Integration of Choice and Latent Variable Models

Abstract

This paper presents a general methodology and framework for including latent variables—in particular, attitudes and perceptions—in choice models. This is something that has long been deemed necessary by behavioral researchers, but is often either ignored in statistical models, introduced in less than optimal ways (e.g., sequential estimation of a latent variable model then a choice model, which produces inconsistent estimates), or introduced for a narrowly defined model structure. The paper is focused on the use of psychometric data to explicitly model attitudes and perceptions and their influences on choices. The methodology requires the estimation of an integrated multi-equation model consisting of a discrete choice model and the latent variable model’s structural and measurement equations. The integrated model is estimated simultaneously using a maximum likelihood estimator, in which the likelihood function includes complex multi-dimensional integrals. The methodology is applicable to any situation in which one is modeling choice behavior (with any type and combination of choice data) where (1) there are important latent variables that are hypothesized to influence the choice and (2) there exist indicators (e.g., responses to survey questions) for the latent variables. Three applications of the methodology provide examples and demonstrate the flexibility of the approach, the resulting gain in explanatory power, and the improved specification of discrete choice models.