Estimating the Mixed Logit Model by Maximum Simulated Likelihood and Hierarchical Bayes

In this study, we compare the parameter estimates of the mixed logit model obtained with maximum likelihood and with hierarchical Bayesian estimation. The choice of the priors in Bayesian estimation and of the type and the number of quasi-random draws for maximum likelihood estimation have a big impact on the estimates. Our main focus is on the effect of the prior for the covariance matrix in hierarchical Bayes estimation. We investigate several priors such as Inverse Wisharts, the Separation Strategy, Scaled Inverse Wisharts and the Huang Half-t priors and we compute the root mean square errors of the resulting estimates for the mean, covariance matrix and individual parameters in a large simulation study. We show that the default settings in many software packages can lead to very unreliable results and that it is important to check the robustness of the results.