A note on corrected scores for logistic regression

This article describes a method for constructing a corrected score for logistic regression that is effective in reducing bias incurred through covariate measurement error. Stefanski (1989) showed there does not exist a corrected likelihood score for the logistic model with normal additive measurement error. To circumvent this result, an approximate likelihood score is defined for the logistic model that is conceptually and computationally straightforward and that is nearly efficient in the absence of measurement error. It is shown that the approximate likelihood score admits a corrected score. The results are extended to the Probit regression model.