Appendix: A Nonparametric Approach to Modeling Choice with Limited Data

Abstract

This document presents supporting materials for the following publication:Farias, Jagabathula and Shah (2012), 'A Nonparametric Approach to Modeling Choice with Limited Data,' Management Science, Articles in Advance, pp. 1-18.Choice models are today ubiquitous across a range of applications in operations and marketing. Real world implementations of many of these models face the formidable stumbling block of simply identifying the 'right' model of choice to use. Since models of choice are inherently high dimensional objects, the typical approach to dealing with this problem is positing, a-priori, a parametric model that one believes adequately captures choice behavior. This approach can be substantially sub-optimal in scenarios where one cares about using the choice model learned to make fine-grained predictions; one must contend with the risks of mis-specification and over/under-fitting. Thus motivated, we visit the following problem: For a 'generic' model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal information about these distributions), how may one predict revenues from offering a particular assortment of choices? An outcome of our investigation is a non-parametric approach in which the data automatically selects the 'right' choice model for revenue predictions. The approach is practical. Using a data set consisting of automobile sales transaction data from a major US automaker, our method demonstrates a 20% improvement in prediction accuracy over state-of-the art benchmark models, which can result in a 10% increase in revenues from optimizing the offer set. We also address a number of theoretical issues, among them a qualitative examination of the choice models implicitly learned by the approach. We believe that this paper takes a step towards 'automating' the crucial task of choice model selection.