What Are Your Customers Still Doing? A Bivariate Generalization of the Latent Attrition Framework
39 Pages Posted: 18 Aug 2010 Last revised: 14 Apr 2011
Date Written: April 2011
Latent attrition models serve as the foundation for customer base analyses in transactional settings. Despite their intuitive appeal, limited research has been conducted to generalize these “buy till you die” models to multivariate contexts to examine the nature of attrition when a firm offers multiple types of transactional activities. Attrition for the different activities may be independent, simultaneous, or separate but related events. To investigate this issue, we develop a coupled hidden Markov model in which we use a Gaussian copula distribution to correlate customers’ latent lifetimes, as well as correlate the inter-activity durations. The proposed dynamic model extends the univariate “buy till you die” framework to a bivariate context and nests models that allow for latent attrition in different ways.
Using the data provided by a website that allows users to purchase digital content and/or use a free ancillary service that promotes customer engagement, we find positive correlations between the two latent lifetimes, as well as between the times at which the two activities occur, suggesting that the firm can benefit from encouraging use of its ancillary service in a timely manner. We further demonstrate how our bivariate model offers a more complete picture of customers’ dynamic behavior than is afforded by examining multiple transactional activities in isolation.
Keywords: Duration model, copula, customer base analysis
Suggested Citation: Suggested Citation