Bayesian estimation of mixed logit models: Selecting an appropriate prior for the covariance matrix

Maximum likelihood and Bayesian estimation are both frequently used to fit mixed logit models to choice data. The type and the number of quasi-random draws used for simulating the likelihood and the choice of the priors in Bayesian estimation have a big impact on the estimates. We compare the different approaches and compute the relative root mean square errors of the resulting estimates for the mean, covariance matrix and individual parameters in a large simulation study. We focus on the prior for the covariance matrix in Bayesian estimation and investigate the effect of Inverse Wishart priors, the Separation Strategy, Scaled Inverse Wishart and Huang Half-t priors. 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.