A robust nonparametric procedure to estimate response functions for binary choice models

Abstract

This paper introduces a promising two-phase nonparametric procedure for estimating response functions for binary choice models. The ℓ p -metric estimation in Phase 1 of the procedure serves to obtain preliminary estimates of group membership of the observations, while in Phase 2 a hyperbolic tangent transformation and simple maximum likelihood procedure result in a response function which closely resembles the logistic function. The advantages of our proposed method over the logistic are that: (1) the transformation in Phase 2 is flexible in that it can accomodate distributions of group membership probabilities with tails of various degrees of thickness, (2) due to the flexible ℓ p -metric estimation criterion in Phase 1, the procedure gives good classificatory results for a variety of distributional properties of the independent variables, and (3) the procedure does not suffer from the potential convergence problem associated with maximum likelihood estimation of the logistic function. The performance of our procedure is evaluated against the logistic method using two published data sets. These preliminary results suggest that our procedure may be a useful alternative to the logistic under certain data conditions.