Back to Vol. 40, No. 2, 2026
Vol. 40, No. 2, 2026

Consumer demand estimation based on mixed-nested logit model

Title

Consumer demand estimation based on mixed-nested logit model

Author

LUO Chenbin; XUE Weili; ZHANG Lianmin

Abstract

In the context of retailers, understanding users' true product demands is a crucial aspect of making decisions related to product assortment management, price optimization, and inventory control. Enhancing the precision of demand forecasting relies upon the selection of an appropriate model capable of effectively capturing consumer scenarios. Over the past two decades, discrete choice models have progressively gained prominence within revenue management research, as they enable the depiction of consumer inclinations towards potential products. This facilitates an understanding of consumers' decision-making patterns across diverse product combinations, attributes, and pricing structures. Unlike offline retail, where analysis is primarily based on order data, the online retail environment presents a more diverse range of data sources and composition. In addition to the characteristics of products such as attributes, prices, and availability, accurate records are also maintained regarding users' demographic descriptors and their multi-stage discrete behaviors. These behaviors include interactions such as clicks, browsing, and purchases of products. The discrete behaviors of users not only elucidate their decision-making processes but also reflect the degree of preference they hold for certain products. Consequently, exploring user behavioral data to establish choice models has emerged as a prominent research focus. Among these models, the Multinomial Logit (MNL) model has been widely employed due to its high flexibility. However, it is limited by the Independence and Irrelevant Alternatives (IIA) assumption and overlooks users' multi-stage choice behaviors. Furthermore, existing methods often employ a single model to analyze the choices of all users, thereby disregarding the heterogeneity in users' choice preferences. Based on the aforementioned background, this paper employs the Nested Logit model to characterize users' multi-stage discrete choice behavior. Assuming a retailer sells a group of substitutable products, which can be divided into several subcategories based on their attributes, each subcategory is considered as a nest. The arriving users exhibit two-stage choice behavior, where in the first stage, users choose a nest through a click behavior or directly exit the system, and in the second stage, users within the selected nest choose to purchase one of the products or not to make a purchase. Due to the heterogeneity of customer preferences, we further introduce user segmentation into the Nested Logit model, incorporating user segmentation and within-segment choice behavior within the same framework using a mixed Nested Logit model. Based on this model, the first part of this paper discusses how to estimate user demand with customer information, product descriptions, and historical orders data. To simultaneously obtain user choice and user segmentation, this paper employs the Expectation-Maximization(EM) algorithm to estimate the parameters of the choice model. Theoretically, we prove that our algorithm can significantly improve estimation efficiency and ensure the convergence of parameter estimation results. In the second part, we demonstrate the performance of our algorithm using real data from JD.com, an online retailer. The results show that, in cases of high data sparsity, where a large number of users exhibit choice behavior for only a small subset of products, our model's prediction accuracy is on average 13.71% higher than benchmark models such as MNL, MMNL, and NL, indicating that considering user heterogeneity and multi-stage discrete behavior can more accurately characterize user choices. By further applying the estimated demand results to product assortment strategy formulation, which refers to the selection of product sets to be presented to users upon their arrival to the system, the results indicate that the assortment average expected profits generated by our model are 5.11% higher than those of benchmark models such as MNL. This observation demonstrates that the inability to accurately capture user demand leads to suboptimal operational decisions. In summary, by considering user heterogeneity and multi-stage choice behavior, our proposed choice model can accurately depict the user choice process and preferences. To simultaneously capture user preferences and segmentation, we introduce a parameter estimation method based on the Expectation-Maximization (EM) algorithm, which exhibits efficient and effective convergence properties. This approach can help retailers obtain more accurate market characterization, which serve as valuable inputs for dynamic pricing, product assortment optimization decisions, and personalized recommendations. Additionally, our designed product assortment experiment further validates the value of accurately characterizing user preferences.

Keywords

Discrete choice model; Mixed-nested logit model; Demand estimation; EM algorithm

Issue

Vol. 40, No. 2, 2026

References