We compare the Metropolis-within-Gibbs (implemented in Sawtooth CBC/HB) versus Hamiltonian Monte Carlo and Variational Bayes (implemented in Stan) for estimating HBMNL models on several real-world choice data sets. The points of comparison are the following:
• Run-time. We plot run-time vs. error rate in estimating market share on hold-out tasks for each method. We estimate market share using the posterior mean as a point estimate for the individual-level beta vectors.
• Convergence. We compute convergence statistics for each method.
• Posterior distributions. We compare the posterior distributions produced by each method. This is of special interest for VB, which produces an approximation to the posterior.
