Rico Krueger, Prateek Bansal, Michel Bierlaire, Ricardo A. Daziano, Taha H. Rashidi
arXiv 1 May 2019 · Statistics — Methodology · 7 citations (OpenAlex)
arXiv:1905.00419 · PDF · DOI · OpenAlex · Extracted main text
Variational Bayes (VB), a method originating from machine learning, enables fast and scalable estimation of complex probabilistic models. Thus far, applications of VB in discrete choice analysis have been limited to mixed logit models with unobserved inter-individual taste heterogeneity. However, such a model formulation may be too restrictive in panel data settings, since tastes may vary both between individuals as well as across choice tasks encountered by the same individual. In this paper, we derive a VB method for posterior inference in mixed logit models with unobserved inter- and intra-individual heterogeneity. In a simulation study, we benchmark the performance of the proposed VB method against maximum simulated likelihood (MSL) and Markov chain Monte Carlo (MCMC) methods in terms of parameter recovery, predictive accuracy and computational efficiency. The simulation study shows that VB can be a fast, scalable and accurate alternative to MSL and MCMC estimation, especially in applications in which fast predictions are paramount. VB is observed to be between 2.8 and 17.7 times faster than the two competing methods, while affording comparable or superior accuracy. Besides, the simulation study demonstrates that a parallelised implementation of the MSL estimator with analytical gradients is a viable alternative to MCMC in terms of both estimation accuracy and computational efficiency, as the MSL estimator is observed to be between 0.9 and 2.1 times faster than MCMC.
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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 | Bansal, P., Krueger, R., Bierlaire, M., Daziano, R. A., and Rashidi,… (2020) Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations self | 1.000 | 8 | 4 | 100% |
| 2 | Becker, F., Danaf, M., Song, X., Atasoy, B., and Ben-Akiva, M (2018) Bayesian estimator for logit mixtures with inter-and intra-consumer heterogeneity | 0.950 | 7 | 5 | 86% |
| 3 | Hess, S. and Rose, J. M (2009) Allowing for intra-respondent variations in coefficients estimated on repeated choice data | 0.811 | 4 | 2 | 100% |
| 4 | Hess, S. and Train, K. E (2011) Recovery of inter-and intra-personal heterogeneity using mixed logit models | 0.811 | 4 | 2 | 100% |
| 5 | Nocedal, J. and Wright, S (2006) Numerical optimization | 0.737 | 3 | 3 | 67% |
| 6 | Train, K. E (2009) Discrete Choice Methods with Simulation | 0.737 | 3 | 3 | 67% |
| 7 | Blei, D. M., Kucukelbir, A., and McAuliffe, J. D (2017) Variational Inference: A Review for Statisticians | 0.737 | 3 | 2 | 100% |
| 8 | Ormerod, J. T. and Wand, M. P (2010) Explaining Variational Approximations | 0.737 | 3 | 2 | 100% |
| 9 | Bhat, C. R (2011) The maximum approximate composite marginal likelihood (macml) estimation of multinomial probit-based unordered response choice m… | 0.644 | 2 | 2 | 100% |
| 10 | Bhat, C. R. and Sidharthan, R (2011) A simulation evaluation of the maximum approximate composite marginal likelihood (macml) estimator for mixed multinomial probit… | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 47 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Discrete Choice Analysis with Machine Learning Capabilities | 0.405 | 1 | 1 |