Extending the BG/NBD: A Simple Model of Purchases and Complaints

Abstract

Extant customer base models like the beta geometric/negative binomial distribution (BG/NBD) predict future purchasing based on the customer’s observed purchase history. We extend the BG/NBD by adding an important non-transactional element that drives future purchases: complaint history. Our model retains several desirable properties of the BG/NBD: it can be implemented in readily available software and estimation requires only sufficient statistics for each customer, rather than detailed transaction-sequence data. The likelihood function is closed-form and managerially relevant metrics are obtained by drawing from beta and gamma densities and transforming these draws to a sample average. Based on more than two years of individual-level data from a major U.S. internet and catalog retailer, our model with complaints outperforms both the original BG/NBD and a modified version. Even though complaints are rare and non-transactional events, they lead to different substantive insights about customer purchasing and drop-out: customers purchase faster, but in particular drop out much faster. Furthermore, there is more heterogeneity in drop-out following a purchase than a complaint.

Keywords: Complaints, Probability Models, Customer Base Analysis, Customer Lifetime Value