Models that are robust to aberrant choice behaviourhave received limited attention in discrete choice analysis . In this paper, we analyse two robust alternatives to the multinomial probit (MNP) model. Both alternative models belong to the family of robit models , whose kernel error distributions are heavy-tailed t-distributions  . 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 alternative , the generalised multinomial robit (Gen-MNR) model, has not been studied in the literature before and is more flexible than MNR, as it allows for alternative-specific marginal heavy-tailedness  of the kernel error distribution. For both models, we devise scalable and gradient-free Bayes estimators. We compare MNP, MNR and Gen-MNR in a simulation study and a case study on transport mode choice behaviour . We find that both MNR and Gen-MNR deliver significantly better in-sample fit and out-of-sample predictive accuracy than MNP. Gen-MNR outperforms MNR due to its more flexible kernel error distribution. Also, Gen-MNR gives more reasonable elasticity estimates than MNP and MNR , in particular regarding the demand for under-represented alternatives in a class-imbalanced dataset .
Inferences of robust behavioural and statistical models are insensitive to outlying observations resulting from aberrant behaviour, misreporting and misclassification. Standard discrete choice models such as logit and probit lack robustness to outliers due to their rigid kernel error distributions . In this paper, we analyse two robust alternatives to the multinomial probit (MNP) model. The two models belong to the family of robit models whose kernel error distributions are heavy-tailed t-distributions which moderate the influence of outlying observations . 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 efficient Gibbs sampling schemes, which also allow for a straightforward inclusion of random parameters. 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 exact elasticity 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 . We also find that the benefits of the more flexible kernel error distributions underlying MNR and Gen-MNR are maintained in the presence of random heterogeneity .
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