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P\'olygamma Data Augmentation to address Non-conjugacy in the Bayesian Estimation of Mixed Multinomial Logit Models

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

Abstract

The standard Gibbs sampler of Mixed Multinomial Logit (MMNL) models involves sampling from conditional densities of utility parameters using Metropolis-Hastings (MH) algorithm due to unavailability of conjugate prior for logit kernel. To address this non-conjugacy concern, we propose the application of P\'olygamma data augmentation (PG-DA) technique for the MMNL estimation. The posterior estimates of the augmented and the default Gibbs sampler are similar for two-alternative scenario (binary choice), but we encounter empirical identification issues in the case of more alternatives ($J \geq 3$).

Suggested Citation

  • Prateek Bansal & Rico Krueger & Michel Bierlaire & Ricardo A. Daziano & Taha H. Rashidi, 2019. "P\'olygamma Data Augmentation to address Non-conjugacy in the Bayesian Estimation of Mixed Multinomial Logit Models," Papers 1904.07688, arXiv.org.
    • Handle: RePEc:arx:papers:1904.07688
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    References listed on IDEAS

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    1. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    2. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    3. Akinc, Deniz & Vandebroek, Martina, 2018. "Bayesian estimation of mixed logit models: Selecting an appropriate prior for the covariance matrix," Journal of choice modelling, Elsevier, vol. 29(C), pages 133-151.
    4. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
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