AbstractThis paper describes and applies a general approach for incorporating factors with structural equations into models for discrete choice. The approach gives form to the covariance matrix in random coefficient models. The factors act directly on the random coefficients as unobserved attributes. The structural equations allow the factors to act on each other building structures that can represent a variety of concepts such as global heterogeneity and segmentation. The practical outcomes include parsimonious and identified models with rich covariances and better fit. Of greater interest is the ability to specify models that represent and test theory on the relationships between the taste heterogeneities for covariates and in particular between the attributes within a discrete choice experiment. The paper describes the general model and then applies it to a discrete choice experiment with seven attributes. Four competing specifications are evaluated, which demonstrates the ability of the model to be identified and parsimonious. The four specifications also demonstrate how competing a priori knowledge of the structure of the attributes used in the experiment can be empirically tested and evaluated. The outcomes include new behavioral insights and knowledge about choice and choice processes for the subject area of discrete choice experiments.