On Theoretical and Empirical Aspects of Marginal Distribution Choice Models

Vinit Kumar Mishra (), Karthik Natarajan (), Dhanesh Padmanabhan (), Chung-Piaw Teo () and Xiaobo Li ()
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Vinit Kumar Mishra: Department of Business Analytics, University of Sydney Business School, New South Wales 2006, Australia
Karthik Natarajan: Engineering Systems and Design, Singapore University of Technology and Design, Singapore 138682
Dhanesh Padmanabhan: General Motors Research and Development--India Science Lab, Bangalore 560066, India
Chung-Piaw Teo: Department of Decision Sciences, National University of Singapore Business School, Singapore 117591
Xiaobo Li: Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455

Management Science, 2014, vol. 60, issue 6, 1511-1531

Abstract: In this paper, we study the properties of a recently proposed class of semiparametric discrete choice models (referred to as the marginal distribution model (MDM)), by optimizing over a family of joint error distributions with prescribed marginal distributions. Surprisingly, the choice probabilities arising from the family of generalized extreme value models of which the multinomial logit model is a special case can be obtained from this approach, despite the difference in assumptions on the underlying probability distributions. We use this connection to develop flexible and general choice models to incorporate consumer and product level heterogeneity in both partworths and scale parameters in the choice model. Furthermore, the extremal distributions obtained from the MDM can be used to approximate the Fisher's information matrix to obtain reliable standard error estimates of the partworth parameters, without having to bootstrap the method. We use simulated and empirical data sets to test the performance of this approach. We evaluate the performance against the classical multinomial logit, mixed logit, and a machine learning approach that accounts for partworth heterogeneity. Our numerical results indicate that MDM provides a practical semiparametric alternative to choice modeling. This paper was accepted by Eric Bradlow, special issue on business analytics .

Keywords: discrete choice model; convex optimization; machine learning; applied probability (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (20)

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