  Outliers in discrete choice response data may result from misclassification
and misreporting of the response variable and from choice behaviour that is
inconsistent with modelling assumptions (e.g. random utility maximisation). In
the presence of outliers, standard discrete choice models produce biased
estimates and suffer from compromised predictive accuracy. Robust statistical
models are less sensitive to outliers than standard non-robust models. This
paper analyses two robust alternatives to the multinomial probit (MNP) model.
The two models are robit models whose kernel error distributions are
heavy-tailed t-distributions to moderate the influence of outliers. The first
model is the multinomial robit (MNR) model, in which a generic degrees of
freedom parameter controls the heavy-tailedness of the kernel error
distribution. The second model, the generalised multinomial robit (Gen-MNR)
model, is more flexible than MNR, as it allows for distinct heavy-tailedness in
each dimension of the kernel error distribution. For both models, we derive
Gibbs samplers for posterior inference. In a simulation study, we illustrate
the excellent finite sample properties of the proposed Bayes estimators and
show that MNR and Gen-MNR produce more accurate estimates if the choice data
contain outliers through the lens of the non-robust MNP model. In a case study
on transport mode choice behaviour, MNR and Gen-MNR outperform MNP by
substantial margins in terms of in-sample fit and out-of-sample predictive
accuracy. The case study also highlights differences in elasticity estimates
across models.
