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), 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 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 respondent and product/attribute 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 various simulated and empirical datasets to test the performance of this approach. We evaluate the performance against the classical Multinomial Logit, Mixed Logit, and a machine learning approach developed by Evgeniou et al. (13) (for partworth heterogeneity). Our numerical results indicate that MDM provides a practical semi-parametric alternative to choice modeling.