Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to  Markov chain Monte Carlo (MCMC) methods for Bayesian estimation of mixed logit models . In this paper, we derive a VB method for posterior inference in mixed multinomial logit models with unobserved inter- and intra-individual heterogeneity. The proposed VB method is benchmarked against MCMC in a simulation study. The results suggest that VB is substantially faster than MCMC but also noticeably less accurate, because the mean-field assumption of VB is too restrictive. Future research should thus focus on enhancing the expressiveness and flexibility of the variational approximation .
Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to maximum simulated likelihood (MSL) and Markov chain Monte Carlo (MCMC) methods for the estimation of discrete choice models. Thus far, the application of VB has been limited to mixed logit models with unobserved inter-individual taste variation. However, such a model formulation may be too restrictive in panel data settings, as tastes may vary both between individuals as well as across choice tasks by the same individual. In this paper, we derive a VB method for posterior inference in mixed logit models with unobserved inter- and intra-individual heterogeneity. In a simulation study, we benchmark the performance of the proposed VB method against MSL and MCMC in terms of parameter recovery, predictive accuracy and computational efficiency. The simulation study demonstrates that VB can be a fast and scalable alternative to MSL and MCMC, especially in applications in which fast predictions are paramount, as VB is observed to be between 2.8 and 17.7 times faster than the two competing methods. Furthermore, the simulation study shows that a parallelised implementation of the MSL estimator with analytical gradients is a viable alternative to MCMC in terms of both estimation accuracy and computational efficiency. In the considered experimental settings, the MSL estimator is between 0.9 and 2.1 times faster than MCMC .
A
maximum simulated likelihood (MSL) and
R
Bayesian estimation of
the estimation of discrete choice models. Thus far, the application of VB has been limited to
R
.
with unobserved inter-individual taste variation. However, such a model formulation may be too restrictive in panel data settings, as tastes may vary both between individuals as well as across choice tasks by the same individual.
D
multinomial
R
The
In a simulation study, we benchmark the performance of the
R
is benchmarked against MCMC in a simulation study. The results suggest that VB is substantially faster than MCMC but also noticeably less accurate, because the mean-field assumption of VB is too restrictive. Future research should thus focus on enhancing the expressiveness and flexibility of the variational approximation
against MSL and MCMC in terms of parameter recovery, predictive accuracy and computational efficiency. The simulation study demonstrates that VB can be a fast and scalable alternative to MSL and MCMC, especially in applications in which fast predictions are paramount, as VB is observed to be between 2.8 and 17.7 times faster than the two competing methods. Furthermore, the simulation study shows that a parallelised implementation of the MSL estimator with analytical gradients is a viable alternative to MCMC in terms of both estimation accuracy and computational efficiency. In the considered experimental settings, the MSL estimator is between 0.9 and 2.1 times faster than MCMC