Nonparametric Unfolding of Binary Choice Data

This paper shows a general nonparametric unfolding technique for maximizing the correct classification of binary choice or two-category data. The motivation for and the primary focus of the unfolding technique are parliamentary roll call voting data. However, the procedures that implement the unfolding also can be applied to the problem of unfolding rank order data as well as analyzing a data set that would normally be the subject of a probit, logit, or linear probability analysis. One aspect of the scaling method greatly improves Manski's “maximum score estimator” technique for estimating limited dependent variable models. To unfold binary choice data two subproblems must be solved. First, given a set of chooser or legislator points, a cutting plane must be found such that it divides the legislators/choosers into two sets that reproduce the actual choices as closely as possible. Second, given a set of cutting planes for the binary choices, a point for each chooser or legislator must be found which reproduces the actual choices as closely as possible. Solutions for these two problems are shown in this paper. Monte Carlo tests of the procedure show it to be highly accurate in the presence of voting error and missing data.