Pólygamma Data Augmentation to address Non-conjugacy in the Bayesian Estimation of Mixed Multinomial Logit Models
This addresses a computational bottleneck for researchers estimating complex choice models, but it is incremental as it builds on existing augmentation techniques and reveals limitations in broader applications.
The paper tackled the non-conjugacy issue in Bayesian estimation of Mixed Multinomial Logit models by proposing Pólygamma data augmentation, but found that while it yields similar posterior estimates to standard methods for binary choices, it faces empirical identification problems with three or more alternatives.
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 ($J \geq 3$).