Choice Models Based on Mixed Discrete/continuous PDFs

This paper introduces a variant of random utility choice models based on mixed probability density functions, hence the adopted moniker k-Mix models. Mixed pdfs contain components with the usual continuous density function specifications that underlie common choice models (e.g. MNL, GEV, MNP), but also contain one or more discrete probability mass points. These mixed pdfs result in models that can be interpreted to reflect different regimes of decision-making. Two exemplars developed in this paper, the 2- and 3-Mix models, are the result of a mixed pdf that combines a continuous pdf, plus one or two mass points, respectively. The 2-Mix permits a specific alternative to be in the Tradeoff Condition (the usual situation for alternatives in extant choice models, and the only regime in which compensatory utility is defined and compared) or in the Rejection Condition (in which an alternative has extreme disutility). The 3-Mix model adds the Dominance Condition (in which an alternative has an extremely attractive utility) interestingly, the inclusion of this condition makes the model capable of simulating a particular form of satisficing decision making. These models are derived, discussed and compared relative to several extant choice models, then applied empirically on both a RP data set (work trip mode choice) and a SP data set (recreation campsite selection)