Recent methodological developments in discrete choice models

The role of discrete choice models in decision-making support has significantly grown during the past 20 years. This is particularly true in the context of marketing and transportation, where it is critical to understand and forecast choice behavior in a detailed way. In this presentation, we will provide an overview of recent methodological developments in this area, with a specific focus on the difficult problem of route choice modeling in transportation. The multinomial logit (MNL) model is probably the most popular random utility model, due to its relative simplicity. However, its derivation is based on strong independence assumptions. Namely, error terms in the utility functions are supposed to be independent across alternatives and individuals. Such assumptions are not valid in many concrete contexts. The family of Multivariate (or Generalized) Extreme Value (GEV) models relax the assumption of independence across alternatives. This family, proposed by McFadden (1978) includes the nested logit model, the crossnested logit model and the network MEV model. Each of them will be btriefly described. Convenient because of the closed form of the probability formula, MEV models suffer from some limitations, one of them being their intrinsic homoscedasticity. Mixtures of MEV models can be derived to overcome these limitations (McFadden and Train, 2000. While mixing provides a great deal of flexibility, it significantly complicates the estimation of the model, as the probability model has no closed any more. Therefore, simulation is required, which is computationnally intensive. We will discuss more specifically Error Component and Random Parameter models, as well as Panel Data models. We will also touch upon the issue of testing if the mixing distribution is adequate (Fosgerau and Bierlaire, 2005). We will conclude the presentation by illustrating the concepts in the specific case of route choice models. Indeed, the structure of the choice set in this context obviously rule out the independence assumption of the MNL framework. We will present recent models designed to efficiently capture the correlation (Ben-Akiva and Bierlaire, 1999, Frejinger and Bierlaire, forthcoming).