A Data Fusion Approach for Interpurchase Timing Models Using Incomplete Purchase Histories

Interpurchase timing models are important for understanding the effects of marketing variables. However, a company's database cannot record purchase histories in competing stores.Its database records only the sum of durations for its own and competing stores. Moreover, it is difficult for companies to know the number of purchases in competing stores between two purchases observed in their own stores. Therefore, a simple application of interpurchase timing models would be incorrect and generate biased results. In this study, we construct a model that predicts the missing number of purchases in competing stores and a gamma proportional hazard model in which parameters are estimated from the sum of the durations. It is difficult to predict the missing number of purchases in competing stores and estimate parameters suitably from the summed durations. Therefore, we propose a Bayesian data fusion approach that combines two datasets and incorporates macro-level information in the model. We show the performance of the proposed method through a simulation study and application using a real purchase history dataset. The results show that the proposed method can correctly estimate the effects of the marketing variables, while the sign of the estimated parameter is reversed in the simple analysis