Asymmetric, closed-form, finite-parameter models of multinomial choice

Abstract

Class imbalance, where there are great differences between the number of observations associated with particular discrete outcomes, is common within transportation and other fields. In the statistics literature, one explanation for class imbalance that has been hypothesized is an asymmetric (rather than the typically symmetric) choice probability function. Unfortunately, few relatively simple models exist for testing this hypothesis in transportation settings-settings that are inherently multinomial. Our paper fills this gap.In particular, we address the following questions: "how can one construct asymmetric, closed-form, finite-parameter models of multinomial choice" and "how do such models compare against commonly used symmetric models?" Methodologically, we introduce (1) a new class of closed-form, finite-parameter, multinomial choice models, (2) a procedure for using these models to extend existing binary choice models to the multinomial setting, and (3) a procedure for creating new binary choice models (both symmetric and asymmetric). Together, our contributions allow us to create new asymmetric, closed-form, finite-parameter multinomial choice models. We demonstrate our methods by developing four new asymmetric, multinomial choice models. Empirically, most of our models strongly dominate the multinomial logit (MNL) model in terms of in-sample and out-of-sample log-likelihoods. Moreover, analyzing two policy applications, we find practical differences between the MNL and our new asymmetric models. Our results suggest that while asymmetric models may not always outperform symmetric ones, asymmetric choice models are worth testing because they might have better statistical performance and entail substantively different policy and financial implications when compared with traditional symmetric models, such as the MNL. 4 The probability equation of open-form models contain analytically intractable integrals or infinite sums. 5 Models with an infinite number of parameters are known as non-parametric or semi-parametric models.

Trust and compassion in willingness to share mobility and sheltering resources in evacuations: A case study of the 2017 and 2018 California Wildfires

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Fleeing from Hurricane Irma: Empirical Analysis of Evacuation Behavior Using Discrete Choice Theory

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A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel

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