Model‐based bootstrapping when correcting for measurement error with application to logistic regression

Model‐based bootstrapping when correcting for measurement error with application to logistic... IntroductionIn fitting regression models, measurement error in predictors may result in biased estimates of coefficients and other incorrect inferences. This problem has received a tremendous amount of attention (see, e.g., Buonaccorsi, ; Carroll et al., ; Gustafson, ; Fuller, for general treatments) and a plethora of correction techniques have been proposed for both linear and non‐linear models. Inferences can be challenging for a variety of reasons. While analytical standard errors are available for some methods these are approximate in nature and usually involve some underlying assumptions. Relatedly, Wald type confidence intervals based on these standard errors rely on approximate normality and unbiasedness of the estimator involved. An additional concern is that the corrected estimators are not unbiased; rather, most are either consistent, or approximately consistent, under suitable conditions. A data driven way of assessing potential bias in either the corrected estimators or naive estimators, which ignore the measurement error, is desirable.One obvious tool for attacking these problems is the bootstrap, which has received limited attention in the measurement error context. The majority of the applications of the bootstrap in measurement error problems have used simple with replacement resampling of observations. This is used in STATA, one of the few http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Biometrics Wiley

Model‐based bootstrapping when correcting for measurement error with application to logistic regression

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Publisher
Wiley
Copyright
© 2018, The International Biometric Society
ISSN
0006-341X
eISSN
1541-0420
D.O.I.
10.1111/biom.12730
Publisher site
See Article on Publisher Site

Abstract

IntroductionIn fitting regression models, measurement error in predictors may result in biased estimates of coefficients and other incorrect inferences. This problem has received a tremendous amount of attention (see, e.g., Buonaccorsi, ; Carroll et al., ; Gustafson, ; Fuller, for general treatments) and a plethora of correction techniques have been proposed for both linear and non‐linear models. Inferences can be challenging for a variety of reasons. While analytical standard errors are available for some methods these are approximate in nature and usually involve some underlying assumptions. Relatedly, Wald type confidence intervals based on these standard errors rely on approximate normality and unbiasedness of the estimator involved. An additional concern is that the corrected estimators are not unbiased; rather, most are either consistent, or approximately consistent, under suitable conditions. A data driven way of assessing potential bias in either the corrected estimators or naive estimators, which ignore the measurement error, is desirable.One obvious tool for attacking these problems is the bootstrap, which has received limited attention in the measurement error context. The majority of the applications of the bootstrap in measurement error problems have used simple with replacement resampling of observations. This is used in STATA, one of the few

Journal

BiometricsWiley

Published: Jan 1, 2018

Keywords: ; ; ;

References

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