Incorporating uncovered structural patterns in value functions construction

A common approach in decision analysis and choice modeling is to infer a preference model in the form of a value function from the holistic choice examples. This paper introduces an analytical framework for estimating individuals’ preferences through uncovering structural patterns that regulate general shapes of value functions. We suggest a simple characterization of structural patterns and investigate the impact of incorporating information on such patterns on the predictive validity and estimation accuracy of preferences through an exhaustive simulation study and analysis of real decision makers’ preferences. We found that accounting for the structural patterns at the population level considerably improves the predictive performance of the constructed value functions at the individual level. This finding is confirmed across a wide range of settings with different levels of heterogeneity among the individuals and various complexity levels in their true preferences. We found, however, that improvement in the predictive performance is more significant when the choice examples come from a larger number of individuals, and when a smaller amount of preference information is available. The proposed model is developed based on a convex optimization problem with linear constraints, thus being computationally efficient and applicable to datasets of realistic size.