Covariate Measurement Error in Logistic Regression

Abstract : In a logistic regression model when covariates are subject to measurement error the naive estimator, obtained by regressing on the observed covariates, is asymptotically biased. This document introduces a bias-adjusted estimator and two estimators appropriate for normally distributed measurement errors; a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency. The four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small. A small Monte-Carlo study illustrates the superiority of the measurement-error estimators in certain situations. Additional keywords: mathematical models.

[1]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[2]  A. Madansky.  The fitting of straight lines when both variables are subject to error , 1959 .

[3]  W. Fuller,et al.  Estimation of Nonlinear Errors-in-Variables Models , 1982 .

[4]  L. Gleser.  Estimation in a Multivariate "Errors in Variables" Regression Model: Large Sample Results , 1981 .

[5]  R. Prentice.  Covariate measurement errors and parameter estimation in a failure time regression model , 1982 .

[6]  Walter W. Hauck,et al.  A Note on Confidence Bands for the Logistic Response Curve , 1983 .

[7]  J. Berkson.  Why I Prefer Logits to Probits , 1951 .

[8]  D. Pregibon.  Logistic Regression Diagnostics , 1981 .

[9]  L. Stefanski.  Influence and measurement error in logistic regression , 1983 .

[10]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[11]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[12]  Ben Armstrong,et al.  Measurement error in the generalised linear model , 1985 .

[13]  I. Olkin,et al.  A Comparison of n Estimators for the Binomial Distribution , 1981 .

[14]  N. Wermuth,et al.  A Simulation Study of Alternatives to Ordinary Least Squares , 1977 .

[15]  R. Tripathi,et al.  The Effect of Errors in Diagnosis and Measurement on the Estimation of the Probability of an Event , 1980 .

[16]  D. R. Cox,et al.  The analysis of binary data , 1971 .

[17]  Wayne A. Fuller,et al.  Estimation of the quadratic errors-in-variables model , 1982 .

[18]  Raymond J. Carroll,et al.  On errors-in-variables for binary regression models , 1984 .

[19]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[20]  Michel Loève,et al.  Probability Theory I , 1977 .

[21]  B. Efron.  The Efficiency of Logistic Regression Compared to Normal Discriminant Analysis , 1975 .