Measurement Error: Models, Methods, and Applications (Chapman & Hall CRC Interdisciplinary Statistics Series)

Cover Page......Page 1
CHAPMAN & HALL/CRC Interdisciplinary Statistics Series......Page 3
Title Page......Page 5
ISBN 9781420066562......Page 6
Contents......Page 8
Preface......Page 17
List of Examples......Page 22
1.2 Some examples......Page 24
1.3 The main ingredients......Page 27
1.4 Some terminology......Page 28
1.4.1 Measurement versus Berkson error models......Page 29
1.4.3 Nondifferential/differential measurement error, conditional independence and surrogacy......Page 30
1.5 A look ahead......Page 31
2.1 Motivating examples......Page 34
2.3 Misclassification models and naive analyses......Page 37
2.4.1 Ignoring uncertainty in the misclassification rates......Page 40
2.4.2 Using external validation data and misclassification rates......Page 42
2.4.3 Internal validation data and the use of reclassification rates......Page 45
2.5 Finite populations......Page 48
2.6 Multiple measures with no direct validation......Page 50
2.7 The multinomial case......Page 51
2.8 Mathematical developments......Page 53
3.1 Introduction......Page 56
3.2 Models for true values......Page 58
3.3 Misclassification models and naive estimators......Page 61
3.4.1 Misclassification in X only......Page 63
3.4.2 Misclassification in Y only......Page 69
3.4.3 Misclassification in X and Y both......Page 70
3.5 Correcting using external validation data......Page 71
3.5.1 Misclassification in X only......Page 72
3.5.2 Misclassification in Y only......Page 78
3.5.3 Misclassification in X and Y both......Page 80
3.6 Correcting using internal validation data......Page 81
3.6.1 Misclassification in X only......Page 83
3.6.3 Misclassification in X and Y both......Page 88
3.7 General two-way tables......Page 89
3.8.1 Some expected values......Page 91
3.8.3 Results for covariance matrices......Page 92
4.1 Introduction......Page 96
4.2 The additive Berkson model and consequences......Page 99
4.3 The additive measurement error model......Page 100
4.4 The behavior of naive analyses......Page 102
4.5 Correcting for additive measurement error......Page 106
4.5.1 Moment-based corrected estimators......Page 107
4.5.2 Inferences for regression coefficients......Page 109
4.5.3 Replication......Page 112
4.6.1 Nitrogen-yield example......Page 113
4.6.2 Defoliation example with error in both variables......Page 116
4.7 Residual analysis......Page 117
4.8 Prediction......Page 119
4.9 Mathematical developments......Page 125
5.1 Introduction......Page 128
5.2 Model for true values......Page 129
5.3 Models and bias in naive estimators......Page 130
5.4 Correcting for measurement error......Page 137
5.4.1 Moment corrected estimators......Page 138
5.4.2 Sampling properties and approximate inferences......Page 139
5.4.3 Replication......Page 141
5.4.4 Correction for negative estimates......Page 144
5.5 Weighted and other estimators......Page 145
5.6.1 Defoliation example revisited......Page 147
5.6.2 LA data with error in one variable......Page 149
5.6.3 House price example......Page 152
5.7 Instrumental variables......Page 153
5.7.1 Example......Page 158
5.8.1 Motivation for moment corrections......Page 159
5.8.2 Defining terms for general combinations of predictors......Page 161
5.8.3 Approximate covariance of estimated coefficients......Page 162
5.8.4 Instrumental variables......Page 164
6.1 Introduction......Page 166
6.2 Models for true values......Page 167
6.3 Analyses without measurement error......Page 171
6.4.1 General concepts and notation......Page 172
6.4.2 Linear and additive measurement error models......Page 174
6.4.3 The linear Berkson model......Page 175
6.4.5 Heteroscedastic measurement error......Page 177
6.4.6 Multiplicative measurement error......Page 181
6.4.7 Working with logs......Page 182
6.4.8 Misclassification from categorizing a quantitative variable......Page 183
6.5.1 Replicate values......Page 186
6.5.2 External replicates: Are reliability ratios exportable?......Page 191
6.5.3 Internal validation data......Page 192
6.5.4 External validation data......Page 194
6.5.5 Other types of data......Page 195
6.6 Assessing bias in naive estimators......Page 196
6.7 Assessing bias using induced models......Page 197
6.7.1 Linear regression with linear Berkson error......Page 198
6.7.2 Second order models with linear Berkson error......Page 199
6.7.3 Exponential models with normal linear Berkson error......Page 200
6.7.5 Generalized linear models......Page 201
6.7.6 Binary regression......Page 202
6.7.7 Linear regression with misclassification of a binary predictor......Page 205
6.8 Assessing bias via estimating equations......Page 209
6.9 Moment-based and direct bias corrections......Page 212
6.9.1 Linearly transforming the naive estimates......Page 213
6.10 Regression calibration and quasi-likelihood methods......Page 214
6.11 Simulation extrapolation (SIMEX)......Page 217
6.12 Correcting using likelihood methods......Page 219
6.12.1 Likelihoods from the main data......Page 221
6.12.2 Likelihood methods with validation data......Page 223
6.12.3 Likelihood methods with replicate data......Page 226
6.13.1 Introduction......Page 227
6.13.2 Basic method and fitting algorithm......Page 229
6.13.3 Further details......Page 231
6.14 Correcting for misclassification......Page 232
6.15.1 Using external validation data......Page 234
6.15.2 Using internal validation data......Page 236
6.16 Bootstrapping......Page 238
6.16.1 Additive error......Page 239
6.16.2 Bootstrapping with validation data......Page 241
6.17.1 Justifying the MEE fitting method......Page 242
6.17.2 The approximate covariance for linearly transformed coefficients......Page 243
6.17.3 The approximate covariance of pseudo-estimators......Page 244
6.17.4 Asymptotics for ML and pseudo-ML estimators with external validation......Page 245
7.1 Introduction......Page 246
7.2.1 Methods......Page 247
7.2.2 Example: Cholesterol and heart disease......Page 254
7.2.3 Example: Heart disease with multiple predictors......Page 264
7.2.5 Fitting with logs......Page 266
7.3 Using validation data......Page 270
7.3.1 Two examples using external validation and the Berkson model......Page 271
7.3.2 Fitting with internal validation data and the Berkson model......Page 273
7.3.3 Using external validation data and the measurement error model......Page 275
7.4 Misclassification of predictors......Page 279
8.1 Introduction......Page 282
8.2 Quadratic regression......Page 283
8.2.1 Biases in naive estimators......Page 284
8.2.2 Correcting for measurement error......Page 288
8.2.3 Paper example......Page 290
8.2.5 Quadratic models with additional predictors......Page 295
8.3 First order models with interaction......Page 298
8.3.1 Bias in naive estimators......Page 300
8.3.2 Correcting for measurement error......Page 302
8.3.3 Example......Page 304
8.3.4 More general interaction models......Page 307
8.4 General nonlinear functions of the predictors......Page 309
8.4.1 Bias of naive estimators......Page 310
8.4.2 Correcting for measurement error......Page 311
8.4.3 Linear regression in log(x)......Page 314
8.5.1 Models and bias in naive estimators......Page 321
8.5.2 Correcting with external validation data......Page 324
8.5.3 External validation example......Page 326
8.5.4 Correcting with internal validation......Page 327
8.5.5 Internal validation example......Page 329
8.6.1 Introduction and bias of naive estimator......Page 332
8.6.2 Correcting for misclassification......Page 335
8.6.3 Further details......Page 337
8.7.1 Bias expressions for naive estimators......Page 338
8.7.2 Likelihood methods in linear models......Page 340
9.1 Poisson regression: Cigarettes and cancer rates......Page 342
9.2 General nonlinear models......Page 345
10.2 Additive error in a single sample......Page 348
10.2.1 Estimating the mean and variance......Page 350
10.2.2 Estimating the mean-variance relationship......Page 352
10.2.3 Nonparametric estimation of the distribution......Page 356
10.2.4 Example......Page 361
10.3 Linear measurement error in the one-way setting......Page 364
10.3.1 One measuring method per group......Page 368
10.3.2 General designs......Page 372
10.4 Measurement error in the response in linear models......Page 373
10.4.1 Models......Page 374
10.4.2 Correcting for measurement error......Page 376
10.4.3 Example......Page 379
10.4.4 Further detail......Page 381
11.1 Introduction, overview and some examples......Page 384
11.2 Berkson error in designed repeated measures......Page 389
11.2.1 Bias in naive estimators......Page 393
11.2.2 Correcting for measurement error......Page 398
11.3.1 Naive estimators and induced models......Page 400
11.3.2 Correcting for measurement error with no additional data......Page 401
11.3.3 Correcting for measurement error with additional data......Page 405
12.1 Introduction......Page 408
12.2 Random walk/population viability models......Page 410
12.2.2 Correcting for measurement error......Page 412
12.2.3 Example......Page 418
12.3 Linear autoregressive models......Page 421
12.3.1 Properties of naive estimators......Page 422
12.3.2 Correcting for measurement error......Page 424
12.3.3 Examples......Page 428
13.2 Double expectations......Page 432
13.4 The delta-method: Approximate moments of nonlinear functions......Page 433
13.5 Fieller\'s method for ratios......Page 434
References......Page 436
Author index......Page 452
Subject index......Page 458
Back Page......Page 461