Measurement error: models, methods, and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2010
|
| Series: | Chapman & Hall, CRC interdisciplinary statistics series
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXVI, 437 S. graph. Darst. |
| ISBN: | 9781420066562 |
Staff View
MARC
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| 245 | 1 | 0 | |a Measurement error |b models, methods, and applications |c John P. Buonaccorsi |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2010 | |
| 300 | |a XXVI, 437 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Chapman & Hall, CRC interdisciplinary statistics series | |
| 490 | 0 | |a A Chapman & Hall book | |
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Record in the Search Index
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| adam_text | П.ШГ
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Contents
Preface
xix
List of Examples
xxv
1
Introduction
1
1.1
What is measurement error?
1
1.2
Some examples
1
1.3
The main ingredients
4
1.4
Some terminology
5
1.4.1
Measurement versus Berkson error models
6
1.4.2
Measurement error models for quantitative values
7
1.4.3
Nondifferential/differential measurement error, condi¬
tional independence and surrogacy
7
1.5
A look ahead
8
2
Misclassiflcation in Estimating a Proportion
11
2.1
Motivating examples
11
2.2
A model for the true values
14
2.3
Misclassification models and naive analyses
14
2.4
Correcting for misclassification
17
2.4.1
Ignoring uncertainty in the misclassification rates
17
2.4.2
Using external validation data and misclassification
rates
19
x
CONTENTS
2.4.3
Internal validation data and the use of reclassification
rates
22
2.5
Finite populations
25
2.6
Multiple measures with no direct validation
27
2.7
The multinomial case
28
2.8
Mathematical developments
30
3
Misclassification in Two-Way Tables
33
3.1
Introduction
33
3.2
Models for true values
35
3.3
Misclassification models and naive estimators
38
3.4
Behavior of naive analyses
40
3.4.1
Misclassification in X only
40
3.4.2
Misclassification in
Y
only
46
3.4.3
Misclassification in X and
Y
both
47
3.5
Correcting using external validation data
48
3.5.1
Misclassification in X only
49
3.5.2
Misclassification in
Y
only
55
3.5.3
Misclassification in X and
Y
both
57
3.6
Correcting using internal validation data
58
3.6.1
Misclassification in X only
60
3.6.2
Misclassification in
Y
only
65
3.6.3
Misclassification in X and
Y
both
65
3.7
General two-way tables
66
3.8
Mathematical developments
68
3.8.1
Some expected values
68
3.8.2
Estimation using internal validation data
69
3.8.3
Results for
co
variance matrices
69
CONTENTS xi
4 Simple Linear Regression 73
4.1
Introduction
73
4.2 The additive Berkson
model and consequences
76
4.3 The additive
measurement error model
77
4.4
The behavior of naive analyses
79
4.5
Correcting for additive measurement error
83
4.5.1
Moment-based corrected estimators
84
4.5.2
Inferences for regression coefficients
86
4.5.3
Replication
89
4.6
Examples
90
4.6.1
Nitrogen-yield example
90
4.6.2
Defoliation example with error in both variables
93
4.7
Residual analysis
94
4.8
Prediction
96
4.9
Mathematical developments
102
5
Multiple Linear Regression
105
5.1
Introduction
105
5.2
Model for true values
106
5.3
Models and bias in naive estimators
107
5.4
Correcting for measurement error
114
5.4.1
Moment corrected estimators
115
5.4.2
Sampling properties and approximate inferences
116
5.4.3
Replication
118
5.4.4
Correction for negative estimates
121
5.4.5
Residual analysis and prediction
122
5.5
Weighted and other estimators
122
5.6
Examples
124
5.6.1
Defoliation example revisited
124
5.6.2
LA data with error in one variable
126
xii CONTENTS
5.6.3
House price example
129
5.7
Instrumental variables
130
5.7.1
Example
135
5.8
Mathematical developments
136
5.8.1
Motivation for moment corrections
136
5.8.2
Defining terms for general combinations of predictors
138
5.8.3
Approximate covariance of estimated coefficients
139
5.8.4
Instrumental variables
141
6
Measurement Error in Regression: A General Overview
143
6.1
Introduction
143
6.2
Models for true values
144
6.3
Analyses without measurement error
148
6.4
Measurement error models
149
6.4.1
General concepts and notation
149
6.4.2
Linear and additive measurement error models
151
6.4.3
The linear Berkson model
152
6.4.4
Nonlinear measurement error models
154
6.4.5
Heteroscedastic measurement error
154
6.4.6
Multiplicative measurement error
158
6.4.7
Working with logs
159
6.4.8
Misclassification from categorizing a quantitative
variable
160
6.5
Extra data
163
6.5.1
Replicate values
163
6.5.2
External replicates: Are reliability ratios exportable?
168
6.5.3
Internal validation data
169
6.5.4
External validation data
171
6.5.5
Other types of data
172
6.6
Assessing bias in naive estimators
173
CONTENTS xiii
6.7
Assessing bias using induced models
174
6.7.1
Linear regression with linear Berkson error
175
6.7.2
Second order models with linear Berkson error
176
6.7.3
Exponential models with normal linear Berkson error
177
6.7.4
Approximate induced regression models
178
6.7.5
Generalized linear models
178
6.7.6
Binary regression
179
6.7.7
Linear regression with misclassification of a binary
predictor
182
6.8
Assessing bias via estimating equations
186
6.9
Moment-based and direct bias corrections
189
6.9.1
Linearly transforming the naive estimates
190
6.10
Regression calibration and quasi-likelihood methods
191
6.11
Simulation extrapolation (SIMEX)
194
6.12
Correcting using likelihood methods
196
6.12.1
Likelihoods from the main data
198
6.12.2
Likelihood methods with validation data
200
6.12.3
Likelihood methods with replicate data
203
6.13
Modified estimating equation approaches
204
6.13.1
Introduction
204
6.13.2
Basic method and fitting algorithm
206
6.13.3
Further details
208
6.14
Correcting for misclassification
209
6.15
Overview on use of validation data
211
6.15.1
Using external validation data
211
6.15.2
Using internal validation data
213
6.16
Bootstrapping
215
6.16.1
Additive error
216
6.16.2
Bootstrapping with validation data
218
6.17
Mathematical developments
219
xiv CONTENTS
6.17.1
Justifying the
MEE fitting
method
219
6.17.2
The approximate covariance for linearly transformed
coefficients
220
6.17.3
The approximate covariance of pseudo-estimators
221
6.17.4
Asymptotics for ML and pseudo-ML estimators with
external validation.
222
7
Binary Regression
223
7.1
Introduction
223
7.2
Additive measurement error
224
7.2.1
Methods
224
7.2.2
Example: Cholesterol and heart disease
231
7.2.3
Example: Heart disease with multiple predictors
241
7.2.4
Notes on ecological applications
243
7.2.5
Fitting with logs
243
7.3
Using validation data
247
7.3.1
Two examples using external validation and the Berk-
son model
248
7.3.2
Fitting with internal validation data and the Berkson
model
250
7.3.3
Using external validation data and the measurement
error model
252
7.4
Misclassification of predictors
256
8
Linear Models with
Nonadditive
Error
259
8.1
Introduction
259
8.2
Quadratic regression
260
8.2.1
Biases in naive estimators
261
8.2.2
Correcting for measurement error
265
8.2.3
Paper example
267
8.2.4
Additive error in the response
272
8.2.5
Quadratic models with additional predictors
272
CONTENTS xv
8.3 First
order models with interaction
275
8.3.1
Bias in naive estimators
277
8.3.2
Correcting for measurement error
279
8.3.3
Example
281
8.3.4
More general interaction models
284
8.4
General nonlinear functions of the predictors
286
8.4.1
Bias of naive estimators
287
8.4.2
Correcting for measurement error
288
8.4.3
Linear regression in log(x)
291
8.5
Linear measurement error with validation data
298
8.5.1
Models and bias in naive estimators
298
8.5.2
Correcting with external validation data
301
8.5.3
External validation example
303
8.5.4
Correcting with internal validation
304
8.5.5
Internal validation example
306
8.6
Misclassification of a categorical predictor
309
8.6.1
Introduction and bias of naive estimator
309
8.6.2
Correcting for misclassification
312
8.6.3
Further details
314
8.7
Miscellaneous
315
8.7.1
Bias expressions for naive estimators
315
8.7.2
Likelihood methods in linear models
317
9
Nonlinear Regression
319
9.1
Poisson
regression: Cigarettes and cancer rates
319
9.2
General nonlinear models
322
xvi CONTENTS
10
Error in the Response
325
10.1
Introduction
325
10.2
Additive error in a single sample
325
10.2.1
Estimating the mean and variance
327
10.2.2
Estimating the mean-variance relationship
329
10.2.3
Nonparametric estimation of the distribution
333
10.2.4
Example
338
10.3
Linear measurement error in the one-way setting
341
10.3.1
One measuring method per group
345
10.3.2
General designs
349
10.4
Measurement error in the response in linear models
350
10.4.1
Models
351
10.4.2
Correcting for measurement error
353
10.4.3
Example
356
10.4.4
Further detail
358
11
Mixed/Longitudinal Models
361
11.1
Introduction, overview and some examples
361
11.2
Berkson error in designed repeated measures
366
11.2.1
Bias in naive estimators
370
11.2.2
Correcting for measurement error
375
11.3
Additive error in the linear mixed model
377
11.3.1
Naive estimators and induced models
377
11.3.2
Correcting for measurement error with no additional
data
378
11.3.3
Correcting for measurement error with additional data
382
CONTENTS xvii
12
Time Series
385
12.1
Introduction
385
12.2
Random walk/population viability models
387
12.2.1
Properties of naive analyses
389
12.2.2
Correcting for measurement error
389
12.2.3
Example
395
12.3
Linear
autoregressive
models
398
12.3.1
Properties of naive estimators
399
12.3.2
Correcting for measurement error
401
12.3.3
Examples
405
13
Background Material
409
13.1
Notation for vectors, covariance matrices, etc.
409
13.2
Double expectations
409
13.3
Approximate
Wald
inferences
410
13.4
The delta-method: Approximate moments of nonlinear func¬
tions
410
13.5
Fieller s method for ratios
411
References
413
Author index
429
Subject index
435
|
| any_adam_object | 1 |
| author | Buonaccorsi, John P. |
| author_GND | (DE-588)1037692160 |
| author_facet | Buonaccorsi, John P. |
| author_role | aut |
| author_sort | Buonaccorsi, John P. |
| author_variant | j p b jp jpb |
| building | Verbundindex |
| bvnumber | BV036064567 |
| callnumber-first | Q - Science |
| callnumber-label | QA275 |
| callnumber-raw | QA275 |
| callnumber-search | QA275 |
| callnumber-sort | QA 3275 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 234 UX 1100 |
| ctrlnum | (OCoLC)156812681 (DE-599)BVBBV036064567 |
| dewey-full | 511/.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.43 |
| dewey-search | 511/.43 |
| dewey-sort | 3511 243 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV036064567 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:10:40Z |
| institution | BVB |
| isbn | 9781420066562 |
| language | English |
| lccn | 2009048849 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018955971 |
| oclc_num | 156812681 |
| open_access_boolean | |
| owner | DE-20 DE-19 DE-BY-UBM DE-739 DE-83 |
| owner_facet | DE-20 DE-19 DE-BY-UBM DE-739 DE-83 |
| physical | XXVI, 437 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Chapman & Hall, CRC interdisciplinary statistics series A Chapman & Hall book |
| spelling | Buonaccorsi, John P. Verfasser (DE-588)1037692160 aut Measurement error models, methods, and applications John P. Buonaccorsi Boca Raton [u.a.] CRC Press 2010 XXVI, 437 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall, CRC interdisciplinary statistics series A Chapman & Hall book Error analysis (Mathematics) Fehlerrechnung (DE-588)4153837-7 gnd rswk-swf Fehleranalyse (DE-588)4016608-9 gnd rswk-swf Messunsicherheit (DE-588)4210374-5 gnd rswk-swf Messfehler (DE-588)4133270-2 gnd rswk-swf Messunsicherheit (DE-588)4210374-5 s DE-604 Messfehler (DE-588)4133270-2 s Fehlerrechnung (DE-588)4153837-7 s Fehleranalyse (DE-588)4016608-9 s Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018955971&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018955971&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Buonaccorsi, John P. Measurement error models, methods, and applications Error analysis (Mathematics) Fehlerrechnung (DE-588)4153837-7 gnd Fehleranalyse (DE-588)4016608-9 gnd Messunsicherheit (DE-588)4210374-5 gnd Messfehler (DE-588)4133270-2 gnd |
| subject_GND | (DE-588)4153837-7 (DE-588)4016608-9 (DE-588)4210374-5 (DE-588)4133270-2 |
| title | Measurement error models, methods, and applications |
| title_auth | Measurement error models, methods, and applications |
| title_exact_search | Measurement error models, methods, and applications |
| title_full | Measurement error models, methods, and applications John P. Buonaccorsi |
| title_fullStr | Measurement error models, methods, and applications John P. Buonaccorsi |
| title_full_unstemmed | Measurement error models, methods, and applications John P. Buonaccorsi |
| title_short | Measurement error |
| title_sort | measurement error models methods and applications |
| title_sub | models, methods, and applications |
| topic | Error analysis (Mathematics) Fehlerrechnung (DE-588)4153837-7 gnd Fehleranalyse (DE-588)4016608-9 gnd Messunsicherheit (DE-588)4210374-5 gnd Messfehler (DE-588)4133270-2 gnd |
| topic_facet | Error analysis (Mathematics) Fehlerrechnung Fehleranalyse Messunsicherheit Messfehler |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018955971&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018955971&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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