Are My Data Outdated? A Bayesian Cross-Cohort Changepoint Model for Customer-Base Analysis

• Activity Number: 398
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Marketing
• Author(s): Arun Gopalakrishnan*+ and Eric Bradlow and Peter Fader
• Companies: and The Wharton School and The Wharton School
• Keywords: Changepoint ; Cross-Cohort ; Hierarchical Bayesian ; Forecasting ; Customer-base analysis ; Reversible-Jump MCMC

Abstract

We develop a Hierarchical Bayesian cross cohort changepoint model framework that (1) allows for cross-sectional heterogeneity within a cohort, (2) identifies regime shifts/changepoints in cohort behavior along the sequence of customer cohorts, and (3) enables predictions of recently acquired cohorts for whom the firm has little to no longitudinal transaction data. The model combines the Reversible-Jump MCMC sampler with a vectorized-changepoint approach which enables each parameter in the cohort-level model to have its own regime configuration.

We calibrate the model in the context of a discrete-time non-contractual setting, using multi-cohort donation data from a U.S. non-profit organization, using the Beta-Geometric Beta-Bernoulli (BG/BB) model developed by Fader, Hardie and Shang (2010) to characterize each cohort's behavior. The results demonstrate strong evidence for changepoints in some dimensions of the BG/BB parameter space but not others, through which we are able to disentangle which parameters are shifting. The prediction of new cohorts using this model has lower bias compared to both a naïve Hierarchical Bayes model without changepoints and a fully-pooled model.