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 interconsumer 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.

Intercity truck route choices incorporating toll road alternatives using enhanced GPS data

“…The large values estimated suggest that it may be useful to also model intra-respondent heterogeneity. Appropriate models and estimation techniques were proposed, for example, by Hess and Rose (2009) and Becker et al (2018).…”

Personalized Choice Model for Managed Lane Travel Behavior

“…Given the intractable nature of computing this posterior distribution K directly, the HB procedure uses a five-step Gibbs sampler to draw from this posterior distribution as follows. (Readers are referred to Becker et al for further details [18]. )…”

“…In addition, the absence of traveler characteristics and the huge amount of trip records present challenges to the commonly used modeling tools. In our paper, these issues are handled with personalization and Bayesian estimation respectively ( 18 ).…”

“…Further, we complemented existing models of managed lane travel behavior with unobserved intrapersonal heterogeneity, which quantifies how an individual's preference fluctuates across trips (15). To circumvent the computational burden commonly associated with this type of model (16,17), we adopted the hierarchical Bayes (HB) estimator introduced by Becker et al (18). This enabled us to train our model with over 120,000 trips in our empirical study.…”

“…To circumvent the computational burden commonly associated with this type of model ( 16 , 17 ), we adopted the hierarchical Bayes (HB) estimator introduced by Becker et al. ( 18 ). This enabled us to train our model with over 120,000 trips in our empirical study.…”