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

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  • Dubey, Subodh
  • Bansal, Prateek
  • Daziano, Ricardo A.
  • Guerra, Erick

Abstract

In multinomial response models, idiosyncratic variations in the indirect utility are generally modeled using Gumbel or normal distributions. This study makes a strong case to substitute these thin-tailed distributions with a t-distribution. First, we demonstrate that a model with a t-distributed error kernel better estimates and predicts preferences, especially in class-imbalanced datasets. Our proposed specification also implicitly accounts for decision-uncertainty behavior, i.e. the degree of certainty that decision-makers hold in their choices relative to the variation in the indirect utility of any alternative. Second – after applying a t-distributed error kernel in a multinomial response model for the first time – we extend this specification to a generalized continuous-multinomial (GCM) model and derive its full-information maximum likelihood estimation procedure. The likelihood involves an open-form expression of the cumulative density function of the multivariate t-distribution, which we propose to compute using a combination of the composite marginal likelihood method and the separation-of-variables approach. Third, we establish finite sample properties of the GCM model with a t-distributed error kernel (GCM-t) and highlight its superiority over the GCM model with a normally-distributed error kernel (GCM-N) in a Monte Carlo study. Finally, we compare GCM-t and GCM-N in an empirical setting related to preferences for electric vehicles (EVs). We observe that accounting for decision-uncertainty behavior in GCM-t results in lower elasticity estimates and a higher willingness to pay for improving the EV attributes than those of the GCM-N model. These differences are relevant in making policies to expedite the adoption of EVs.

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  • Dubey, Subodh & Bansal, Prateek & Daziano, Ricardo A. & Guerra, Erick, 2020. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 114-141.
  • Handle: RePEc:eee:transb:v:133:y:2020:i:c:p:114-141
    DOI: 10.1016/j.trb.2019.12.007
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    1. Jean Peyhardi, 2020. "Robustness of Student link function in multinomial choice models," Post-Print hal-03227808, HAL.
    2. Peyhardi, Dr Jean, 2020. "Robustness of Student link function in multinomial choice models," Journal of choice modelling, Elsevier, vol. 36(C).
    3. Rico Krueger & Michel Bierlaire & Thomas Gasos & Prateek Bansal, 2020. "Robust discrete choice models with t-distributed kernel errors," Papers 2009.06383, arXiv.org, revised Dec 2022.

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