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. This paper addresses two gaps: extant VB methods are limited to individual-specific taste parameters, and the finite-sample properties of VB estimators are unknown. The study extends VB methods to include fixed and random utility parameters and conducts a simulation-based evaluation benchmarking the extended VB methods against MCMC and MSLE. Results suggest that VB variants (except those using a modified Jensen's inequality lower bound) perform as well as MCMC and MSLE in prediction and parameter recovery, with VB-NCVMP-Δ up to 16 times faster than MCMC and MSLE.

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