When are Your Customers Active and is Their Buying Regular or Random? An Erlang Mixture State-Switching Model for Customer Scoring

Abstract

Scoring customers with regard to the expected number of their future transactions is of fundamental interest to direct marketers. For the purpose of customer scoring, a variety of models have been developed, based on the negative binomial distribution. Extensions of such models allow for customer defection (“buy until you die”). We extend customer scoring models in two ways: (1) We assume that customers switch between an active state in which they buy and an inactive state in which they do not purchase. Switching between states can occur in both directions, implying that defection is temporary. (2) We allow for heterogeneity among households with regard to the regularity of purchasing. We achieve this by modeling purchasing in the active state as a mixture of Erlang-distributed interpurchase times. Our model nests the BG-NBD model and other variants of the NBD as special cases. We develop MCMC simulation methods for our model and apply it to five different data sets, comparing the results to several benchmark models. Our results imply that it is often erroneous to assume that customers “buy until they die”. , the results support the assumption of transient switching between an active and inactive state. We show that, when the model does not account for transient switching, customer scoring is biased. We discuss both the theoretical and managerial implications of our results, and potential areas for future research.