This paper introduces a promising two-phase nonparametric procedure for estimating response functions for binary choice models. The lp-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 the present proposed method over the logistic are that: (1) the transformation in Phase 2 is flexible in that it can accommodate distributions of group membership probabilities with tails of various degrees of thickness, (2) due to the flexible lp-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 estimates of the logistic function. The performance of the procedure is evaluated against the logistic method using two published data sets. These preliminary results suggest that the present procedure may be a useful alternative to the logistic method under certain data conditions.
