A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel. (March 2020) - Dubey, Subodh; Bansal, Prateek; Daziano, Ricardo A.; Guerra, Erick
Highlights: Propose first multinomial response model with t-distributed error kernel (robit link) Show benefits of robit over probit - models decision uncertainty and better model fit Extend to joint model of continuous and multinomial responses with robit link (GCM-t) Derive full information maximum likelihood estimation procedure for GCM-t model Establish finite sample properties of GCM-t estimator in a simulation study Compare probit and robit links in a study related to adoption of electric vehicles 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.