Modeling Dynamic Heterogeneity Using Gaussian Processes

Abstract

Marketing research relies on individual-level estimates to understand the rich heterogeneity of consumers, firms, and products. While much of the literature focuses on capturing static cross-sectional heterogeneity, little research has been done on modeling dynamic heterogeneity, or the heterogeneous evolution of individual-level model parameters. In this work, the authors propose a novel framework for capturing the dynamics of heterogeneity, using individual-level, latent, Bayesian nonparametric Gaussian processes. Similar to standard heterogeneity specifications, this Gaussian process dynamic heterogeneity (GPDH) specification models individual-level parameters as flexible variations around population-level trends, allowing for sharing of statistical information both across individuals and within individuals over time. This hierarchical structure provides precise individual-level insights regarding parameter dynamics. The authors show that GPDH nests existing heterogeneity specifications and that not flexibly capturing individual-level dynamics may result in biased parameter estimates. Substantively, they apply GPDH to understand preference dynamics and to model the evolution of online reviews. Across both applications, they find robust evidence of dynamic heterogeneity and illustrate GPDH’s rich managerial insights, with implications for targeting, pricing, and market structure analysis.