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

## TL;DR

This paper introduces Pólygamma data augmentation to improve Bayesian estimation of Mixed Multinomial Logit models, addressing non-conjugacy issues in the Gibbs sampler, with empirical results highlighting identification challenges for models with three or more choices.

## Contribution

The paper proposes a novel PG-DA technique for MMNL models to handle non-conjugacy, enhancing Bayesian estimation methods.

## Key findings

- Posterior estimates are similar for binary choice scenarios.
- Identification issues arise with three or more alternatives.
- The method's effectiveness varies with the number of choices.

## 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 ($J \geq 3$).