Bayesian Deep Learning for Discrete Choice

Discrete choice models (DCMs) are used to analyze individual decision-making in contexts such as transportation choices, political elections, and consumer preferences. DCMs play a central role in applied econometrics by enabling inference on key economic variables, such as marginal rates of substitution, rather than focusing solely on predicting choices on new unlabeled data. However, while traditional DCMs offer high interpretability and support for point and interval estimation of economic quantities, these models often underperform in predictive tasks compared to deep learning (DL) models. Despite their predictive advantages, DL models remain largely underutilized in discrete choice due to concerns about their lack of interpretability, unstable parameter estimates, and the absence of established methods for uncertainty quantification. Here, we introduce a deep learning model architecture specifically designed to integrate with approximate Bayesian inference methods, such as Stochastic Gradient Langevin Dynamics (SGLD). Our proposed model collapses to be-haviorally informed hypotheses when data is limited, mitigating overfitting and instability in underspecified settings while retaining the flexibility to capture complex nonlinear relationships when sufficient data is available. We demonstrate our approach using SGLD through a Monte Carlo simulation study, evaluating both predictive metrics--such as out-of-sample balanced accuracy--and inferential metrics--such as empirical coverage for marginal rates of substitution interval estimates. Additionally, we present results from two empirical case studies: one using revealed mode choice data in NYC, and the other based on the widely used Swiss train choice stated preference data. Introduction Discrete choice is a fundamental area of econometrics that examines how individuals make decisions among a finite set of alternatives. For example, in transportation systems, discrete choice models are often used to estimate individuals' willingness to pay for a reduction in travel time, considering factors such as cost, trip duration, level of service, and other attributes of competing transportation modes. Given that inference is fundamental in the discrete choice field, researchers often rely on transparent and interpretable statistical binary or multinomial classification models such as logistic and probit regressions, along with their more complex variations. Traditional discrete choice models (DCMs) allow for point and interval estimation of key economic quantities, including marginal rates of substitution and odds ratios.