Customer Lifetime Value Model that Accommodates Cyclic Purchase Behavior: Overcoming the limitation of Pareto/NBD models using Complete Purchase History

In non-contractual CRM whereby customer churn cannot be observed, BTYD (Buy Till You Die) models permit one to infer the churn. Amongst these models, the most popular one, Pareto/NBD posits strong assumptions on purchase behavior in order to allow its model estimation from a minimal amount of information, namely, customers' recency and frequency (RF) data. The assumptions, however, place two serious restrictions. First, the Poisson purchase is not appropriate for stores, categories, and products that exhibit cyclic transaction behavior. Second, the independence of two gamma mixture distributions for the purchase and churn rates ignores the association between purchase and churn behaviors. This research proposes a customer lifetime (CLV) model that can accommodate both memoryless and cyclic purchase behaviors from customers' complete purchase history. Identical to extensively studied Pareto/NBD and its variant models, the proposed model assumes random churn and stochastic spending per transaction following a lognormal distribution. In contrast, purchase behavior, to address its cyclicity, is captured by a logistic threshold model. This CY(cyclic) model provides customer-specific marketing metrics that are useful for one-to-one marketing, including CLV and purchase cyclicity. Using purchase history from hair salon customers, the proposed model (CY) is compared against two models, both of which assume memoryless purchase: one is an individual-level Poisson purchase / Exponential churn (PE) model, and the other is a Pareto/NBD that captures customer heterogeneity through independent gamma mixture distributions. CY model resulted in superior performance over PE and Pareto/NBD in terms of both fit/prediction and parameter estimate. In order to demonstrate application to a retention tactic, the model derived customer-specific optimal level of interception that maximizes the return on CLV.