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Biometrika 1984 71(1):19-25; doi:10.1093/biomet/71.1.19
© 1984 by Biometrika Trust
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On errors-in-variables for binary regression models

RAYMOND J. CARROLL, CLIFFORD H. SPIEGELMAN, K. K. GORDON LAN, KENT T. BAILEY and ROBERT D. ABBOTT

Department of Statistics, University of North Carolina Chapel Hill, North Carolina, U.S.A.
Statistical Engineering Division, National Bureau of Standards Washington, D.C., U.S.A.
National Heart, Lung and Blood Institute Bethesda, Maryland, U.S.A.

We consider binary regression models when some of the predictors are measured with error. For normal measurement errors, structural maximum likelihood estimates are considered. We show that if the measurement error is large, the usual estimate of the probability of the event in question can be substantially in error, especially for high risk groups. In the situation of large measurement error, we investigate a conditional maximum likelihood estimator and its properties.

Key Words: Functional model • Logistic regression • Measurement error • Probit regression • Structural model


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