On errors-in-variables for binary regression models

Carroll, Raymond J.; Spiegelman, Clifford H.; Lan, K. K. Gordon; Bailey, Kent T.; Abbott, Robert D.

doi:10.1093/biomet/71.1.19

Cited by 196 publications

(63 citation statements)

References 10 publications

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“…Indeed, the case of normally distributed covariates with normally distributed errors (Carroll et al 1984;Schafer 1987 has received the most attention. The usefulness of these methods is limited by the fact that they may not be robust for alternative measurement error structures.…”

Section: Discussionmentioning

confidence: 99%

A Nonparametric Method for Dealing with Mismeasured Covariate Data

Pepe

Fleming

1991

Journal of the American Statistical Association

166

105

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Mismeasurement of covariate data is a frequent problem in statistical data analysis. However, when true and mismeasured data are obtained for a subsample of the observations, it is possible to estimate the parameters relating the outcome to the covariate of interest. Maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success. Realistic models for the mismeasurement process are difficult to construct; the form of the likelihood is often intractable and, more important, such methods are not robust to model misspecification. We propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data, errors in variables, or use of imperfect surrogate covariates. Specifically, denote the outcome variable by Y, the covariate data subject to mismeasurement by X, and the remaining covariates, including perhaps surrogates or mismeasured values of X, by Z. We consider a general regression model of the form P~(Y IX, Z). Suppose data regarding Y, X, and Z are available for a validation sample V, a random subsample of the total sample, whereas data regarding only Y and Z are available for the remainder, the nonvalidation sample V. We propose to base inference on the estimated likelihood for {3, L(f3) = ",EV P~(Yi IXi' Zi) lljEV P~(Yj IZ), where P~(Yj IZ) is estimated empirically using the validation sample covariate data. Asymptotic results are derived for the case in which the surrogate or mismeasured covariates are categorical. The asymptotic variance of the estimated score involves not only the second derivative of the log estimated likelihood but also a term that captures the variability induced by estimating the nonvalidation sample likelihood. An example and a small simulation study demonstrate that this method may be of value for the missing covariate data and covariate measurement error problems.

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Section: Discussionmentioning

confidence: 99%

A Nonparametric Method for Dealing with Mismeasured Covariate Data

Pepe

Fleming

1991

Journal of the American Statistical Association

166

105

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“…, x, represent unknown fixed parameters and when they represent independent random variables having some parametric distribution (e.g., Cochran 1968;Fuller 1987;Gleser 1981;Kelly 1984;Robertson 1974;Ware 1972). Although most of the results have been based on Gaussian assumptions for response and true and measured covariates, recent attention has turned to other distributional assumptions for these variables and to nonlinear regression models relating response to the true covariate (Burr-Doss 1985;Carroll, Spiegelman, Lan, Bailey, and Abbot 1984;Prentice 1982Prentice , 1986Wolter and Fuller 1982). The computations needed, however, to obtain maximum likelihood or maximum quasilikelihood parameter estimates in this more general setting typically are arduous or intractable (e.g., Carroll et al 1984;Prentice 1986).…”

Section: Discussionmentioning

confidence: 99%

“…Although most of the results have been based on Gaussian assumptions for response and true and measured covariates, recent attention has turned to other distributional assumptions for these variables and to nonlinear regression models relating response to the true covariate (Burr-Doss 1985;Carroll, Spiegelman, Lan, Bailey, and Abbot 1984;Prentice 1982Prentice , 1986Wolter and Fuller 1982). The computations needed, however, to obtain maximum likelihood or maximum quasilikelihood parameter estimates in this more general setting typically are arduous or intractable (e.g., Carroll et al 1984;Prentice 1986). The difficulty in computing these estimates has prompted the development of approximations to them, some of which are valid only when the covariate measurement error is small (Stafanski 1985;Whittemore and Keller 1988).…”

Section: Discussionmentioning

confidence: 99%

Errors-in-Variables Regression Using Stein Estimates

Whittemore

1989

The American Statistician

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A method is proposed for estimating regression parameters from data containing covariate measurement errors by using Stein estimates of the unobserved true covariates. The method produces consistent estimates for the slope parameter in the classical linear errors-in-variables model and applies to a broad range of nonlinear regression problems, provided the measurement error is Gaussian with known variance. Simulations are used to examine the performance of the estimates in a nonlinear regression problem and to compare them with the usual naive ones obtained by ignoring error and with other estimates proposed recently in the literature.

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“…The related work can be found in Anderson [1], Carroll et al [8], Stefanski [23], Fan and Truong [13] among others. The problem with error-in-response has received less attention, mainly because when the measurement error is additive, standard methodology can be used to handle this case.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric regression function estimation with surrogate data and validation sampling

Wang

2006

Journal of Multivariate Analysis

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This paper develops estimation approaches for nonparametric regression analysis with surrogate data and validation sampling when response variables are measured with errors. Without assuming any error model structure between the true responses and the surrogate variables, a regression calibration kernel regression estimate is defined with the help of validation data. The proposed estimator is proved to be asymptotically normal and the convergence rate is also derived. A simulation study is conducted to compare the proposed estimators with the standard Nadaraya-Watson estimators with the true observations in the validation data set and the complete observations, respectively. The Nadaraya-Watson estimator with the complete observations can serve as a gold standard, even though it is practically unachievable because of the measurement errors.

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On errors-in-variables for binary regression models

Cited by 196 publications

References 10 publications

A Nonparametric Method for Dealing with Mismeasured Covariate Data

A Nonparametric Method for Dealing with Mismeasured Covariate Data

Errors-in-Variables Regression Using Stein Estimates

Nonparametric regression function estimation with surrogate data and validation sampling

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