Relaxing Functional Form in Choice Models Through Gaussian Processes

• Activity Number: 439 - Topics in Marketing
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics in Marketing
• Author(s): Samuel I Levy* and Richard Mirman and Alan Montgomery
• Companies: Carnegie Mellon University and Dynamic Loyalty Systems Inc. and Carnegie Mellon University
• Keywords: Gaussian Processes; Choice Modeling; Bayesian statistics; Satiation; Category pricing

Abstract

Consumers change their choice as expenditures within a category increase. Traditional choice models usually make restrictive structural assumptions to specify the expenditure elasticity. This imposed functional form of utility strongly influences the range of estimable substitution patterns across goods. Consumers with highly nonlinear preferences may have consumption thresholds in which buying patterns dramatically change when price or budget changes. Understanding these thresholds with a flexible utility-based model could lead to improved pricing and promotion decisions. Using Gaussian process priors on utility functions, we relax the functional form of both inside goods and outside good, within the context of constrained utility maximization. We estimate a general direct utility choice model for simultaneous purchases within a product category. Our model captures non-linear rates of satiation for inside and outside goods alike, that traditional non-homothetic parametric models fail to capture by assuming a given functional form of utility. The proposed model automatically detects non-linear patterns of consumption from the data and provide a more precise statistical inference.