Bayesian estimator for Logit Mixtures with inter- and intra-consumer heterogeneity

Abstract

Estimating discrete choice models on panel data allows for the estimation of preference heterogeneity in the sample. While the Logit Mixture model with random parameters is mostly used to account for variation across individuals, preferences may also vary across different choice situations of the same individual. Up to this point, Logit Mixtures incorporating both inter- and intra-consumer heterogeneity are estimated with the classical Maximum Simulated Likelihood (MSL) procedure. The MSL procedure becomes computationally expensive with an increasing sample size and can be burdensome in the presence of a multi-modal likelihood function. We therefore propose a Hierarchical Bayes estimator for Logit Mixtures with both levels of heterogeneity. It builds on the Allenby-Train procedure, which considers only inter-consumer heterogeneity. To test the proposed procedures, we analyze how well the true patterns of heterogeneity are recovered in a simulation environment. Results from the Monte Carlo simulation suggest that falsely ignoring intra-consumer heterogeneity despite its presence in the data leads to biased estimates and a decreased goodness of fit. The latter is confirmed by a real-world example of explaining mode choices for GPS traces. We further show that the runtime of the proposed estimator is substantially faster than for the corresponding MSL estimator.