Sampling of alternatives in Logit Mixture models

• We extend to Logit Mixture previous results in sampling of alternatives for Logit and MEV.
• Study a Naïve approach in which the kernel is simply replaced by the Logit correction.
• Show that the Naïve approach provides consistent estimators and derive their asymptotic distribution.
• Provide further empirical evidence suggesting the suitability of the Naïve approach.

Employing a strategy of sampling of alternatives is necessary for various transportation models that have to deal with large choice-sets. In this article, we propose a method to obtain consistent, asymptotically normal and relatively efficient estimators for Logit Mixture models while sampling alternatives. Our method is an extension of previous results for Logit and MEV models. We show that the practical application of the proposed method for Logit Mixture can result in a Naïve approach, in which the kernel is replaced by the usual sampling correction for Logit. We give theoretical support for previous applications of the Naïve approach, showing not only that it yields consistent estimators, but also providing its asymptotic distribution for proper hypothesis testing. We illustrate the proposed method using Monte Carlo experimentation and real data. Results provide further evidence that the Naïve approach is suitable and practical. The article concludes by summarizing the findings of this research, assessing their potential impact, and suggesting extensions of the research in this area.