About the categorization of latent variables in hybrid choice models

Although hybrid choice models are fairly popular nowadays, the way in which different types of latent variables are considered into the utility function has not been extensively analysed. Latent variables accounting for attitudes resemble socioeconomic characteristics and, therefore, systematic taste variations and categorizations of the latent variables should be considered. Nevertheless, categorizing a latent variable is not an easy subject, as these variables are not observed and consequently exhibit an intrinsic variability. Under these circumstances it is not possibly to assign an individual to a specific group, but only to establish a probability with which an individual should be categorized in given way. In this paper we explore different ways to categorize individuals based on latent characteristics, focusing on the categorization of latent variables. This approach exhibits as main advantage (over latent-classes for instance) a clear interpretation of the function utilized in the categorization process, as well as taking exogenous information into account. Unfortunately, technical issues (associated with the estimation technique via simulation) arise when attempting a direct categorization. We propose an alternative to attempt a direct categorization of latent variables (based on an auxiliary variable) and conduct a theoretical and empirical analysis (two case studies), contrasting this alternative with other approaches (latent variable-latent class approach and latent classes with perceptual indicators approach). Based on this analysis, we conclude that the direct categorization is the superior approach, as it offers a consistent treatment of the error term, in accordance with underlying theories, and a better goodness-of-fit.