Analyzing Recurrent Customer Purchases and Unobserved Defections: a Bayesian Data Augmentation Scheme

Understanding customer purchase behavior is important for firms’ customer relationship management (CRM) efforts. In certain contexts of firm-customer relationship (e.g., retailing and catalog marketing), a firm does not observe customer defections or termination of relationship. Thus, specifying and estimating models of customer lifetime purchases is more difficult in such contexts, specifically in analyzing two key issues, viz. how often will a customer purchase from the firm (purchase frequency) and how long will the customer continue purchasing from the firm (customer lifetime). In this paper, we use a Bayesian data augmentation scheme that overcomes the estimation constraints and allows the use of all available information on customers. Using data from a direct marketing company and also an online classifieds company, we demonstrate the flexibility of this scheme by estimating existing models of lifetime purchase behavior, along with a new proposed model. We show how different types of customer heterogeneity (i.e., observed, unobserved, and time varying) can be incorporated in these models, which is made possible due to the data augmentation.