  Single index linear models for binary response with random coefficients have
been extensively employed in many econometric settings under various parametric
specifications of the distribution of the random coefficients. Nonparametric
maximum likelihood estimation (NPMLE) as proposed by Cosslett (1983) and
Ichimura and Thompson (1998), in contrast, has received less attention in
applied work due primarily to computational difficulties. We propose a new
approach to computation of NPMLEs for binary response models that significantly
increase their computational tractability thereby facilitating greater
flexibility in applications. Our approach, which relies on recent developments
involving the geometry of hyperplane arrangements, is contrasted with the
recently proposed deconvolution method of Gautier and Kitamura (2013). An
application to modal choice for the journey to work in the Washington DC area
illustrates the methods.
