Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
2002
|
| Ausgabe: | Corr. 2. print. |
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 527 - 558 |
| Beschreibung: | XXII, 568 S. graph. Darst. : 25 cm |
| ISBN: | 0387952322 |
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| 250 | |a Corr. 2. print. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 2002 | |
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Datensatz im Suchindex
| _version_ | 1804129459586990080 |
|---|---|
| adam_text | FRANK E. HARREIL, JR. REGRESSION MODELING STRATEGIES WITH APPLICATIONS
TO LINEAR MODELS, LOGISTIC REGRESSION, AND SURVIVAL ANALYSIS WITH 141
FIGURES SPRINGER CONTENTS PREFACE VII TYPOGRAPHICAL CONVENTIONS XXIII 1
INTRODUCTION 1 1.1 HYPOTHESIS TESTING, ESTIMATION, AND PREDICTION 1 1.2
EXAMPLES OF USES OF PREDICTIVE MULTIVARIABLE MODELING 3 1.3 PLANNING FOR
MODELING 4 1.3.1 EMPHASIZING CONTINUOUS VARIABLES 6 1.4 CHOICE OF THE
MODEL 6 1.5 FURTHER READING 8 2 GENERAL ASPECTS OF FITTING REGRESSION
MODELS 11 2.1 NOTATION FOR MULTIVARIABLE REGRESSION MODELS 11 2.2 MODEL
FORMULATIONS 12 2.3 INTERPRETING MODEL PARAMETERS 13 2.3.1 NOMINAL
PREDICTORS 14 2.3.2 INTERACTIONS 14 XIV CONTENTS 2.3.3 EXAMPLE:
INFERENCE FOR A SIMPLE MODEL 15 2.4 RELAXING LINEARITY ASSUMPTION FOR
CONTINUOUS PREDICTORS 16 2.4.1 SIMPLE NONLINEAR TERMS 16 2.4.2 SPLINES
FOR ESTIMATING SHAPE OF REGRESSION FUNCTION AND DE- TERMINING PREDICTOR
TRANSFORMATIONS 18 2.4.3 CUBIC SPLINE FUNCTIONS 19 2.4.4 RESTRICTED
CUBIC SPLINES 20 2.4.5 CHOOSING NUMBER AND POSITION OF KNOTS 23 2.4.6
NONPARAMETRIC REGRESSION 24 2.4.7 ADVANTAGES OF REGRESSION SPLINES OVER
OTHER METHODS . . . . 26 2.5 RECURSIVE PARTITIONING: TREE-BASED MODELS
26 2.6 MULTIPLE DEGREE OF FREEDOM TESTS OF ASSOCIATION 27 2.7 ASSESSMENT
OF MODEL FIT 29 2.7.1 REGRESSION ASSUMPTIONS 29 2.7.2 MODELING AND
TESTING COMPLEX INTERACTIONS 32 2.7.3 FITTING ORDINAL PREDICTORS 34
2.7.4 DISTRIBUTIONAL ASSUMPTIONS 35 2.8 FURTHER READING 36 2.9 PROBLEMS
37 3 MISSING DATA 41 3.1 TYPES OF MISSING DATA 41 3.2 PRELUDE TO
MODELING 42 3.3 MISSING VALUES FOR DIFFERENT TYPES OF RESPONSE VARIABLES
43 3.4 PROBLEMS WITH SIMPLE ALTERNATIVES TO IMPUTATION 43 3.5 STRATEGIES
FOR DEVELOPING IMPUTATION ALGORITHMS 44 3.6 SINGLE CONDITIONAL MEAN
IMPUTATION 47 3.7 MULTIPLE IMPUTATION 47 3.8 SUMMARY AND ROUGH
GUIDELINES 48 3.9 FURTHER READING 50 3.10 PROBLEMS . . 51 4
MULTIVARIABLE MODELING STRATEGIES 53 4.1 PRESPECIFICATION OF PREDICTOR
COMPLEXITY WITHOUT LATER SIMPLIFICATION 53 CONTENTS XV 4.2 CHECKING
ASSUMPTIONS OF MULTIPLE PREDICTORS SIMULTANEOUSLY ... 56 4.3 VARIABLE
SELECTION 56 4.4 OVERFITTING AND LIMITS ON NUMBER OF PREDICTORS 60 4.5
SHRINKAGE 61 4.6 COLLINEARITY 64 4.7 DATA REDUCTION 66 4.7.1 VARIABLE
CLUSTERING 66 4.7.2 TRANSFORMATION AND SCALING VARIABLES WITHOUT USING Y
. . . 67 4.7.3 SIMULTANEOUS TRANSFORMATION AND IMPUTATION 69 4.7.4
SIMPLE SCORING OF VARIABLE CLUSTERS 70 4.7.5 SIMPLIFYING CLUSTER SCORES
72 4.7.6 HOW MUCH DATA REDUCTION IS NECESSARY? 73 4.8 OVERLY INFLUENTIAL
OBSERVATIONS 74 4.9 COMPARING TWO MODELS 77 4.10 SUMMARY: POSSIBLE
MODELING STRATEGIES 79 4.10.1 DEVELOPING PREDICTIVE MODELS 79 4.10.2
DEVELOPING MODELS FOR EFFECT ESTIMATION 82 4.10.3 DEVELOPING MODELS FOR
HYPOTHESIS TESTING 83 4.11 FURTHER READING 84 5 RESAMPLING, VALIDATING,
DESCRIBING, AND SIMPLIFYING THE MODEL 87 5.1 THE BOOTSTRAP 87 5.2 MODEL
VALIDATION 90 5.2.1 INTRODUCTION 90 5.2.2 WHICH QUANTITIES SHOULD BE
USED IN VALIDATION? 91 5.2.3 DATA-SPLITTING 91 5.2.4 IMPROVEMENTS ON
DATA-SPLITTING: RESAMPLING 93 5.2.5 VALIDATION USING THE BOOTSTRAP 94
5.3 DESCRIBING THE FITTED MODEL 97 5.4 SIMPLIFYING THE FINAL MODEL BY
APPROXIMATING IT 98 5.4.1 DIFFICULTIES USING FUELL MODELS 98 5.4.2
APPROXIMATING THE FUELL MODEL 99 5.5 FURTHER READING 101 6 S-PLUS
SOFTWARE 105 XVI CONTENTS 6.1 THE S MODELING LANGUAGE 106 6.2
USER-CONTRIBUTED FUNCTIONS 107 6.3 THE DESIGN LIBRARY 108 6.4 OTHER
FUNCTIONS 119 6.5 FURTHER READING 120 7 CASE STUDY IN LEAST SQUARES
FITTING AND INTERPRETATION OF A LINEAR MODEL 121 7.1 DESCRIPTIVE
STATISTICS 122 7.2 SPENDING DEGREES OF FREEDOM/SPECIFYING PREDICTOR
COMPLEXITY . . 127 7.3 FITTING THE MODEL USING LEAST SQUARES 128 7.4
CHECKING DISTRIBUTIONAL ASSUMPTIONS 131 7.5 CHECKING GOODNESS OF FIT 135
7.6 OVERLY INFLUENTIAL OBSERVATIONS 135 7.7 TEST STATISTICS AND PARTIAL
R 2 136 7.8 INTERPRETING THE MODEL 137 7.9 PROBLEMS 142 8 CASE STUDY IN
IMPUTATION AND DATA REDUCTION 147 8.1 DATA 147 8.2 HOW MANY PARAMETERS
CAN BE ESTIMATED? 150 8.3 VARIABLE CLUSTERING 151 8.4 SINGLE IMPUTATION
USING CONSTANTS OR RECURSIVE PARTITIONING . . . 154 8.5 TRANSFORMATION
AND SINGLE IMPUTATION USING TRANSCAN 157 8.6 DATA REDUCTION USING
PRINCIPAL COMPONENTS 160 8.7 DETAILED EXAMINATION OF INDIVIDUAL
TRANSFORMATIONS 168 8.8 EXAMINATION OF VARIABLE CLUSTERS ON TRANSFORMED
VARIABLES . . . . 169 8.9 TRANSFORMATION USING NONPARAMETRIC SMOOTHERS
170 8.10 MULTIPLE IMPUTATION 172 8.11 FURTHER READING 175 8.12 PROBLEMS
176 9 OVERVIEW OF MAXIMUM LIKELIHOOD ESTIMATION 179 9.1 GENERAL
NOTIONS*SIMPLE CASES 179 9.2 HYPOTHESIS TESTS 183 CONTENTS XVII 9.2.1
LIKELIHOOD RATIO TEST 183 9.2.2 WALD TEST 184 9.2.3 SCORE TEST 184 9.2.4
NORMAL DISTRIBUTION*ONE SAMPLE 185 9.3 GENERAL CASE 186 9.3.1 GLOBAL
TEST STATISTICS 187 9.3.2 TESTING A SUBSET OF THE PARAMETERS 187 9.3.3
WHICH TEST STATISTICS TO USE WHEN 189 9.3.4 EXAMPLE: BINOMIAL*COMPARING
TWO PROPORTIONS 190 9.4 ITERATIVE ML ESTIMATION 192 9.5 ROBUST
ESTIMATION OF THE COVARIANCE MATRIX 193 9.6 WALD, SCORE, AND
LIKELIHOOD-BASED CONFIDENCE INTERVALS 194 9.7 BOOTSTRAP CONFIDENCE
REGIONS 195 9.8 FURTHER USE OF THE LOG LIKELIHOOD 202 9.8.1 RATING TWO
MODELS, PENALIZING FOR COMPLEXITY 202 9.8.2 TESTING WHETHER ONE MODEL IS
BETTER THAN ANOTHER . . . . 203 9.8.3 UNITLESS INDEX OF PREDICTIVE
ABILITY 203 9.8.4 UNITLESS INDEX OF ADEQUACY OF A SUBSET OF PREDICTORS .
. . . 205 9.9 WEIGHTED MAXIMUM LIKELIHOOD ESTIMATION 206 9.10 PENALIZED
MAXIMUM LIKELIHOOD ESTIMATION 207 9.11 FURTHER READING 210 9.12 PROBLEMS
212 10 BINARY LOGISTIC REGRESSION 215 10.1 MODEL 215 10.1.1 MODEL
ASSUMPTIONS AND INTERPRETATION OF PARAMETERS . . . . 217 10.1.2 ODDS
RATIO, RISK RATIO, AND RISK DIFFERENCE 220 10.1.3 DETAILED EXAMPLE 221
10.1.4 DESIGN FORMULATIONS 227 10.2 ESTIMATION 228 10.2.1 MAXIMUM
LIKELIHOOD ESTIMATES 228 10.2.2 ESTIMATION OF ODDS RATIOS AND
PROBABILITIES 228 10.3 TEST STATISTICS 229 10.4 RESIDUAIS 230 XVIII
CONTENTS 10.5 ASSESSMENT OF MODEL FIT 230 10.6 COLLINEARITY 244 10.7
OVERLY INFLUENTIAL OBSERVATIONS 245 10.8 QUANTIFYING PREDICTIVE ABILITY
247 10.9 VALIDATING THE FITTED MODEL 249 10.10 DESCRIBING THE FITTED
MODEL 253 10.11 S-PLUS FUNCTIONS 257 10.12 FURTHER READING 264 10.13
PROBLEMS 265 11 LOGISTIC MODEL CASE STUDY 1: PREDICTING CAUSE OF DEATH
269 11.1 PREPARATION FOR MODELING 269 11.2 REGRESSION ON PRINCIPAL
COMPONENTS, CLUSTER SCORES, AND PRETRANS- FORMATIONS 271 11.3 FIT AND
DIAGNOSTICS FOR A FUELL MODEL, AND INTERPRETING PRETRANSFOR- MATIONS 276
11.4 DESCRIBING RESULTS USING A REDUCED MODEL 285 11.5 APPROXIMATING THE
FUELL MODEL USING RECURSIVE PARTITIONING . . . . 291 11.6 VALIDATING THE
REDUCED MODEL 294 12 LOGISTIC MODEL CASE STUDY 2: SURVIVAL OF TITANIC
PASSENGERS 299 12.1 DESCRIPTIVE STATISTICS 300 12.2 EXPLORING TRENDS
WITH NONPARAMETRIC REGRESSION 305 12.3 BINARY LOGISTIC MODEL WITH
CASEWISE DELETION OF MISSING VALUES . 305 12.4 EXAMINING MISSING DATA
PATTERNS 312 12.5 SINGLE CONDITIONAL MEAN IMPUTATION 316 12.6 MULTIPLE
IMPUTATION 320 12.7 SUMMARIZING THE FITTED MODEL 322 12.8 PROBLEMS 326
13 ORDINAL LOGISTIC REGRESSION 331 13.1 BACKGROUND 331 13.2 ORDINALITY
ASSUMPTION 332 13.3 PROPORTIONAL ODDS MODEL 333 13.3.1 MODEL 333 13.3.2
ASSUMPTIONS AND INTERPRETATION OF PARAMETERS 333 CONTENTS XIX 13.3.3
ESTIMATION 334 13.3.4 RESIDUAIS 334 13.3.5 ASSESSMENT OF MODEL FIT 335
13.3.6 QUANTIFYING PREDICTIVE ABILITY 335 13.3.7 VALIDATING THE FITTED
MODEL 337 13.3.8 S-PLUS FUNCTIONS 337 13.4 CONTINUATION RATIO MODEL 338
13.4.1 MODEL 338 13.4.2 ASSUMPTIONS AND INTERPRETATION OF PARAMETERS 338
13.4.3 ESTIMATION 339 13.4.4 RESIDUAIS 339 13.4.5 ASSESSMENT OF MODEL
FIT 339 13.4.6 EXTENDED CR MODEL 339 13.4.7 ROLE OF PENALIZATION IN
EXTENDED CR MODEL 340 13.4.8 VALIDATING THE FITTED MODEL 341 13.4.9
S-PLUS FUNCTIONS 341 13.5 FURTHER READING 342 13.6 PROBLEMS 342 14 CASE
STUDY IN ORDINAL REGRESSION, DATA REDUCTION, AND PENALIZA- TION 345 14.1
RESPONSE VARIABLE 346 14.2 VARIABLE CLUSTERING 347 14.3 DEVELOPING
CLUSTER SUMMARY SCORES 349 14.4 ASSESSING ORDINALITY OF Y FOR EACH X,
AND UNADJUSTED CHECKING OF PO AND CR ASSUMPTIONS 351 14.5 A TENTATIVE
FUELL PROPORTIONAL ODDS MODEL 352 14.6 RESIDUAL PLOTS 355 14.7 GRAPHICAL
ASSESSMENT OF FIT OF CR MODEL 357 14.8 EXTENDED CONTINUATION RATIO MODEL
357 14.9 PENALIZED ESTIMATION 359 14.10 USING APPROXIMATIONS TO SIMPLIFY
THE MODEL 364 14.11 VALIDATING THE MODEL 367 14.12 SUMMARY 369 14.13
FURTHER READING 371 XX CONTENTS 14.14 PROBLEMS 371 15 MODELS USING
NONPARAMETRIC TRANSFORMATIONS OF X AND Y 375 15.1 BACKGROUND 375 15.2
GENERALIZED ADDITIVE MODELS 376 15.3 NONPARAMETRIC ESTIMATION OF
F-TRANSFORMATION 376 15.4 OBTAINING ESTIMATES ON THE ORIGINAL SCALE 377
15.5 S-PLUS FUNCTIONS 378 15.6 CASE STUDY 379 16 INTRODUCTION TO
SURVIVAL ANALYSIS 389 16.1 BACKGROUND 389 16.2 CENSORING, DELAYED ENTRY,
AND TRUNCATION 391 16.3 NOTATION, SURVIVAL, AND HAZARD FUNCTIONS 392
16.4 HOMOGENEOUS FAILURE TIME DISTRIBUTIONS 398 16.5 NONPARAMETRIC
ESTIMATION OF S AND A 400 16.5.1 KAPLAN-MEIER ESTIMATOR 400 16.5.2
ALTSCHULER-NELSON ESTIMATOR 403 16.6 ANALYSIS OF MULTIPLE ENDPOINTS 404
16.6.1 COMPETING RISKS 404 16.6.2 COMPETING DEPENDENT RISKS 405 16.6.3
STATE TRANSITIONS AND MULTIPLE TYPES OF NONFATAL EVENTS . . 406 16.6.4
JOINT ANALYSIS OF TIME AND SEVERITY OF AN EVENT 407 16.6.5 ANALYSIS OF
MULTIPLE EVENTS 407 16.7 S-PLUS FUNCTIONS 408 16.8 FURTHER READING 410
16.9 PROBLEMS 411 17 PARAMETRIC SURVIVAL MODELS 413 17.1 HOMOGENEOUS
MODELS (NO PREDICTORS) 413 17.1.1 SPECIFIC MODELS 413 17.1.2 ESTIMATION
414 17.1.3 ASSESSMENT OF MODEL FIT 416 17.2 PARAMETRIC PROPORTIONAL
HAZARDS MODELS 417 17.2.1 MODEL 417 CONTENTS XXI 17.2.2 MODEL
ASSUMPTIONS AND INTERPRETATION OF PARAMETERS . . . . 418 17.2.3 HAZARD
RATIO, RISK RATIO, AND RISK DIFFERENCE 419 17.2.4 SPECIFIC MODELS 421
17.2.5 ESTIMATION 422 17.2.6 ASSESSMENT OF MODEL FIT 423 17.3
ACCELERATED FAILURE TIME MODELS 426 17.3.1 MODEL 426 17.3.2 MODEL
ASSUMPTIONS AND INTERPRETATION OF PARAMETERS .... 427 17.3.3 SPECIFIC
MODELS 427 17.3.4 ESTIMATION 428 17.3.5 RESIDUAIS 429 17.3.6 ASSESSMENT
OF MODEL FIT 430 17.3.7 VALIDATING THE FITTED MODEL 434 17.4
BUCKLEY-JAMES REGRESSION MODEL 435 17.5 DESIGN FORMULATIONS 435 17.6
TEST STATISTICS 435 17.7 QUANTIFYING PREDICTIVE ABILITY 436 17.8 S-PLUS
FUNCTIONS 436 17.9 FURTHER READING 441 17.10 PROBLEMS 441 18 CASE STUDY
IN PARAMETRIC SURVIVAL MODELING AND MODEL APPROXI- MATION 443 18.1
DESCRIPTIVE STATISTICS 443 18.2 CHECKING ADEQUACY OF LOG-NORMAL
ACCELERATED FAILURE TIME MODEL 448 18.3 SUMMARIZING THE FITTED MODEL 454
18.4 INTERNAL VALIDATION OF THE FITTED MODEL USING THE BOOTSTRAP . . . .
454 18.5 APPROXIMATING THE FUELL MODEL 458 18.6 PROBLEMS 464 19 COX
PROPORTIONAL HAZARDS REGRESSION MODEL 465 19.1 MODEL 465 19.1.1
PRELIMINARIES 465 19.1.2 MODEL DEFINITION 466 19.1.3 ESTIMATION OF SS 466
XXII CONTENTS 19.1.4 MODEL ASSUMPTIONS AND INTERPRETATION OF PARAMETERS
. . . . 468 19.1.5 EXAMPLE 468 19.1.6 DESIGN FORMULATIONS 470 19.1.7
EXTENDING THE MODEL BY STRATIFICATION 470 19.2 ESTIMATION OF SURVIVAL
PROBABILITY AND SECONDARY PARAMETERS . . . 472 19.3 TEST STATISTICS 474
19.4 RESIDUAIS 476 19.5 ASSESSMENT OF MODEL FIT 476 19.5.1 REGRESSION
ASSUMPTIONS 477 19.5.2 PROPORTIONAL HAZARDS ASSUMPTION 483 19.6 WHAT TO
DO WHEN PH FAILS 489 19.7 COLLINEARITY 491 19.8 OVERLY INFLUENTIAL
OBSERVATIONS 492 19.9 QUANTIFYING PREDICTIVE ABILITY 492 19.10
VALIDATING THE FITTED MODEL 493 19.10.1 VALIDATION OF MODEL CALIBRATION
493 19.10.2 VALIDATION OF DISCRIMINATION AND OTHER STATISTICAL INDEXES .
494 19.11 DESCRIBING THE FITTED MODEL 496 19.12 S-PLUS FUNCTIONS 499
19.13 FURTHER READING 506 20 CASE STUDY IN COX REGRESSION 509 20.1
CHOOSING THE NUMBER OF PARAMETERS AND FITTING THE MODEL . . . . 509 20.2
CHECKING PROPORTIONAL HAZARDS 513 20.3 TESTING INTERACTIONS 516 20.4
DESCRIBING PREDICTOR EFFECTS 517 20.5 VALIDATING THE MODEL 517 20.6
PRESENTING THE MODEL 519 20.7 PROBLEMS 522 APPENDIX 523 REFERENCES 527
INDEX 559
|
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| id | DE-604.BV014724995 |
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| indexdate | 2024-07-09T19:05:29Z |
| institution | BVB |
| isbn | 0387952322 |
| language | English |
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| spelling | Harrell, Frank E. Verfasser aut Regression modeling strategies with applications to linear models, logistic regression, and survival analysis Frank E. Harrell, Jr. Corr. 2. print. New York u.a. Springer 2002 XXII, 568 S. graph. Darst. : 25 cm txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 527 - 558 Regressionsmodell Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009978348&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harrell, Frank E. Regression modeling strategies with applications to linear models, logistic regression, and survival analysis Regressionsmodell Regressionsmodell (DE-588)4127980-3 gnd |
| subject_GND | (DE-588)4127980-3 |
| title | Regression modeling strategies with applications to linear models, logistic regression, and survival analysis |
| title_auth | Regression modeling strategies with applications to linear models, logistic regression, and survival analysis |
| title_exact_search | Regression modeling strategies with applications to linear models, logistic regression, and survival analysis |
| title_full | Regression modeling strategies with applications to linear models, logistic regression, and survival analysis Frank E. Harrell, Jr. |
| title_fullStr | Regression modeling strategies with applications to linear models, logistic regression, and survival analysis Frank E. Harrell, Jr. |
| title_full_unstemmed | Regression modeling strategies with applications to linear models, logistic regression, and survival analysis Frank E. Harrell, Jr. |
| title_short | Regression modeling strategies |
| title_sort | regression modeling strategies with applications to linear models logistic regression and survival analysis |
| title_sub | with applications to linear models, logistic regression, and survival analysis |
| topic | Regressionsmodell Regressionsmodell (DE-588)4127980-3 gnd |
| topic_facet | Regressionsmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009978348&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT harrellfranke regressionmodelingstrategieswithapplicationstolinearmodelslogisticregressionandsurvivalanalysis |