Within the continuous search for flexible models capable of dealing with different practical and realistic situations, discrete choice modeling has developed especially quickly: the simple but restrictive Multinomial Logit model has evolved into the powerful Logit Mixture model. In the last few years this flexibility search has been extended to the next level, and discrete choice modeling now aims to explicitly incorporate psychological factors affecting decision making, with the goal of enhancing the behavioral representation of the choice process. The Hybrid Choice Modeling (HCM) approach embraces this improved representation. Hybrid Models expand on standard choice models by including attitudes, opinions and perceptions as psychometric latent variables, which become observable through a group of measurement relationships or indicators. In this context, the understanding of consumer behavior is improved while the model gains in predictive power.

On the other hand, the search for flexibility has continuously faced the problem of a more involved and extremely demanding estimation process. Under a classical statistics perspective, flexible models estimation eventually requires the optimization of a likelihood function containing multi-dimensional integrals that in many cases do not have a closed form. Therefore, a lot of effort has been carried out to develop simulated maximum likelihood methods in order to solve an approximation of the original problem.

In this paper we describe the classical estimation techniques for a simulated maximum likelihood solution for Hybrid Choice Models. We apply these classical estimation techniques to data of stated personal vehicle choices made by Canadian consumers when faced with technological innovations.

We then go beyond classical methods, and we introduce Hierarchical Bayes. Based on the rapid development of Markov chain Monte Carlo techniques, and on the idea that Bayesian tools could be used to produce estimators that are asymptotically equivalent to those obtained using classical methods, we describe the theoretical implementation of a Bayesian approach to Hybrid Choice modeling. Specifically, we present the details of the HCM sequence of full conditional posterior distributions – for both a Probit and a Logit Mixture discrete choice kernel – necessary for iterative Gibbs sampling.  We then carry out a Monte Carlo experiment to test how the HCM Gibbs sampler works in practice. To our knowledge, this is the first practical application of HCM Bayesian estimation.  

We show that although HCM estimation requires the evaluation of complex multi-dimensional integrals, simulated maximum likelihood can be successfully implemented and offers an unbiased, consistent and smooth estimator of the true probabilities. The HCM framework not only proves to be capable of introducing latent variables, but also makes it possible to tackle the problem of measurement errors in variables in a very natural way. We also show that working with Bayesian methods breaks down the complexity of classical estimation. In fact, we show that HCM Bayesian estimation with a Probit kernel is not only straightforward, but also easier to implement than the Logit Mixture kernel because it allows the exploitation of data augmentation techniques, whereas the intricate classical Multinomial Probit estimation technique reduces the practicability of the standard Probit model.