Estimation, Prediction, and Assortment Optimization for Markov Chain Choice Models with Panel Data

2026-07-10

AI Summary

This study addresses the limitation of traditional choice models in neglecting inter-temporal dependencies among customers’ historical transactions, which hinders effective utilization of preference information embedded in panel data. To overcome this, the authors introduce panel data into the Markov chain choice model for the first time, establishing a unified framework that integrates partial ranking preference information. They further propose a novel EM estimation algorithm that explicitly incorporates such partial orderings. Theoretical analysis reveals the computational complexity of conditional choice prediction and assortment optimization under this framework. Empirical evaluations demonstrate that the proposed algorithm consistently outperforms conventional Markov chain estimation methods and multinomial logit–based partial ranking benchmarks on both synthetic and real-world sushi datasets.

Abstract

We propose a framework for the Markov chain (MC) choice model with panel data, including parameter estimation, personalized choice prediction, and personalized assortment optimization. In contrast to the traditional setting, which assumes that each transaction is independently drawn from a random utility model, our framework accounts for dependencies among transactions for the same customer in historical data, captured by partial-ordering preference information. To the best of our knowledge, our framework initiates the study of choice modeling with panel data under MC. As our primary result, we propose novel expectation-maximization (EM) algorithms for MC parameter estimation by incorporating partial-ordering-based customer preference information. On synthetic datasets and the sushi dataset, our EM algorithms outperform the traditional EM algorithm of Simsek and Topaloglu (Operations Research, 66, 2018) and multinomial-logit-based partial-order benchmarks adapted from Jagabathula and Vulcano (Management Science, 64, 2018). As our secondary contribution, we present hardness and computational results for conditional choice prediction and assortment optimization problems. These results complement our estimation framework and clarify the computational landscape of conditional choice and assortment optimization, which may be of independent interest.

Problem

• Markov chain choice model
• panel data
• partial-ordering preference
• choice prediction
• assortment optimization

Innovation

• Markov chain choice model
• panel data
• partial-ordering preference
• expectation-maximization algorithm
• assortment optimization