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

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.

Robust discrete choice models with t-distributed kernel errors

“…Robustness has received limited attention in multinomial choice analysis. Dubey et al (2020) present the first multinomial robit (MNR) model, i.e. a multinomial choice model defined through a t-distributed kernel error with an estimable DOF.…”

“…a multinomial choice model defined through a t-distributed kernel error with an estimable DOF. Dubey et al (2020) make a strong empirical case to adopt the MNR model over the multinomial probit (MNP) model. First, the estimates of the MNP model are inconsistent, if the kernel errors in the data generating process are heavy-tailed.…”

“…We identify two research gaps in the formulation and estimation of MNR models. First, Dubey et al (2020) and Peyhardi (2020) constrain the flexibility of the kernel error distribution by assuming that a single, generic DOF parameter controls the heavy-tailedness of the kernel error distribution.…”

“…Second, the estimation approaches employed in both studies are not scalable. Dubey et al (2020) are unable to derive analytical gradients of the MNR model and thus rely on computationallyexpensive numerical gradient approximations during the maximisation of the simulated log-likelihood of the model. Peyhardi (2020) estimates the DOF parameter by performing a grid search, which requires the model to be estimated at multiple values of the DOF parameter and suffers from the curse of dimensionality if the underlying kernel distribution had multiple DOF parameters.…”