Sampling of Alternatives in Random Regret Minimization Models

Sampling of alternatives is often required in discrete choice models to reduce the computational burden and to avoid describing a large number of attributes. This approach has been used in many areas, including modeling of route choice, vehicle ownership, trip destination, residential location, and activity scheduling. The need for sampling of alternatives is accentuated for Random Regret Minimization (RRM) models, because, different from Random Utility Models (RUM), the regret function for each alternative depends on all the alternatives in the choice-set. In this paper we develop and test a method to achieve consistency, asymptotic normality and relative efficiency, while sampling alternatives in a class of models that includes RRM. The proposed method can be seen as an extension of the approach used to address sampling of alternatives in Multivariate Extreme Value (MEV) models. We illustrate the methodology using Monte Carlo experimentation and a case study with real data. Experiments show that the proposed method is practical, performs better than an uncorrected model, and results in estimates that are statistically equal to those obtained with a model considering all the alternatives. Guevara, Chorus&Ben-Akiva 3