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

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

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

Machine Learning 2019-04-17 v1 Machine Learning Econometrics Applications

Authors: 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 ( $J \geq 3$ ).

Keywords

mixed multinomial logit bayesian estimation polygamma data augmentation non-conjugacy gibbs sampler metropolis-hastings

Cite

@article{arxiv.1904.07688,
  title  = {P\'olygamma Data Augmentation to address Non-conjugacy in the Bayesian Estimation of Mixed Multinomial Logit Models},
  author = {Prateek Bansal and Rico Krueger and Michel Bierlaire and Ricardo A. Daziano and Taha H. Rashidi},
  journal= {arXiv preprint arXiv:1904.07688},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1904.03647

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

Abstract

Keywords

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