On Theoretical and Empirical Aspects of Marginal Distribution Choice Models

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.