On errors-in-variables for binary regression models

We c0nsider in detail probit and logistic regression models when some of the predictors are measured with error. For normal measurement errors, the functional and structural maximum likelihood estimates (MLE) are considered; in the functional case the MLE is not generally consistent. Non-normality in the structural case is also considered. By an example and a simulation, 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. Some key words: Probit regression; Logistic regression; Functional models; Structural models; Measurement errors. 3