A Nonparametric Approach with Marginals for Modeling Consumer Choice
- URL: http://arxiv.org/abs/2208.06115v4
- Date: Mon, 24 Jul 2023 09:11:19 GMT
- Title: A Nonparametric Approach with Marginals for Modeling Consumer Choice
- Authors: Yanqiu Ruan, Xiaobo Li, Karthyek Murthy, Karthik Natarajan
- Abstract summary: The marginal distribution model (MDM) is inspired by the utility of similar characterizations for the random utility model (RUM)
This paper aims to establish necessary and sufficient conditions for given choice data to be consistent with the MDM hypothesis.
Numerical experiments show that MDM provides better representational power and prediction accuracy than multinominal logit.
- Score: 4.880424147378901
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Given data on the choices made by consumers for different offer sets, a key
challenge is to develop parsimonious models that describe and predict consumer
choice behavior while being amenable to prescriptive tasks such as pricing and
assortment optimization. The marginal distribution model (MDM) is one such
model, that requires only the specification of marginal distributions of the
random utilities. This paper aims to establish necessary and sufficient
conditions for given choice data to be consistent with the MDM hypothesis,
inspired by the utility of similar characterizations for the random utility
model (RUM). This endeavor leads to an exact characterization of the set of
choice probabilities that the MDM can represent. Verifying the consistency of
choice data with this characterization is equivalent to solving a
polynomial-sized linear program. Since the analogous verification task for RUM
is computationally intractable and neither of these models subsumes the other,
MDM is helpful in striking a balance between tractability and representational
power. The characterization is convenient to be used with robust optimization
for making data-driven sales and revenue predictions for new unseen
assortments. When the choice data lacks consistency with the MDM hypothesis,
finding the best-fitting MDM choice probabilities reduces to solving a mixed
integer convex program. The results extend naturally to the case where the
alternatives can be grouped based on the similarity of the marginal
distributions of the utilities. Numerical experiments show that MDM provides
better representational power and prediction accuracy than multinominal logit
and significantly better computational performance than RUM.
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