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Edited by André de Palma, Robin Lindsey, Emile Quinet and Roger Vickerman
8 Advances in discrete choice: mixture models Joan L. Walker and Moshe Ben-Akiva INTRODUCTION Recent advances in discrete choice models have been driven by the growth in computer power and use of simulation, which have allowed for unprecedented flexibility in model form. In this chapter, we review both the basic discrete choice models and the latest formulations. In particular, we focus on the concept of mixture models. Mixture models are currently being used in a wide array of statistical modeling procedures as a way to relax restrictive assumptions and generalize model forms. As mixing allows for any distributional form to be approximated, this represents a powerful and important advancement in discrete choice analysis. We first briefly review the foundations of discrete choice analysis and the classic model forms of probit and the generalized extreme value family (or GEV), for example, logit, nested logit and cross-nested logit. Then we will move onto mixture models, beginning with basic formulations and then covering more advanced forms, including what we call behavioral (or structural) mixture models. The last section presents empirical results from a land use and transportation study, which we use to demonstrate the various choice model formulations. FOUNDATIONS OF DISCRETE CHOICE ANALYSIS We start by providing the foundations of choice analysis, including the choice modeling framework and the random utility model. This section is based on Ben-Akiva and Lerman (1985), where further details can be obtained. Choice Modeling Framework This section presents the basic elements that are used to model a decision...
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