASYMPTOTIC PROPERTIES OF THE M L E 662
B.4.4 LIKELIHOOD-BASED TESTS O F LINEAR HYPOTHESES 662
B.4.5 MODEL CHOICE 664
B.5 BAYESIAN INFERENCE 665
B.5.1 BASIC CONCEPTS O F BAYESIAN INFERENCE 665
B.5.2 POINT AND INTERVAL ESTIMATION 669
B.5.3 MCMC METHODS 670
B.5.4 MODEL SELECTION 676
B.5.5 MODEL AVERAGING 679
BIBLIOGRAPHY 681
INDEX 691 |
| any_adam_object | 1 |
| author | Fahrmeir, Ludwig 1945- Kneib, Thomas 1976- Lang, Stefan 1970- Marx, Brian D. 1960- |
| author_GND | (DE-588)120635682 (DE-588)131555332 (DE-588)123447496 (DE-588)1136402950 |
| author_facet | Fahrmeir, Ludwig 1945- Kneib, Thomas 1976- Lang, Stefan 1970- Marx, Brian D. 1960- |
| author_role | aut aut aut aut |
| author_sort | Fahrmeir, Ludwig 1945- |
| author_variant | l f lf t k tk s l sl b d m bd bdm |
| building | Verbundindex |
| bvnumber | BV040801776 |
| classification_rvk | CM 3000 CM 4000 QH 234 SK 840 |
| classification_tum | MAT 628f |
| ctrlnum | (OCoLC)854684994 (DE-599)DNB1026184177 |
| dewey-full | 519.536 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.536 |
| dewey-search | 519.536 |
| dewey-sort | 3519.536 |
| dewey-tens | 510 - Mathematics |
| discipline | Psychologie Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV040801776 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:36:18Z |
| institution | BVB |
| isbn | 9783642343322 9783642433764 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025781868 |
| oclc_num | 854684994 |
| open_access_boolean | |
| owner | DE-11 DE-521 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-945 DE-29T DE-473 DE-BY-UBG DE-188 DE-20 DE-384 DE-91G DE-BY-TUM DE-B768 DE-355 DE-BY-UBR DE-898 DE-BY-UBR DE-634 DE-Grf2 |
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| physical | xiv, 698 Seiten Illustrationen, Diagramme |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| spelling | Fahrmeir, Ludwig 1945- Verfasser (DE-588)120635682 aut Regression Regression models, methods and applications Ludwig Fahrmeir, Thomas Kneib, Stefan Lang, Brian Marx Berlin ; Heidelberg Springer [2013] © 2013 xiv, 698 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Aus dem Vorwort: "This book is partly based on a preceding German version that has been translated and considerably extended." Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s DE-604 Kneib, Thomas 1976- Verfasser (DE-588)131555332 aut Lang, Stefan 1970- Verfasser (DE-588)123447496 aut Marx, Brian D. 1960- Verfasser (DE-588)1136402950 aut Erscheint auch als Online-Ausgabe 978-3-642-34333-9 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4126684&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025781868&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fahrmeir, Ludwig 1945- Kneib, Thomas 1976- Lang, Stefan 1970- Marx, Brian D. 1960- Regression models, methods and applications Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4129903-6 |
| title | Regression models, methods and applications |
| title_alt | Regression |
| title_auth | Regression models, methods and applications |
| title_exact_search | Regression models, methods and applications |
| title_full | Regression models, methods and applications Ludwig Fahrmeir, Thomas Kneib, Stefan Lang, Brian Marx |
| title_fullStr | Regression models, methods and applications Ludwig Fahrmeir, Thomas Kneib, Stefan Lang, Brian Marx |
| title_full_unstemmed | Regression models, methods and applications Ludwig Fahrmeir, Thomas Kneib, Stefan Lang, Brian Marx |
| title_short | Regression |
| title_sort | regression models methods and applications |
| title_sub | models, methods and applications |
| topic | Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Regressionsanalyse |
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