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Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations

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  • Prateek Bansal
  • Rico Krueger
  • Michel Bierlaire
  • Ricardo A. Daziano
  • Taha H. Rashidi

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-Delta) is up to 16 times faster than MCMC and MSLE. Thus, VB-NCVMP-Delta can be an attractive alternative to MCMC and MSLE for fast, scalable and accurate estimation of MMNL models.

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  • Prateek Bansal & Rico Krueger & Michel Bierlaire & Ricardo A. Daziano & Taha H. Rashidi, 2019. "Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations," Papers 1904.03647, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1904.03647
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    Cited by:

    1. Rico Krueger & Prateek Bansal & Michel Bierlaire & Ricardo A. Daziano & Taha H. Rashidi, 2019. "Variational Bayesian Inference for Mixed Logit Models with Unobserved Inter- and Intra-Individual Heterogeneity," Papers 1905.00419, arXiv.org, revised Jan 2020.
    2. Krueger, Rico & Rashidi, Taha H. & Vij, Akshay, 2020. "A Dirichlet process mixture model of discrete choice: Comparisons and a case study on preferences for shared automated vehicles," Journal of choice modelling, Elsevier, vol. 36(C).
    3. Youssef M. Aboutaleb & Mazen Danaf & Yifei Xie & Moshe Ben-Akiva, 2021. "Discrete Choice Analysis with Machine Learning Capabilities," Papers 2101.10261, arXiv.org.
    4. Rico Krueger & Taha H. Rashidi & Akshay Vij, 2019. "Semi-Parametric Hierarchical Bayes Estimates of New Yorkers' Willingness to Pay for Features of Shared Automated Vehicle Services," Papers 1907.09639, arXiv.org.

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