On Robustness in the Logistic Regression Model

SUMMARY We investigate robustness in the logistic regression model. Copas has studied two forms of robust estimator: A robust-resistant estimate of Pregibon and an estimate based on a misclassification model. He concluded that robust-resistant estimates are much more biased in small samples than the usual logistic estimate is and recommends a bias-corrected version of the misclassification estimate. We show that there are other versions of robust-resistant estimates which have bias often approximately the same as and sometimes even less than the logistic estimate; these estimates belong to the Mallows class. In addition, the corrected misclassification estimate is inconsistent at the logistic model; we develop a simple consistent modification. The modified estimate is a member of the Mallows class but, unlike most robust estimates, it has an interpretable tuning constant. The results are illustrated on data sets featuring different kinds of outliers.