Rico Krueger, Michel Bierlaire, Thomas Gasos, Prateek Bansal
arXiv 14 Sep 2020 · Econometrics · publishedStatistics and Computing (2022) · 6 citations (OpenAlex)
arXiv:2009.06383 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Burgette, L. F. and Nordheim, E. V (2012) The trace restriction: An alternative identification strategy for the Bayesian multinomial probit model | 1.000 | 5 | 3 | 100% |
| 2 | Imai, K. and Van Dyk, D. A (2005) A Bayesian analysis of the multinomial probit model using marginal data augmentation | 1.000 | 5 | 3 | 100% |
| 3 | Jiang, Z. and Ding, P (2016) Robust modeling using non-elliptically contoured multivariate t distributions | 0.928 | 10 | 4 | 80% |
| 4 | McCulloch, R. and Rossi, P. E (1994) An exact likelihood analysis of the multinomial probit model | 0.928 | 4 | 4 | 100% |
| 5 | Ding, P (2014) Bayesian robust inference of sample selection using selection-t models | 0.909 | 8 | 4 | 75% |
| 6 | Train, K. E (2009) Discrete choice methods with simulation | 0.874 | 6 | 2 | 100% |
| 7 | Benoit, D. F., Van Aelst, S., and Van den Poel, D (2016) Outlier-Robust Bayesian Multinomial Choice Modeling | 0.737 | 3 | 2 | 100% |
| 8 | Dubey, S., Bansal, P., Daziano, R. A., and Guerra, E (2020) A generalized continuous-multinomial response model with a t-distributed error kernel self | 0.693 | 5 | 1 | 100% |
| 9 | Peyhardi, D. J (2020) Robustness of student link function in multinomial choice models | 0.644 | 4 | 1 | 100% |
| 10 | Albert, J. H. and Chib, S (1993) Bayesian analysis of binary and polychotomous response data | 0.644 | 2 | 2 | 100% |
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