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

## TL;DR

This paper introduces a generalized multinomial response model with a t-distributed error kernel, improving preference estimation especially in class-imbalanced datasets by accounting for decision-uncertainty behavior.

## Contribution

It extends the GCM model to include a t-distributed error kernel, providing a new estimator and demonstrating its advantages over the normal distribution in preference modeling.

## Key findings

- GCM-t outperforms GCM-N in preference prediction accuracy.
- Accounting for decision-uncertainty affects elasticity and willingness-to-pay estimates.
- The model is applied to electric vehicle preferences, influencing policy insights.

## 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 estimator. 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.