Rational Choice Models: The Temporal Tree Representation

Choice models, which specify the consumers’ choice probabilities of options over a given choice set, are widely studied and applied in many fields. We propose a temporal tree representation of choice that covers all rational choice models. Compared with existing structural choice models, the tree representation exhibits two major advantages that address the key challenges of model identification. First, all rational choice models have a tree representation, and a subclass of tree representation (with set-dependent branching) has a one-to-one correspondence with the rational choice models. This bridges the gap in the existing characterizations of structural models, which are unidentifiable, impose uninterpretable conditions, or do not cover the entire space of rational choice models. Second, the tree representation allows for the flexibility of systematically specifying the choice model structure based on available knowledge and data. In particular, the number of parameters needed to specify a tree representation can be primarily determined by the sufficient knowledge level, which corresponds to a specific layer of the tree branching. The sufficient knowledge level can be empirically determined based on the amount of available data, which, in turn, determines the number of parameters needed for model estimation. Therefore, the tree representation allows for a natural way of data integration, avoiding misspecification from restrictive assumptions and overfitting for general models. This paper was accepted by David Simchi-Levi, operations management. Funding: M. Xue’s research is partly support by the National Natural Science Foundation of China [72201257, 72571069, 72371240]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03967 .