Minimum Distance Estimation for the Logistic Regression Model

• Activity Number: 430
• Type: Contributed
• Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
• Sponsor: General Methodology
• Author(s): Howard Bondell*+
• Companies: Rutgers University
• Keywords: logistic regression ; robustness ; minimum distance estimation ; goodness of fit ; case-control study

Abstract

A new class of estimation procedures for the logistic regression model is introduced. The estimates are constructed via a minimum distance approach after identifying the model under case-control sampling with a semiparametric biased sampling model. In simple logistic regression, using the weighted Cramer-Von Mises distance measures, the resulting estimators can be highly efficient, yet strictly robust in the sense that their influence function remains bounded. Hence these procedures are less sensitive than the MLE to outlying observations. The approach is shown to remain applicable if the sampling was done prospectively via its equivalence to a particular residual process in the standard setting. Based on this equivalence, the asymptotic normality of the class of procedures is derived. In order to maintain affine equivariance in multiple regression, a projection-based extension is proposed. The estimates are shown to compare favorably to the MLE and existing robust modifications in small sample simulations and real data examples. Finally, this approach also yields a natural goodness-of-fit measure, and hence may be used to test the model assumptions.