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In this paper, we provide a comparison of implementations of Bayesian estimation of mixed multinomial logit (MMNL) models. Our objective is to provide a systematic comparison of the runtime, efficiency, and model implementation details associated with several alternative workflows. The analysis is based on three case studies. We argue that previous comparisons in the transportation literature have lacked appropriate metrics for comparison. Effective sample size statistics are proposed as a means of accurately comparing the ability of Bayesian samplers to generate independent draws for use in statistical inference. The Allenby-Train algorithm implemented in the R package Apollo is compared with the NUTS sampler implemented in Stan. While the Allenby-Train algorithm tends to generate draws much faster than NUTS, we find that the high correlation between success samples makes the two methods comparable. In addition to traditional MCMC sampling, we also examine the method of variational Bayes (VB).

Bayesian estimation of discrete choice models: a comparative analysis using effective sample size