[Paper Review] Counterfactual Inference for Consumer Choice Across Many Product Categories

Robert Donnelly, Francisco J. R. Ruiz+2 more|arXiv (Cornell University)|Jun 6, 2019

Consumer Market Behavior and PricingBusiness, Management and Accounting53 references17 citations

TL;DR

This paper proposes a scalable Bayesian hierarchical model that jointly estimates consumer preferences across multiple product categories by leveraging latent factorization of product attributes and consumer heterogeneity. By incorporating time-varying prices and out-of-stock events, the model improves counterfactual inference—especially for price sensitivity and personalized promotions—over isolated category models, with significant gains in predictive accuracy and personalization effectiveness on held-out data.

ABSTRACT

This paper proposes a method for estimating consumer preferences among discrete choices, where the consumer chooses at most one product in a category, but selects from multiple categories in parallel. The consumer's utility is additive in the different categories. Her preferences about product attributes as well as her price sensitivity vary across products and are in general correlated across products. We build on techniques from the machine learning literature on probabilistic models of matrix factorization, extending the methods to account for time-varying product attributes and products going out of stock. We evaluate the performance of the model using held-out data from weeks with price changes or out of stock products. We show that our model improves over traditional modeling approaches that consider each category in isolation. One source of the improvement is the ability of the model to accurately estimate heterogeneity in preferences (by pooling information across categories); another source of improvement is its ability to estimate the preferences of consumers who have rarely or never made a purchase in a given category in the training data. Using held-out data, we show that our model can accurately distinguish which consumers are most price sensitive to a given product. We consider counterfactuals such as personally targeted price discounts, showing that using a richer model such as the one we propose substantially increases the benefits of personalization in discounts.

Motivation & Objective

• To model consumer demand across many product categories simultaneously, capturing cross-category preference correlations.
• To improve estimation of price sensitivity and heterogeneity, especially for low-purchase-frequency products.
• To enable accurate counterfactual prediction of consumer responses to personalized discounts and price changes.
• To develop a model that leverages data pooling across categories to enhance inference for consumers with sparse purchase histories.
• To tune hyperparameters based on counterfactual performance rather than standard prediction metrics, improving real-world utility.

Proposed method

• Uses a nested factorization model that decomposes consumer utility into latent factors for product attributes, price sensitivity, and consumer preferences.
• Applies variational inference with a mean-field Gaussian approximation to scale to large datasets.
• Introduces 'sessions' where prices and availability are constant, enabling modeling of time-varying conditions and out-of-stock events.
• Employs a reparameterization trick for stochastic gradient descent to optimize the evidence lower bound (ELBO).
• Incorporates product-level and category-level latent factors, with separate dimensions for non-price attributes and price sensitivity.
• Tunes hyperparameters via validation on counterfactual price changes and stock-out events, prioritizing counterfactual performance over predictive accuracy.

Experimental results

Research questions

• RQ1 How does joint modeling across product categories improve estimation of consumer price sensitivity compared to isolated category models?
• RQ2 To what extent can the model accurately infer preferences for consumers with no or few purchases in a given category?
• RQ3 How does the model’s ability to predict counterfactual outcomes—such as the impact of targeted discounts—improve with richer latent structure?
• RQ4 What is the impact of incorporating time-varying prices and out-of-stock events on model performance?
• RQ5 How does tuning hyperparameters based on counterfactual performance affect model utility compared to standard prediction-based tuning?

Key findings

• The Nested Factorization model achieved a median own-price elasticity of -1.7121, significantly more negative than multinomial logit models (-1.1841) and nested logit models (-1.2976), indicating stronger estimated price sensitivity.
• The model reduced the standard deviation of mean elasticities across products (SD(Mean) = 1.2008) compared to mixed logit models (SD(Mean) = 1.7822), suggesting more consistent elasticity estimates.
• The model demonstrated superior performance in predicting consumer responses to price changes and stock-outs, with improved counterfactual accuracy on held-out data.
• By pooling information across categories, the model enabled accurate estimation of preferences for consumers who had never purchased in a category, improving inference for rare items.
• Hyperparameter tuning based on counterfactual performance led to better real-world utility than tuning based on prediction quality alone.
• The model with 80-dimensional latent factors for product attributes and 20 for price sensitivity, along with linear price terms, was selected as optimal based on validation on price change events.