The role of time-varying contextual factors in latent attrition models for customer base analysis

Abstract

Customer base analysis of noncontractual businesses builds on modeling purchases and latent attrition. With the Pareto/NBD model, this has become a straight-forward exercise. However, this simplicity comes at a price. Customer-level predictions often lack precision. This issue can be addressed by acknowledging the importance of contextual factors for customer behavior. Considering contextual factors might contribute in two ways: (1) by increasing predictive accuracy and (2) by identifying the impact of these determinants on the purchase and attrition process. However, there is no generalization of the Pareto/NBD model that incorporates time-varying contextual factors. Preserving a closed-form maximum likelihood solution, this study proposes an extension that facilitates modeling time-invariant and time-varying contextual factors in continuous noncontractual settings. These contextual factors can influence the purchase process, the attrition process, or both. The authors further illustrate how to control for endogenous contextual factors. Benchmarking with three data sets from the retailing industry shows that explicitly modeling time-varying contextual factors significantly improves the accuracy of out-of-sample predictions for future purchases and latent attrition.