Measurement error in nonlinear models: a modern perspective
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2006
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Monographs on statistics and applied probability
105 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVIII, 455 S. graph. Darst. |
| ISBN: | 1584886331 9781584886334 |
Internformat
MARC
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| 245 | 1 | 0 | |a Measurement error in nonlinear models |b a modern perspective |c Raymond. J. Carroll ... |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2006 | |
| 300 | |a XXVIII, 455 S. |b graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs on statistics and applied probability |v 105 | |
| 650 | 4 | |a Analyse de régression | |
| 650 | 7 | |a Modelos não lineares (pesquisa e planejamento) |2 larpcal | |
| 650 | 7 | |a Pesquisa e planejamento estatístico |2 larpcal | |
| 650 | 4 | |a Théories non linéaires | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a Regression analysis | |
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Datensatz im Suchindex
| _version_ | 1804135653564219392 |
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| adam_text | IMAGE 1
CONTENTS
INTRODUCTION 1
1.1 THE DOUBLE/TRIPLE WHAMMY OF MEASUREMENT ERROR 1 1.2 CLASSICAL
MEASUREMENT ERROR: A NUTRITION EXAMPLE 2 1.3 MEASUREMENT ERROR EXAMPLES
3
1.4 RADIATION EPIDEMIOLOGY AND BERKSON ERRORS 4
1.4.1 THE DIFFERENCE BETWEEN BERKSON AND CLASSICAL ERRORS: HOW TO GAIN
MORE POWER WITHOUT REALLY TRYING 5
1.5 CLASSICAL MEASUREMENT ERROR MODEL EXTENSIONS 7 1.6 OTHER EXAMPLES OF
MEASUREMENT ERROR MODELS 9
1.6.1 NHANES 9
1.6.2 NURSES HEALTH STUDY 10
1.6.3 THE ATHEROSCLEROSIS RISK IN COMMUNITIES STUDY 11 1.6.4 BIOASSAY IN
A HERBICIDE STUDY 11
1.6.5 LUNG FUNCTION IN CHILDREN 12
1.6.6 CORONARY HEART DISEASE AND BLOOD PRESSURE 12 1.6.7 A-BOMB
SURVIVORS DATA 13
1.6.8 BLOOD PRESSURE AND URINARY SODIUM CHLORIDE 13 1.6.9 MULTIPLICATIVE
ERROR FOR CONFIDENTIALITY 14
1.6.10 CERVICAL CANCER AND HERPES SIMPLEX VIRUS 14 1.7 CHECKING THE
CLASSICAL ERROR MODEL 14
1.8 LOSS OF POWER 18
1.8.1 LINEAR REGRESSION EXAMPLE 18
1.8.2 RADIATION EPIDEMIOLOGY EXAMPLE 20
1.9 A BRIEF TOUR 23
BIBLIOGRAPHIC NOTES 23
IMPORTANT CONCEPTS 25
2.1 FUNCTIONAL AND STRUCTURAL MODELS 25
2.2 MODELS FOR MEASUREMENT ERROR 26
2.2.1 GENERAL APPROACHES: BERKSON AND CLASSICAL MODELS 26 2.2.2 IS IT
BERKSON OR CLASSICAL? 27
2.2.3 BERKSON MODELS FROM CLASSICAL 28
2.2.4 TRANSPORTABILITY OF MODELS 29
IMAGE 2
2.2.5 POTENTIAL DANGERS OF TRANSPORTING MODELS 30
2.2.6 SEMICONTINUOUS VARIABLES 32
2.2.7 MISCLASSIFICATION OF A DISCRETE COVARIATE 32 2.3 SOURCES OF DATA
32
2.4 IS THERE AN EXACT PREDICTOR? WHAT IS TRUTH? 33
2.5 DIFFERENTIAL AND NONDIFFERENTIAL ERROR 36
2.6 PREDICTION 38
BIBLIOGRAPHIC NOTES 39
LINEAR REGRESSION AND ATTENUATION 41 3.1 INTRODUCTION 41
3.2 BIAS CAUSED BY MEASUREMENT ERROR 41
3.2.1 SIMPLE LINEAR REGRESSION WITH ADDITIVE ERROR 42 3.2.2 REGRESSION
CALIBRATION: CLASSICAL ERROR AS BERKSON ERROR 44
3.2.3 SIMPLE LINEAR REGRESSION WITH BERKSON ERROR 45 3.2.4 SIMPLE LINEAR
REGRESSION, MORE COMPLEX ERROR STRUCTURE 46
3.2.5 SUMMARY OF SIMPLE LINEAR REGRESSION 49
3.3 MULTIPLE AND ORTHOGONAL REGRESSION 52
3.3.1 MULTIPLE REGRESSION: SINGLE COVARIATE MEASURED WITH ERROR 52
3.3.2 MULTIPLE COVARIATES MEASURED WITH ERROR 53 3.4 CORRECTING FOR BIAS
55
3.4.1 METHOD OF MOMENTS 55
3.4.2 ORTHOGONAL REGRESSION 57
3.5 BIAS VERSUS VARIANCE 60
3.5.1 THEORETICAL BIAS-VARIANCE TRADEOFF CALCULATIONS 61 3.6 ATTENUATION
IN GENERAL PROBLEMS 63
BIBLIOGRAPHIC NOTES 64
REGRESSION CALIBRATION 65
4.1 OVERVIEW 65
4.2 THE REGRESSION CALIBRATION ALGORITHM 66
4.3 NHANES EXAMPLE 66
4.4 ESTIMATING THE CALIBRATION FUNCTION PARAMETERS 70 4.4.1 OVERVIEW AND
FIRST METHODS 70
4.4.2 BEST LINEAR APPROXIMATIONS USING REPLICATE DATA 70 4.4.3
ALTERNATIVES WHEN USING PARTIAL REPLICATES 72 4.4.4 JAMES STEIN
CALIBRATION 72
4.5 MULTIPLICATIVE MEASUREMENT ERROR 72
4.5.1 SHOULD PREDICTORS BE TRANSFORMED? 73
4.5.2 LOGNORMAL X AND U 74
IMAGE 3
4.5.3 LINEAR REGRESSION 77
4.5.4 ADDITIVE AND MULTIPLICATIVE ERROR 78
4.6 STANDARD ERRORS 79
4.7 EXPANDED REGRESSION CALIBRATION MODELS 79
4.7.1 THE EXPANDED APPROXIMATION DEFINED 81
4.7.2 IMPLEMENTATION 83
4.7.3 BIOASSAY DATA 85
4.8 EXAMPLES OF THE APPROXIMATIONS 90
4.8.1 LINEAR REGRESSION 90
4.8.2 LOGISTIC REGRESSION 90
4.8.3 LOGLINEAR MEAN MODELS 93
4.9 THEORETICAL EXAMPLES 94
4.9.1 HOMOSCEDASTIC REGRESSION 94
4.9.2 QUADRATIC REGRESSION WITH HOMOSCEDASTIC REGRES- SION CALIBRATION
94
4.9.3 LOGLINEAR MEAN MODEL 95
BIBLIOGRAPHIC NOTES AND SOFTWARE 95
SIMULATION E X T R A P O L A T I ON 97
5.1 OVERVIEW 97
5.2 SIMULATION EXTRAPOLATION HEURISTICS 98
5.2.1 SIMEX IN SIMPLE LINEAR REGRESSION 98
5.3 THE SIMEX ALGORITHM 100
5.3.1 SIMULATION AND EXTRAPOLATION STEPS 100
5.3.2 EXTRAPOLANT FUNCTION CONSIDERATIONS 108
5.3.3 SIMEX STANDARD ERRORS 110
5.3.4 EXTENSIONS AND REFINEMENTS 111
5.3.5 MULTIPLE COVARIATES WITH MEASUREMENT ERROR 112 5.4 APPLICATIONS
112
5.4.1 FRAMINGHAM HEART STUDY 112
5.4.2 SINGLE COVARIATE MEASURED WITH ERROR 113
5.4.3 MULTIPLE COVARIATES MEASURED WITH ERROR 118
5.5 SIMEX IN SOME IMPORTANT SPECIAL CASES 120
5.5.1 MULTIPLE LINEAR REGRESSION 120
5.5.2 LOGLINEAR MEAN MODELS 122
5.5.3 QUADRATIC MEAN MODELS 122
5.6 EXTENSIONS AND RELATED METHODS 123
5.6.1 MIXTURE OF BERKSON AND CLASSICAL ERROR 123
5.6.2 MISCLASSIFICATION SIMEX 125
5.6.3 CHECKING STRUCTURAL MODEL ROBUSTNESS VIA RE- MEASUREMENT 126
BIBLIOGRAPHIC NOTES 128
IMAGE 4
6 INSTRUMENTAL VARIABLES 129
6.1 OVERVIEW 129
6.1.1 A NOTE ON NOTATION 130
6.2 INSTRUMENTAL VARIABLES IN LINEAR MODELS 131
6.2.1 INSTRUMENTAL VARIABLES VIA DIFFERENTIATION 131 6.2.2 SIMPLE LINEAR
REGRESSION WITH ONE INSTRUMENT 132 6.2.3 LINEAR REGRESSION WITH MULTIPLE
INSTRUMENTS 134 6.3 APPROXIMATE INSTRUMENTAL VARIABLE ESTIMATION 137
6.3.1 IV ASSUMPTIONS 137
6.3.2 MEAN AND VARIANCE FUNCTION MODELS 138
6.3.3 FIRST REGRESSION CALIBRATION IV ALGORITHM 139 6.3.4 SECOND
REGRESSION CALIBRATION IV ALGORITHM 140 6.4 ADJUSTED SCORE METHOD 140
6.5 EXAMPLES 143
6.5.1 FRAMINGHAM DATA 143
6.5.2 SIMULATED DATA 145
6.6 OTHER METHODOLOGIES 145
6.6.1 HYBRID CLASSICAL AND REGRESSION CALIBRATION 145 6.6.2 ERROR MODEL
APPROACHES 147
BIBLIOGRAPHIC NOTES 148
7 SCORE FUNCTION METHODS 151
7.1 OVERVIEW 151
7.2 LINEAR AND LOGISTIC REGRESSION 152
7.2.1 LINEAR REGRESSION CORRECTED AND CONDITIONAL SCORES 152
7.2.2 LOGISTIC REGRESSION CORRECTED AND CONDITIONAL SCORES 157
7.2.3 FRAMINGHAM DATA EXAMPLE 159
7.3 CONDITIONAL SCORE FUNCTIONS 162
7.3.1 CONDITIONAL SCORE BASIC THEORY 162
7.3.2 CONDITIONAL SCORES FOR BASIC MODELS 164
7.3.3 CONDITIONAL SCORES FOR MORE COMPLICATED MODELS 166 7.4 CORRECTED
SCORE FUNCTIONS 169
7.4.1 CORRECTED SCORE BASIC THEORY 170
7.4.2 MONTE CARLO CORRECTED SCORES 170
7.4.3 SOME EXACT CORRECTED SCORES 172
7.4.4 SIMEX CONNECTION 173
7.4.5 CORRECTED SCORES WITH REPLICATE MEASUREMENTS 173 7.5 COMPUTATION
AND ASYMPTOTIC APPROXIMATIONS 174 7.5.1 KNOWN MEASUREMENT ERROR VARIANCE
175
7.5.2 ESTIMATED MEASUREMENT ERROR VARIANCE 176 7.6 COMPARISON OF
CONDITIONAL AND CORRECTED SCORES 177
IMAGE 5
7.7 BIBLIOGRAPHIC NOTES 178
BIBLIOGRAPHIC NOTES 178
LIKELIHOOD A ND QUASILIKELIHOOD 181 8.1 INTRODUCTION 181
8.1.1 STEP 1: THE LIKELIHOOD IF X WERE OBSERVABLE 183 8.1.2 A GENERAL
CONCERN: IDENTIFIABLE MODELS 184 8.2 STEPS 2 AND 3: CONSTRUCTING
LIKELIHOODS 184
8.2.1 THE DISCRETE CASE 185
8.2.2 LIKELIHOOD CONSTRUCTION FOR GENERAL ERROR MODELS 186 8.2.3 THE
BERKSON MODEL 188
8.2.4 ERROR MODEL CHOICE 189
8.3 STEP 4: NUMERICAL COMPUTATION OF LIKELIHOODS 190 8.4 CERVICAL CANCER
AND HERPES 190
8.5 FRAMINGHAM DATA 192
8.6 NEVADA TEST SITE REANALYSIS 193
8.6.1 REGRESSION CALIBRATION IMPLEMENTATION 195 8.6.2 MAXIMUM LIKELIHOOD
IMPLEMENTATION 196
8.7 BRONCHITIS EXAMPLE 197
8.7.1 CALCULATING THE LIKELIHOOD 198
8.7.2 EFFECTS OF MEASUREMENT ERROR ON THRESHOLD MODELS 199 8.7.3
SIMULATION STUDY AND MAXIMUM LIKELIHOOD 199 8.7.4 BERKSON ANALYSIS OF
THE DATA 201
8.8 QUASILIKELIHOOD AND VARIANCE FUNCTION MODELS 201 8.8.1 DETAILS OF
STEP 3 FOR QVF MODELS 202
8.8.2 DETAILS OF STEP 4 FOR QVF MODELS 203
BIBLIOGRAPHIC NOTES 203
BAYESIAN METHODS 205
9.1 OVERVIEW 205
9.1.1 PROBLEM FORMULATION 205
9.1.2 POSTERIOR INFERENCE 207
9.1.3 BAYESIAN FUNCTIONAL AND STRUCTURAL MODELS 208 9.1.4 MODULARITY OF
BAYESIAN MCMC 209
9.2 THE GIBBS SAMPLER 209
9.3 METROPOLIS HASTINGS ALGORITHM 211
9.4 LINEAR REGRESSION 213
9.4.1 EXAMPLE 216
9.5 NONLINEAR MODELS 219
9.5.1 A GENERAL MODEL 219
9.5.2 POLYNOMIAL REGRESSION 220
9.5.3 MULTIPLICATIVE ERROR 221
9.5.4 SEGMENTED REGRESSION 222
IMAGE 6
9.6 LOGISTIC REGRESSION 223
9.7 BERKSON ERRORS 225
9.7.1 NONLINEAR REGRESSION WITH BERKSON ERRORS 225 9.7.2 LOGISTIC
REGRESSION WITH BERKSON ERRORS 227
9.7.3 BRONCHITIS DATA 228
9.8 AUTOMATIC IMPLEMENTATION 230
9.8.1 IMPLEMENTATION AND SIMULATIONS IN WINBUGS 231 9.8.2 MORE COMPLEX
MODELS 234
9.9 CERVICAL CANCER AND HERPES 235
9.10 FRAMINGHAM DATA 237
9.11 OPEN DATA: A VARIANCE COMPONENTS MODEL 238
BIBLIOGRAPHIC NOTES 240
10 H Y P O T H E S IS T E S T I NG 243
10.1 OVERVIEW 243
10.1.1 SIMPLE LINEAR REGRESSION, NORMALLY DISTRIBUTED X 243
10.1.2 ANALYSIS OF COVARIANCE 246
10.1.3 GENERAL CONSIDERATIONS: WHAT IS A VALID TEST? 248 10.1.4 SUMMARY
OF MAJOR RESULTS 248
10.2 THE REGRESSION CALIBRATION APPROXIMATION 249
10.2.1 TESTING H A : (3 X = 0 250
10.2.2 TESTING H O : /? Z = 0 250
10.2.3 TESTING H Q : (/%,/?*)* = 0 250
10.3 ILLUSTRATION: OPEN DATA 251
10.4 HYPOTHESES ABOUT SUBVECTORS OF (3 X AND J3 Z 251
10.4.1 ILLUSTRATION: FRAMINGHAM DATA 252
10.5 EFFICIENT SCORE TESTS OF H O : (3 X = 0 253
10.5.1 GENERALIZED SCORE TESTS 254
BIBLIOGRAPHIC NOTES 257
11 L O N G I T U D I N AL DATA A ND M I X ED MODELS 259 11.1 MIXED
MODELS FOR LONGITUDINAL DATA 259
11.1.1 SIMPLE LINEAR MIXED MODELS 259
11.1.2 THE GENERAL LINEAR MIXED MODEL 260
11.1.3 THE LINEAR LOGISTIC MIXED MODEL 261
11.1.4 THE GENERALIZED LINEAR MIXED MODEL 261
11.2 MIXED MEASUREMENT ERROR MODELS 262
11.2.1 THE VARIANCE COMPONENTS MODEL REVISITED 262 11.2.2 GENERAL
CONSIDERATIONS 263
11.2.3 SOME SIMPLE EXAMPLES 263
11.2.4 MODELS FOR WITHIN-SUBJECT X-CORRELATION 265 11.3 A BIAS-CORRECTED
ESTIMATOR 265
IMAGE 7
11.4 SIMEX FOR GLMMEMS 267
11.5 REGRESSION CALIBRATION FOR GLMMS 267
11.6 MAXIMUM LIKELIHOOD ESTIMATION 268
11.7 JOINT MODELING 268
11.8 OTHER MODELS AND APPLICATIONS 269
11.8.1 MODELS WITH RANDOM EFFECTS MULTIPLIED BY X 269 11.8.2 MODELS WITH
RANDOM EFFECTS DEPENDING NONLIN- EAR LY ON X 270
11.8.3 INDUCING A TRUE-DATA MODEL FROM A STANDARD OBSERVED DATA MODEL
270
11.8.4 AUTOREGRESSIVE MODELS IN LONGITUDINAL DATA 271 11.9 EXAMPLE: THE
CHOICE STUDY 272
11.9.1 BASIC MODEL 273
11.9.2 NAIVE REPLICATION AND SENSITIVITY 273
11.9.3 ACCOUNTING FOR BIOLOGICAL VARIABILITY 274
BIBLIOGRAPHIC NOTES 276
12 NONPARAMETRIC ESTIMATION 279
12.1 DECONVOLUTION 279
12.1.1 THE PROBLEM 279
12.1.2 FOURIER INVERSION 280
12.1.3 METHODOLOGY 280
12.1.4 PROPERTIES OF DECONVOLUTION METHODS 281
12.1.5 IS IT POSSIBLE TO ESTIMATE THE BANDWIDTH? 282 12.1.6 PARAMETRIC
DECONVOLUTION 284
12.1.7 ESTIMATING DISTRIBUTION FUNCTIONS 287
12.1.8 OPTIMAL SCORE TESTS 288
12.1.9 FRAMINGHAM DATA 289
12.1.10NHANES DATA 290
12.1.11BAYESIAN DENSITY ESTIMATION BY NORMAL MIXTURES 291 12.2
NONPARAMETRIC REGRESSION 293
12.2.1 LOCAL-POLYNOMIAL, KERNEL-WEIGHTED REGRESSION 293 12.2.2 SPLINES
294
12.2.3 QVF AND LIKELIHOOD MODELS 295
12.2.4 SIMEX FOR NONPARAMETRIC REGRESSION 296 12.2.5 REGRESSION
CALIBRATION 297
12.2.6 STRUCTURAL SPLINES 297
12.2.7 TAYLEX AND OTHER METHODS 298
12.3 BASELINE CHANGE EXAMPLE 299
12.3.1 DISCUSSION OF THE BASELINE CHANGE CONTROLS DATA 301 BIBLIOGRAPHIC
NOTES 302
13 SEMIPARAMETRIC REGRESSION 303
IMAGE 8
13.1 OVERVIEW 303
13.2 ADDITIVE MODELS 303
13.3 MCMC FOR ADDITIVE SPLINE MODELS 304
13.4 MONTE CARLO EM-ALGORITHM 305
13.4.1 STARTING VALUES 306
13.4.2 METROPOLIS HASTINGS FACT 306
13.4.3 THE ALGORITHM 306
13.5 SIMULATION WITH CLASSICAL ERRORS 309
13.6 SIMULATION WITH BERKSON ERRORS 311
13.7 SEMIPARAMETRICS: X MODELED PARAMETRICALLY 312 13.8 PARAMETRIC
MODELS: NO ASSUMPTIONS ON X 314
13.8.1 DECONVOLUTION METHODS 314
13.8.2 MODELS LINEAR IN FUNCTIONS OF X 315
13.8.3 LINEAR LOGISTIC REGRESSION WITH REPLICATES 316 13.8.4 DOUBLY
ROBUST PARAMETRIC MODELING 317 BIBLIOGRAPHIC NOTES 318
14 SURVIVAL DATA 319
14.1 NOTATION AND ASSUMPTIONS 319
14.2 INDUCED HAZARD FUNCTION 320
14.3 REGRESSION CALIBRATION FOR SURVIVAL ANALYSIS 321 14.3.1 METHODOLOGY
AND ASYMPTOTIC PROPERTIES 321 14.3.2 RISK SET CALIBRATION 322
14.4 SIMEX FOR SURVIVAL ANALYSIS 323
14.5 CHRONIC KIDNEY DISEASE PROGRESSION 324
14.5.1 REGRESSION CALIBRATION FOR CKD PROGRESSION 325 14.5.2 SIMEX FOR
CKD PROGRESSION 326
14.6 SEMI AND NONPARAMETRIC METHODS 329
14.6.1 NONPARAMETRIC ESTIMATION WITH VALIDATION DATA 330 14.6.2
NONPARAMETRIC ESTIMATION WITH REPLICATED DATA 332 14.6.3 LIKELIHOOD
ESTIMATION 333
14.7 LIKELIHOOD INFERENCE FOR FRAILTY MODELS 336
BIBLIOGRAPHIC NOTES 337
15 RESPONSE VARIABLE ERROR 339
15.1 RESPONSE ERROR AND LINEAR REGRESSION 339
15.2 OTHER FORMS OF ADDITIVE RESPONSE ERROR 343
15.2.1 BIASED RESPONSES 343
15.2.2 RESPONSE ERROR IN HETEROSEEDASTIC REGRESSION 344 15.3 LOGISTIC
REGRESSION WITH RESPONSE ERROR 345
15.3.1 THE IMPACT OF RESPONSE MISCLASSIFICATION 345 15.3.2 CORRECTING
FOR RESPONSE MISCLASSIFICATION 347 15.4 LIKELIHOOD METHODS 353
IMAGE 9
15.4.1 GENERAL LIKELIHOOD THEORY AND SURROGATES 353
15.4.2 VALIDATION DATA 354
15.5 USE OF COMPLETE DATA ONLY 355
15.5.1 LIKELIHOOD OF THE VALIDATION DATA 355
15.5.2 OTHER METHODS 356
15.6 SEMIPARAMETRIC METHODS FOR VALIDATION DATA 356
15.6.1 SIMPLE RANDOM SAMPLING 356
15.6.2 OTHER TYPES OF SAMPLING 357
BIBLIOGRAPHIC NOTES 358
BACKGROUND MATERIAL 359
A.I OVERVIEW 359
A.2 NORMAL AND LOGNORMAL DISTRIBUTIONS 359
A.3 GAMMA AND INVERSE-GAMMA DISTRIBUTIONS 360
A.4 BEST AND BEST LINEAR PREDICTION AND REGRESSION 361
A.4.1 LINEAR PREDICTION 361
A.4.2 BEST LINEAR PREDICTION WITHOUT AN INTERCEPT 363 A.4.3 NONLINEAR
PREDICTION 363
A.5 LIKELIHOOD METHODS 364
A.5.1 NOTATION 364
A.5.2 MAXIMUM LIKELIHOOD ESTIMATION 364
A.5.3 LIKELIHOOD RATIO TESTS 365
A.5.4 PROFILE LIKELIHOOD AND LIKELIHOOD RATIO CONFIDENCE INTERVALS 365
A.5.5 EFFICIENT SCORE TESTS 366
A.6 UNBIASED ESTIMATING EQUATIONS 367
A.6.1 INTRODUCTION AND BASIC LARGE SAMPLE THEORY 367 A.6.2 SANDWICH
FORMULA EXAMPLE: LINEAR REGRESSION WITHOUT MEASUREMENT ERROR 369
A.6.3 SANDWICH METHOD AND LIKELIHOOD-TYPE INFERENCE 370 A.6.4 UNBIASED,
BUT CONDITIONALLY BIASED, ESTIMATING EQUATIONS 372
A.6.5 BIASED ESTIMATING EQUATIONS 372
A.6.6 STACKING ESTIMATING EQUATIONS: USING PRIOR ESTI- MATES OF SOME
PARAMETERS 372
A.7 QUASILIKELIHOOD AND VARIANCE FUNCTION MODELS (QVF) 374 A.7.1 GENERAL
IDEAS 374
A.7.2 ESTIMATION AND INFERENCE FOR QVF MODELS 375
A.8 GENERALIZED LINEAR MODELS 377
A.9 BOOTSTRAP METHODS 377
A.9.1 INTRODUCTION 377
A.9.2 NONLINEAR REGRESSION WITHOUT MEASUREMENT ERROR 378 A.9.3
BOOTSTRAPPING HETEROSCEDASTIC REGRESSION MODELS 380
IMAGE 10
A.9.4 BOOTSTRAPPING LOGISTIC REGRESSION MODELS 380
A.9.5 BOOTSTRAPPING MEASUREMENT ERROR MODELS 381 A.9.6 BOOTSTRAP
CONFIDENCE INTERVALS 382
B TECHNICAL DETAILS 385
B.I APPENDIX TO CHAPTER 1: POWER IN BERKSON AND CLASSICAL ERROR MODELS
385
B.2 APPENDIX TO CHAPTER 3: LINEAR REGRESSION AND ATTENUA- TION 386
B.3 APPENDIX TO CHAPTER 4: REGRESSION CALIBRATION 387 B.3.1 STANDARD
ERRORS AND REPLICATION 387
B.3.2 QUADRATIC REGRESSION: DETAILS OF THE EXPANDED CALIBRATION MODEL
391
B.3.3 HEURISTICS AND ACCURACY OF THE APPROXIMATIONS 391 B.4 APPENDIX TO
CHAPTER 5: SIMEX 392
B.4.1 SIMULATION EXTRAPOLATION VARIANCE ESTIMATION 393 B.4.2 ESTIMATING
EQUATION APPROACH TO VARIANCE ESTI- MATION 395
B.5 APPENDIX TO CHAPTER 6: INSTRUMENTAL VARIABLES 399 B.5.1 DERIVATION
OF THE ESTIMATORS 399
B.5.2 ASYMPTOTIC DISTRIBUTION APPROXIMATIONS 401 B.6 APPENDIX TO CHAPTER
7: SCORE FUNCTION METHODS 406 B.6.1 TECHNICAL COMPLEMENTS TO CONDITIONAL
SCORE THEORY 406
B.6.2 TECHNICAL COMPLEMENTS TO DISTRIBUTION THEORY FOR ESTIMATED ** 406
B.7 APPENDIX TO CHAPTER 8: LIKELIHOOD AND QUASILIKELIHOOD 407 B.7.1
MONTE CARLO COMPUTATION OF INTEGRALS 407 B.7.2 LINEAR, PROBIT, AND
LOGISTIC REGRESSION 408 B.8 APPENDIX TO CHAPTER 9: BAYESIAN METHODS 409
B.8.1 CODE FOR SECTION 9.8.1 409
B.8.2 CODE FOR SECTION 9.11 410
REFERENCES 413
APPLICATIONS AND EXAMPLES INDEX 439
AUTHOR INDEX 441
SUBJECT INDEX 447
|
| adam_txt |
IMAGE 1
CONTENTS
INTRODUCTION 1
1.1 THE DOUBLE/TRIPLE WHAMMY OF MEASUREMENT ERROR 1 1.2 CLASSICAL
MEASUREMENT ERROR: A NUTRITION EXAMPLE 2 1.3 MEASUREMENT ERROR EXAMPLES
3
1.4 RADIATION EPIDEMIOLOGY AND BERKSON ERRORS 4
1.4.1 THE DIFFERENCE BETWEEN BERKSON AND CLASSICAL ERRORS: HOW TO GAIN
MORE POWER WITHOUT REALLY TRYING 5
1.5 CLASSICAL MEASUREMENT ERROR MODEL EXTENSIONS 7 1.6 OTHER EXAMPLES OF
MEASUREMENT ERROR MODELS 9
1.6.1 NHANES 9
1.6.2 NURSES' HEALTH STUDY 10
1.6.3 THE ATHEROSCLEROSIS RISK IN COMMUNITIES STUDY 11 1.6.4 BIOASSAY IN
A HERBICIDE STUDY 11
1.6.5 LUNG FUNCTION IN CHILDREN 12
1.6.6 CORONARY HEART DISEASE AND BLOOD PRESSURE 12 1.6.7 A-BOMB
SURVIVORS DATA 13
1.6.8 BLOOD PRESSURE AND URINARY SODIUM CHLORIDE 13 1.6.9 MULTIPLICATIVE
ERROR FOR CONFIDENTIALITY 14
1.6.10 CERVICAL CANCER AND HERPES SIMPLEX VIRUS 14 1.7 CHECKING THE
CLASSICAL ERROR MODEL 14
1.8 LOSS OF POWER 18
1.8.1 LINEAR REGRESSION EXAMPLE 18
1.8.2 RADIATION EPIDEMIOLOGY EXAMPLE 20
1.9 A BRIEF TOUR 23
BIBLIOGRAPHIC NOTES 23
IMPORTANT CONCEPTS 25
2.1 FUNCTIONAL AND STRUCTURAL MODELS 25
2.2 MODELS FOR MEASUREMENT ERROR 26
2.2.1 GENERAL APPROACHES: BERKSON AND CLASSICAL MODELS 26 2.2.2 IS IT
BERKSON OR CLASSICAL? 27
2.2.3 BERKSON MODELS FROM CLASSICAL 28
2.2.4 TRANSPORTABILITY OF MODELS 29
IMAGE 2
2.2.5 POTENTIAL DANGERS OF TRANSPORTING MODELS 30
2.2.6 SEMICONTINUOUS VARIABLES 32
2.2.7 MISCLASSIFICATION OF A DISCRETE COVARIATE 32 2.3 SOURCES OF DATA
32
2.4 IS THERE AN "EXACT" PREDICTOR? WHAT IS TRUTH? 33
2.5 DIFFERENTIAL AND NONDIFFERENTIAL ERROR 36
2.6 PREDICTION 38
BIBLIOGRAPHIC NOTES 39
LINEAR REGRESSION AND ATTENUATION 41 3.1 INTRODUCTION 41
3.2 BIAS CAUSED BY MEASUREMENT ERROR 41
3.2.1 SIMPLE LINEAR REGRESSION WITH ADDITIVE ERROR 42 3.2.2 REGRESSION
CALIBRATION: CLASSICAL ERROR AS BERKSON ERROR 44
3.2.3 SIMPLE LINEAR REGRESSION WITH BERKSON ERROR 45 3.2.4 SIMPLE LINEAR
REGRESSION, MORE COMPLEX ERROR STRUCTURE 46
3.2.5 SUMMARY OF SIMPLE LINEAR REGRESSION 49
3.3 MULTIPLE AND ORTHOGONAL REGRESSION 52
3.3.1 MULTIPLE REGRESSION: SINGLE COVARIATE MEASURED WITH ERROR 52
3.3.2 MULTIPLE COVARIATES MEASURED WITH ERROR 53 3.4 CORRECTING FOR BIAS
55
3.4.1 METHOD OF MOMENTS 55
3.4.2 ORTHOGONAL REGRESSION 57
3.5 BIAS VERSUS VARIANCE 60
3.5.1 THEORETICAL BIAS-VARIANCE TRADEOFF CALCULATIONS 61 3.6 ATTENUATION
IN GENERAL PROBLEMS 63
BIBLIOGRAPHIC NOTES 64
REGRESSION CALIBRATION 65
4.1 OVERVIEW 65
4.2 THE REGRESSION CALIBRATION ALGORITHM 66
4.3 NHANES EXAMPLE 66
4.4 ESTIMATING THE CALIBRATION FUNCTION PARAMETERS 70 4.4.1 OVERVIEW AND
FIRST METHODS 70
4.4.2 BEST LINEAR APPROXIMATIONS USING REPLICATE DATA 70 4.4.3
ALTERNATIVES WHEN USING PARTIAL REPLICATES 72 4.4.4 JAMES STEIN
CALIBRATION 72
4.5 MULTIPLICATIVE MEASUREMENT ERROR 72
4.5.1 SHOULD PREDICTORS BE TRANSFORMED? 73
4.5.2 LOGNORMAL X AND U 74
IMAGE 3
4.5.3 LINEAR REGRESSION 77
4.5.4 ADDITIVE AND MULTIPLICATIVE ERROR 78
4.6 STANDARD ERRORS 79
4.7 EXPANDED REGRESSION CALIBRATION MODELS 79
4.7.1 THE EXPANDED APPROXIMATION DEFINED 81
4.7.2 IMPLEMENTATION 83
4.7.3 BIOASSAY DATA 85
4.8 EXAMPLES OF THE APPROXIMATIONS 90
4.8.1 LINEAR REGRESSION 90
4.8.2 LOGISTIC REGRESSION 90
4.8.3 LOGLINEAR MEAN MODELS 93
4.9 THEORETICAL EXAMPLES 94
4.9.1 HOMOSCEDASTIC REGRESSION 94
4.9.2 QUADRATIC REGRESSION WITH HOMOSCEDASTIC REGRES- SION CALIBRATION
94
4.9.3 LOGLINEAR MEAN MODEL 95
BIBLIOGRAPHIC NOTES AND SOFTWARE 95
SIMULATION E X T R A P O L A T I ON 97
5.1 OVERVIEW 97
5.2 SIMULATION EXTRAPOLATION HEURISTICS 98
5.2.1 SIMEX IN SIMPLE LINEAR REGRESSION 98
5.3 THE SIMEX ALGORITHM 100
5.3.1 SIMULATION AND EXTRAPOLATION STEPS 100
5.3.2 EXTRAPOLANT FUNCTION CONSIDERATIONS 108
5.3.3 SIMEX STANDARD ERRORS 110
5.3.4 EXTENSIONS AND REFINEMENTS 111
5.3.5 MULTIPLE COVARIATES WITH MEASUREMENT ERROR 112 5.4 APPLICATIONS
112
5.4.1 FRAMINGHAM HEART STUDY 112
5.4.2 SINGLE COVARIATE MEASURED WITH ERROR 113
5.4.3 MULTIPLE COVARIATES MEASURED WITH ERROR 118
5.5 SIMEX IN SOME IMPORTANT SPECIAL CASES 120
5.5.1 MULTIPLE LINEAR REGRESSION 120
5.5.2 LOGLINEAR MEAN MODELS 122
5.5.3 QUADRATIC MEAN MODELS 122
5.6 EXTENSIONS AND RELATED METHODS 123
5.6.1 MIXTURE OF BERKSON AND CLASSICAL ERROR 123
5.6.2 MISCLASSIFICATION SIMEX 125
5.6.3 CHECKING STRUCTURAL MODEL ROBUSTNESS VIA RE- MEASUREMENT 126
BIBLIOGRAPHIC NOTES 128
IMAGE 4
6 INSTRUMENTAL VARIABLES 129
6.1 OVERVIEW 129
6.1.1 A NOTE ON NOTATION 130
6.2 INSTRUMENTAL VARIABLES IN LINEAR MODELS 131
6.2.1 INSTRUMENTAL VARIABLES VIA DIFFERENTIATION 131 6.2.2 SIMPLE LINEAR
REGRESSION WITH ONE INSTRUMENT 132 6.2.3 LINEAR REGRESSION WITH MULTIPLE
INSTRUMENTS 134 6.3 APPROXIMATE INSTRUMENTAL VARIABLE ESTIMATION 137
6.3.1 IV ASSUMPTIONS 137
6.3.2 MEAN AND VARIANCE FUNCTION MODELS 138
6.3.3 FIRST REGRESSION CALIBRATION IV ALGORITHM 139 6.3.4 SECOND
REGRESSION CALIBRATION IV ALGORITHM 140 6.4 ADJUSTED SCORE METHOD 140
6.5 EXAMPLES 143
6.5.1 FRAMINGHAM DATA 143
6.5.2 SIMULATED DATA 145
6.6 OTHER METHODOLOGIES 145
6.6.1 HYBRID CLASSICAL AND REGRESSION CALIBRATION 145 6.6.2 ERROR MODEL
APPROACHES 147
BIBLIOGRAPHIC NOTES 148
7 SCORE FUNCTION METHODS 151
7.1 OVERVIEW 151
7.2 LINEAR AND LOGISTIC REGRESSION 152
7.2.1 LINEAR REGRESSION CORRECTED AND CONDITIONAL SCORES 152
7.2.2 LOGISTIC REGRESSION CORRECTED AND CONDITIONAL SCORES 157
7.2.3 FRAMINGHAM DATA EXAMPLE 159
7.3 CONDITIONAL SCORE FUNCTIONS 162
7.3.1 CONDITIONAL SCORE BASIC THEORY 162
7.3.2 CONDITIONAL SCORES FOR BASIC MODELS 164
7.3.3 CONDITIONAL SCORES FOR MORE COMPLICATED MODELS 166 7.4 CORRECTED
SCORE FUNCTIONS 169
7.4.1 CORRECTED SCORE BASIC THEORY 170
7.4.2 MONTE CARLO CORRECTED SCORES 170
7.4.3 SOME EXACT CORRECTED SCORES 172
7.4.4 SIMEX CONNECTION 173
7.4.5 CORRECTED SCORES WITH REPLICATE MEASUREMENTS 173 7.5 COMPUTATION
AND ASYMPTOTIC APPROXIMATIONS 174 7.5.1 KNOWN MEASUREMENT ERROR VARIANCE
175
7.5.2 ESTIMATED MEASUREMENT ERROR VARIANCE 176 7.6 COMPARISON OF
CONDITIONAL AND CORRECTED SCORES 177
IMAGE 5
7.7 BIBLIOGRAPHIC NOTES 178
BIBLIOGRAPHIC NOTES 178
LIKELIHOOD A ND QUASILIKELIHOOD 181 8.1 INTRODUCTION 181
8.1.1 STEP 1: THE LIKELIHOOD IF X WERE OBSERVABLE 183 8.1.2 A GENERAL
CONCERN: IDENTIFIABLE MODELS 184 8.2 STEPS 2 AND 3: CONSTRUCTING
LIKELIHOODS 184
8.2.1 THE DISCRETE CASE 185
8.2.2 LIKELIHOOD CONSTRUCTION FOR GENERAL ERROR MODELS 186 8.2.3 THE
BERKSON MODEL 188
8.2.4 ERROR MODEL CHOICE 189
8.3 STEP 4: NUMERICAL COMPUTATION OF LIKELIHOODS 190 8.4 CERVICAL CANCER
AND HERPES 190
8.5 FRAMINGHAM DATA 192
8.6 NEVADA TEST SITE REANALYSIS 193
8.6.1 REGRESSION CALIBRATION IMPLEMENTATION 195 8.6.2 MAXIMUM LIKELIHOOD
IMPLEMENTATION 196
8.7 BRONCHITIS EXAMPLE 197
8.7.1 CALCULATING THE LIKELIHOOD 198
8.7.2 EFFECTS OF MEASUREMENT ERROR ON THRESHOLD MODELS 199 8.7.3
SIMULATION STUDY AND MAXIMUM LIKELIHOOD 199 8.7.4 BERKSON ANALYSIS OF
THE DATA 201
8.8 QUASILIKELIHOOD AND VARIANCE FUNCTION MODELS 201 8.8.1 DETAILS OF
STEP 3 FOR QVF MODELS 202
8.8.2 DETAILS OF STEP 4 FOR QVF MODELS 203
BIBLIOGRAPHIC NOTES 203
BAYESIAN METHODS 205
9.1 OVERVIEW 205
9.1.1 PROBLEM FORMULATION 205
9.1.2 POSTERIOR INFERENCE 207
9.1.3 BAYESIAN FUNCTIONAL AND STRUCTURAL MODELS 208 9.1.4 MODULARITY OF
BAYESIAN MCMC 209
9.2 THE GIBBS SAMPLER 209
9.3 METROPOLIS HASTINGS ALGORITHM 211
9.4 LINEAR REGRESSION 213
9.4.1 EXAMPLE 216
9.5 NONLINEAR MODELS 219
9.5.1 A GENERAL MODEL 219
9.5.2 POLYNOMIAL REGRESSION 220
9.5.3 MULTIPLICATIVE ERROR 221
9.5.4 SEGMENTED REGRESSION 222
IMAGE 6
9.6 LOGISTIC REGRESSION 223
9.7 BERKSON ERRORS 225
9.7.1 NONLINEAR REGRESSION WITH BERKSON ERRORS 225 9.7.2 LOGISTIC
REGRESSION WITH BERKSON ERRORS 227
9.7.3 BRONCHITIS DATA 228
9.8 AUTOMATIC IMPLEMENTATION 230
9.8.1 IMPLEMENTATION AND SIMULATIONS IN WINBUGS 231 9.8.2 MORE COMPLEX
MODELS 234
9.9 CERVICAL CANCER AND HERPES 235
9.10 FRAMINGHAM DATA 237
9.11 OPEN DATA: A VARIANCE COMPONENTS MODEL 238
BIBLIOGRAPHIC NOTES 240
10 H Y P O T H E S IS T E S T I NG 243
10.1 OVERVIEW 243
10.1.1 SIMPLE LINEAR REGRESSION, NORMALLY DISTRIBUTED X 243
10.1.2 ANALYSIS OF COVARIANCE 246
10.1.3 GENERAL CONSIDERATIONS: WHAT IS A VALID TEST? 248 10.1.4 SUMMARY
OF MAJOR RESULTS 248
10.2 THE REGRESSION CALIBRATION APPROXIMATION 249
10.2.1 TESTING H A : (3 X = 0 250
10.2.2 TESTING H O : /? Z = 0 250
10.2.3 TESTING H Q : (/%,/?*)* = 0 250
10.3 ILLUSTRATION: OPEN DATA 251
10.4 HYPOTHESES ABOUT SUBVECTORS OF (3 X AND J3 Z 251
10.4.1 ILLUSTRATION: FRAMINGHAM DATA 252
10.5 EFFICIENT SCORE TESTS OF H O : (3 X = 0 253
10.5.1 GENERALIZED SCORE TESTS 254
BIBLIOGRAPHIC NOTES 257
11 L O N G I T U D I N AL DATA A ND M I X ED MODELS 259 11.1 MIXED
MODELS FOR LONGITUDINAL DATA 259
11.1.1 SIMPLE LINEAR MIXED MODELS 259
11.1.2 THE GENERAL LINEAR MIXED MODEL 260
11.1.3 THE LINEAR LOGISTIC MIXED MODEL 261
11.1.4 THE GENERALIZED LINEAR MIXED MODEL 261
11.2 MIXED MEASUREMENT ERROR MODELS 262
11.2.1 THE VARIANCE COMPONENTS MODEL REVISITED 262 11.2.2 GENERAL
CONSIDERATIONS 263
11.2.3 SOME SIMPLE EXAMPLES 263
11.2.4 MODELS FOR WITHIN-SUBJECT X-CORRELATION 265 11.3 A BIAS-CORRECTED
ESTIMATOR 265
IMAGE 7
11.4 SIMEX FOR GLMMEMS 267
11.5 REGRESSION CALIBRATION FOR GLMMS 267
11.6 MAXIMUM LIKELIHOOD ESTIMATION 268
11.7 JOINT MODELING 268
11.8 OTHER MODELS AND APPLICATIONS 269
11.8.1 MODELS WITH RANDOM EFFECTS MULTIPLIED BY X 269 11.8.2 MODELS WITH
RANDOM EFFECTS DEPENDING NONLIN- EAR LY ON X 270
11.8.3 INDUCING A TRUE-DATA MODEL FROM A STANDARD OBSERVED DATA MODEL
270
11.8.4 AUTOREGRESSIVE MODELS IN LONGITUDINAL DATA 271 11.9 EXAMPLE: THE
CHOICE STUDY 272
11.9.1 BASIC MODEL 273
11.9.2 NAIVE REPLICATION AND SENSITIVITY 273
11.9.3 ACCOUNTING FOR BIOLOGICAL VARIABILITY 274
BIBLIOGRAPHIC NOTES 276
12 NONPARAMETRIC ESTIMATION 279
12.1 DECONVOLUTION 279
12.1.1 THE PROBLEM 279
12.1.2 FOURIER INVERSION 280
12.1.3 METHODOLOGY 280
12.1.4 PROPERTIES OF DECONVOLUTION METHODS 281
12.1.5 IS IT POSSIBLE TO ESTIMATE THE BANDWIDTH? 282 12.1.6 PARAMETRIC
DECONVOLUTION 284
12.1.7 ESTIMATING DISTRIBUTION FUNCTIONS 287
12.1.8 OPTIMAL SCORE TESTS 288
12.1.9 FRAMINGHAM DATA 289
12.1.10NHANES DATA 290
12.1.11BAYESIAN DENSITY ESTIMATION BY NORMAL MIXTURES 291 12.2
NONPARAMETRIC REGRESSION 293
12.2.1 LOCAL-POLYNOMIAL, KERNEL-WEIGHTED REGRESSION 293 12.2.2 SPLINES
294
12.2.3 QVF AND LIKELIHOOD MODELS 295
12.2.4 SIMEX FOR NONPARAMETRIC REGRESSION 296 12.2.5 REGRESSION
CALIBRATION 297
12.2.6 STRUCTURAL SPLINES 297
12.2.7 TAYLEX AND OTHER METHODS 298
12.3 BASELINE CHANGE EXAMPLE 299
12.3.1 DISCUSSION OF THE BASELINE CHANGE CONTROLS DATA 301 BIBLIOGRAPHIC
NOTES 302
13 SEMIPARAMETRIC REGRESSION 303
IMAGE 8
13.1 OVERVIEW 303
13.2 ADDITIVE MODELS 303
13.3 MCMC FOR ADDITIVE SPLINE MODELS 304
13.4 MONTE CARLO EM-ALGORITHM 305
13.4.1 STARTING VALUES 306
13.4.2 METROPOLIS HASTINGS FACT 306
13.4.3 THE ALGORITHM 306
13.5 SIMULATION WITH CLASSICAL ERRORS 309
13.6 SIMULATION WITH BERKSON ERRORS 311
13.7 SEMIPARAMETRICS: X MODELED PARAMETRICALLY 312 13.8 PARAMETRIC
MODELS: NO ASSUMPTIONS ON X 314
13.8.1 DECONVOLUTION METHODS 314
13.8.2 MODELS LINEAR IN FUNCTIONS OF X 315
13.8.3 LINEAR LOGISTIC REGRESSION WITH REPLICATES 316 13.8.4 DOUBLY
ROBUST PARAMETRIC MODELING 317 BIBLIOGRAPHIC NOTES 318
14 SURVIVAL DATA 319
14.1 NOTATION AND ASSUMPTIONS 319
14.2 INDUCED HAZARD FUNCTION 320
14.3 REGRESSION CALIBRATION FOR SURVIVAL ANALYSIS 321 14.3.1 METHODOLOGY
AND ASYMPTOTIC PROPERTIES 321 14.3.2 RISK SET CALIBRATION 322
14.4 SIMEX FOR SURVIVAL ANALYSIS 323
14.5 CHRONIC KIDNEY DISEASE PROGRESSION 324
14.5.1 REGRESSION CALIBRATION FOR CKD PROGRESSION 325 14.5.2 SIMEX FOR
CKD PROGRESSION 326
14.6 SEMI AND NONPARAMETRIC METHODS 329
14.6.1 NONPARAMETRIC ESTIMATION WITH VALIDATION DATA 330 14.6.2
NONPARAMETRIC ESTIMATION WITH REPLICATED DATA 332 14.6.3 LIKELIHOOD
ESTIMATION 333
14.7 LIKELIHOOD INFERENCE FOR FRAILTY MODELS 336
BIBLIOGRAPHIC NOTES 337
15 RESPONSE VARIABLE ERROR 339
15.1 RESPONSE ERROR AND LINEAR REGRESSION 339
15.2 OTHER FORMS OF ADDITIVE RESPONSE ERROR 343
15.2.1 BIASED RESPONSES 343
15.2.2 RESPONSE ERROR IN HETEROSEEDASTIC REGRESSION 344 15.3 LOGISTIC
REGRESSION WITH RESPONSE ERROR 345
15.3.1 THE IMPACT OF RESPONSE MISCLASSIFICATION 345 15.3.2 CORRECTING
FOR RESPONSE MISCLASSIFICATION 347 15.4 LIKELIHOOD METHODS 353
IMAGE 9
15.4.1 GENERAL LIKELIHOOD THEORY AND SURROGATES 353
15.4.2 VALIDATION DATA 354
15.5 USE OF COMPLETE DATA ONLY 355
15.5.1 LIKELIHOOD OF THE VALIDATION DATA 355
15.5.2 OTHER METHODS 356
15.6 SEMIPARAMETRIC METHODS FOR VALIDATION DATA 356
15.6.1 SIMPLE RANDOM SAMPLING 356
15.6.2 OTHER TYPES OF SAMPLING 357
BIBLIOGRAPHIC NOTES 358
BACKGROUND MATERIAL 359
A.I OVERVIEW 359
A.2 NORMAL AND LOGNORMAL DISTRIBUTIONS 359
A.3 GAMMA AND INVERSE-GAMMA DISTRIBUTIONS 360
A.4 BEST AND BEST LINEAR PREDICTION AND REGRESSION 361
A.4.1 LINEAR PREDICTION 361
A.4.2 BEST LINEAR PREDICTION WITHOUT AN INTERCEPT 363 A.4.3 NONLINEAR
PREDICTION 363
A.5 LIKELIHOOD METHODS 364
A.5.1 NOTATION 364
A.5.2 MAXIMUM LIKELIHOOD ESTIMATION 364
A.5.3 LIKELIHOOD RATIO TESTS 365
A.5.4 PROFILE LIKELIHOOD AND LIKELIHOOD RATIO CONFIDENCE INTERVALS 365
A.5.5 EFFICIENT SCORE TESTS 366
A.6 UNBIASED ESTIMATING EQUATIONS 367
A.6.1 INTRODUCTION AND BASIC LARGE SAMPLE THEORY 367 A.6.2 SANDWICH
FORMULA EXAMPLE: LINEAR REGRESSION WITHOUT MEASUREMENT ERROR 369
A.6.3 SANDWICH METHOD AND LIKELIHOOD-TYPE INFERENCE 370 A.6.4 UNBIASED,
BUT CONDITIONALLY BIASED, ESTIMATING EQUATIONS 372
A.6.5 BIASED ESTIMATING EQUATIONS 372
A.6.6 STACKING ESTIMATING EQUATIONS: USING PRIOR ESTI- MATES OF SOME
PARAMETERS 372
A.7 QUASILIKELIHOOD AND VARIANCE FUNCTION MODELS (QVF) 374 A.7.1 GENERAL
IDEAS 374
A.7.2 ESTIMATION AND INFERENCE FOR QVF MODELS 375
A.8 GENERALIZED LINEAR MODELS 377
A.9 BOOTSTRAP METHODS 377
A.9.1 INTRODUCTION 377
A.9.2 NONLINEAR REGRESSION WITHOUT MEASUREMENT ERROR 378 A.9.3
BOOTSTRAPPING HETEROSCEDASTIC REGRESSION MODELS 380
IMAGE 10
A.9.4 BOOTSTRAPPING LOGISTIC REGRESSION MODELS 380
A.9.5 BOOTSTRAPPING MEASUREMENT ERROR MODELS 381 A.9.6 BOOTSTRAP
CONFIDENCE INTERVALS 382
B TECHNICAL DETAILS 385
B.I APPENDIX TO CHAPTER 1: POWER IN BERKSON AND CLASSICAL ERROR MODELS
385
B.2 APPENDIX TO CHAPTER 3: LINEAR REGRESSION AND ATTENUA- TION 386
B.3 APPENDIX TO CHAPTER 4: REGRESSION CALIBRATION 387 B.3.1 STANDARD
ERRORS AND REPLICATION 387
B.3.2 QUADRATIC REGRESSION: DETAILS OF THE EXPANDED CALIBRATION MODEL
391
B.3.3 HEURISTICS AND ACCURACY OF THE APPROXIMATIONS 391 B.4 APPENDIX TO
CHAPTER 5: SIMEX 392
B.4.1 SIMULATION EXTRAPOLATION VARIANCE ESTIMATION 393 B.4.2 ESTIMATING
EQUATION APPROACH TO VARIANCE ESTI- MATION 395
B.5 APPENDIX TO CHAPTER 6: INSTRUMENTAL VARIABLES 399 B.5.1 DERIVATION
OF THE ESTIMATORS 399
B.5.2 ASYMPTOTIC DISTRIBUTION APPROXIMATIONS 401 B.6 APPENDIX TO CHAPTER
7: SCORE FUNCTION METHODS 406 B.6.1 TECHNICAL COMPLEMENTS TO CONDITIONAL
SCORE THEORY 406
B.6.2 TECHNICAL COMPLEMENTS TO DISTRIBUTION THEORY FOR ESTIMATED ** 406
B.7 APPENDIX TO CHAPTER 8: LIKELIHOOD AND QUASILIKELIHOOD 407 B.7.1
MONTE CARLO COMPUTATION OF INTEGRALS 407 B.7.2 LINEAR, PROBIT, AND
LOGISTIC REGRESSION 408 B.8 APPENDIX TO CHAPTER 9: BAYESIAN METHODS 409
B.8.1 CODE FOR SECTION 9.8.1 409
B.8.2 CODE FOR SECTION 9.11 410
REFERENCES 413
APPLICATIONS AND EXAMPLES INDEX 439
AUTHOR INDEX 441
SUBJECT INDEX 447 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author_GND | (DE-588)111805708 |
| building | Verbundindex |
| bvnumber | BV021780825 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278.2 |
| callnumber-search | QA278.2 |
| callnumber-sort | QA 3278.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 234 SK 800 SK 840 |
| ctrlnum | (OCoLC)67405697 (DE-599)BVBBV021780825 |
| dewey-full | 519.5/36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/36 |
| dewey-search | 519.5/36 |
| dewey-sort | 3519.5 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021780825 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:41:29Z |
| indexdate | 2024-07-09T20:43:56Z |
| institution | BVB |
| isbn | 1584886331 9781584886334 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014993599 |
| oclc_num | 67405697 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-188 DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-188 DE-11 |
| physical | XXVIII, 455 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Measurement error in nonlinear models a modern perspective Raymond. J. Carroll ... 2. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2006 XXVIII, 455 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 105 Analyse de régression Modelos não lineares (pesquisa e planejamento) larpcal Pesquisa e planejamento estatístico larpcal Théories non linéaires Nonlinear theories Regression analysis Messfehler (DE-588)4133270-2 gnd rswk-swf Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd rswk-swf Nichtlineares mathematisches Modell (DE-588)4127859-8 gnd rswk-swf Nichtlineares mathematisches Modell (DE-588)4127859-8 s Messfehler (DE-588)4133270-2 s DE-604 Nichtlineares Regressionsmodell (DE-588)4251078-8 s Carroll, Raymond J. 1949- Sonstige (DE-588)111805708 oth Monographs on statistics and applied probability 105 (DE-604)BV002494005 105 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014993599&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Measurement error in nonlinear models a modern perspective Monographs on statistics and applied probability Analyse de régression Modelos não lineares (pesquisa e planejamento) larpcal Pesquisa e planejamento estatístico larpcal Théories non linéaires Nonlinear theories Regression analysis Messfehler (DE-588)4133270-2 gnd Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd Nichtlineares mathematisches Modell (DE-588)4127859-8 gnd |
| subject_GND | (DE-588)4133270-2 (DE-588)4251078-8 (DE-588)4127859-8 |
| title | Measurement error in nonlinear models a modern perspective |
| title_auth | Measurement error in nonlinear models a modern perspective |
| title_exact_search | Measurement error in nonlinear models a modern perspective |
| title_exact_search_txtP | Measurement error in nonlinear models a modern perspective |
| title_full | Measurement error in nonlinear models a modern perspective Raymond. J. Carroll ... |
| title_fullStr | Measurement error in nonlinear models a modern perspective Raymond. J. Carroll ... |
| title_full_unstemmed | Measurement error in nonlinear models a modern perspective Raymond. J. Carroll ... |
| title_short | Measurement error in nonlinear models |
| title_sort | measurement error in nonlinear models a modern perspective |
| title_sub | a modern perspective |
| topic | Analyse de régression Modelos não lineares (pesquisa e planejamento) larpcal Pesquisa e planejamento estatístico larpcal Théories non linéaires Nonlinear theories Regression analysis Messfehler (DE-588)4133270-2 gnd Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd Nichtlineares mathematisches Modell (DE-588)4127859-8 gnd |
| topic_facet | Analyse de régression Modelos não lineares (pesquisa e planejamento) Pesquisa e planejamento estatístico Théories non linéaires Nonlinear theories Regression analysis Messfehler Nichtlineares Regressionsmodell Nichtlineares mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014993599&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT carrollraymondj measurementerrorinnonlinearmodelsamodernperspective |