  Discrete choice models (DCMs) are the canonical methods for travel behavior
modeling and prediction. However, in many scenarios, the collected data for
DCMs are subject to measurement errors. Previous studies on measurement errors
mostly focus on "better estimating model parameters" with training data. In
this study, we focus on "better predicting new samples' behavior" when there
are measurement errors in testing data. To this end, we propose a robust
discrete choice model framework that is able to account for data uncertainties
in both features and labels. The model is based on robust optimization theory
that minimizes the worst-case loss over a set of uncertainty data scenarios.
Specifically, for feature uncertainties, we assume that the $\ell_p$-norm of
the measurement errors in features is smaller than a pre-established threshold.
We model label uncertainties by limiting the number of mislabeled choices to at
most $\Gamma$. Based on these assumptions, we derive a tractable robust
counterpart for robust-feature and robust-label DCM models. The derived
robust-feature binary logit (BNL) and the robust-label multinomial logit (MNL)
models are exact. However, the formulation for the robust-feature MNL model is
an approximation of the exact robust optimization problem. The proposed models
are validated in a binary choice data set and a multinomial choice data set,
respectively. Results show that the robust models (both features and labels)
can outperform the conventional BNL and MNL models in prediction accuracy and
log-likelihood. We show that the robustness works like "regularization" and
thus has better generalizability.
