Modeling Dynamic Heterogeneity using Gaussian Processes

69 Pages Posted: 13 Feb 2017

See all articles by Ryan Dew

Ryan Dew

University of Pennsylvania - Marketing Department

Asim Ansari

Columbia Business School - Marketing

Yang Li

Cheung Kong Graduate School of Business

Date Written: January 17, 2019

Abstract

Marketing research relies on individual-level estimates to understand the rich heterogeneity that exists in 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, we propose a novel framework for capturing the dynamics of heterogeneity, using individual-level, latent, Bayesian nonparametric Gaussian processes. Similar to standard heterogeneity specifications, our 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. We show that GPDH nests existing heterogeneity specifications, and that not flexibly capturing individual-level dynamics may result in biased parameter estimates. Substantively, we apply GPDH to two problems: understanding preference dynamics, and modeling the evolution of online reviews. Across both applications, we find robust evidence of dynamic heterogeneity, and illustrate GPDH's rich managerial insights, with implications for targeting, pricing, and market structure analysis.

Keywords: dynamics, heterogeneity, Bayesian nonparametrics, Gaussian processes, choice models, topic models, machine learning

JEL Classification: C01, C11, C14, C23, M37

Suggested Citation

Dew, Ryan and Ansari, Asim and Li, Yang, Modeling Dynamic Heterogeneity using Gaussian Processes (January 17, 2019). Available at SSRN: https://ssrn.com/abstract=2915632 or http://dx.doi.org/10.2139/ssrn.2915632

Ryan Dew (Contact Author)

University of Pennsylvania - Marketing Department ( email )

700 Jon M. Huntsman Hall
3730 Walnut Street
Philadelphia, PA 19104-6340
United States

Asim Ansari

Columbia Business School - Marketing ( email )

New York, NY 10027
United States

Yang Li

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E2
One East Chang An Avenue
Beijing, Beijing 100738
China
+861085188858 (Phone)

HOME PAGE: http://english.ckgsb.edu.cn/?q=node/381

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