Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations. (January 2020)

• Record Type: Journal Article
• Authors: Bansal, Prateek; Krueger, Rico; Bierlaire, Michel; Daziano, Ricardo A.; Rashidi, Taha H.
• Is Part Of: Transportation research. Volume 131(2020)
• Page Start: 124
• Page End: 142
• Publication Date: 2020-01
• Subjects: Variational bayes -- Bayesian inference -- Mixed logit -- Nonconjugate variational message passing; Transportation -- Research -- Periodicals; Transportation -- Mathematical models -- Periodicals
• DOI: 10.1016/j.trb.2019.12.001
• Languages: English
• ISSNs: 0191-2615

Abstract

Highlights: Address gaps in use of Variational Bayes (VB) for Mixed Multinomial Logit (MMNL). Extend VB methods for MMNL to admit utility with fixed and random parameters. Compare VB with Gibbs sampler & classical estimator of MMNL in Monte Carlo study. VB variant is as good as Gibbs sampler & classical estimator at parameter recovery. One VB variant is up to 16 times faster than Gibbs sampler & classical estimator. Abstract: Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substantially faster than MCMC at practically no compromises in predictive accuracy. In this paper, we address two critical gaps concerning the usage and understanding of VB for MMNL. First, extant VB methods are limited to utility specifications involving only individual-specific taste parameters. Second, the finite-sample properties of VB estimators and the relative performance of VB, MCMC and maximum simulated likelihood estimation (MSLE) are not known. To address the former, this study extends several VB methods for MMNL to admit utility specifications including both fixed and random utility parameters. To address the latter, we conduct an extensive simulation-based evaluation to benchmark the extended VB methods against MCMC and MSLE in terms of estimation times, parameter recovery and predictive accuracy. The results suggest that all VB variants with the exception of the ones relying on an alternative variational lower bound constructed with the help of the modified Jensen's inequality perform as well as MCMC and MSLE at prediction and parameter recovery. In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Δ) is up to 16 times faster than MCMC and MSLE. Thus, VB-NCVMP-Δ can be an attractive alternative to MCMC and MSLE for fast, scalable and accurate estimation of MMNL models.