Pólygamma Data Augmentation to address Non-conjugacy in the Bayesian Estimation of Mixed Multinomial Logit Models

2019/04/13 by Bansal, Prateek, Krueger, Rico, Bierlaire, Michel +2
#Applications (stat.AP) #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.1904.07688

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 Pólygamma 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 ≥ 3).

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