Hybrid choice models: the identification problem

In this chapter, we introduce the identification problem in the context of Hybrid Choice Models (HCMs), we develop a general framework for the theoretical and empirical identification of HCMs, and we apply it to the case of HCMs that combine the mixed logit model with the choice and latent variable model. We break apart the HCM into a discrete choice model where the latent variables are treated as observable variables, and a structural equation model with latent variables, assembling the rules of identification that have been developed independently for each of these two constituent pieces elsewhere in the literature, and deriving some of our own for specific cases that haven’t been addressed before, into a set of sufficient but not necessary conditions of theoretical identification for the HCM as a whole. Subsequently, we discuss common causes of empirical unidentification or underidentification of HCMs. We use a case study on travel behavior to demonstrate the kinds of identification issues that might arise in practice.