The Need for Market Segmentation in Buy-Till-You-Defect Models

Buy-till-you-defect [BTYD] models are built for companies operating in a non- contractual setting to predict customers’ transaction frequency, amount and timing as well as customer lifetime. These models tend to perform well, although they often predict unrealistically long lifetimes for a substantial fraction of the customer base. This obvious lack of face validity limits the adoption of these models by practitioners. Moreover, it highlights a flaw in these models. Based on a simulation study and an empirical analysis of different datasets, we argue that such long lifetime predictions can result from the existence of multiple segments in the customer base. In most cases there are at least two segments: one consisting of customers who purchase the service or product only a few times and the other of those who are frequent purchasers. Customer heterogeneity modeling in the current BTYD models is insufficient to account for such segments, thereby producing unrealistic lifetime predictions. We present an extension over the current BTYD models to address the extreme lifetime prediction issue where we allow for segments within the customer base. More specifically, we consider a mixture of log-normals distribution to capture the heterogeneity across customers. Our model can be seen as a variant of the hierarchical Bayes [HB] Pareto/NBD model. In addition, the proposed model allows us to relate segment membership as well as within segment customer heterogeneity to selected customer characteristics. Our model, therefore, also increases the explanatory power of BTYD models to a great extent. We are now able to evaluate the impact of customers’ characteristics on the membership probabilities of different segments. This allows, for example, one to a-priori predict which customers are likely to become frequent purchasers. The proposed model is compared against the benchmark Pareto/NBD model (Schmittlein, Morrison, and Colombo 1987) and its HB extension (Abe 2009) on simulated datasets as well as on a real dataset from a large grocery e-retailer in a Western European country. Our BTYD model indeed provides a useful customer segmentation that allows managers to draw conclusions on how customers’ purchase and defection behavior are associated with their shopping characteristics such as basket size and the delivery fee paid

"Counting Your Customers": When will they buy next? An empirical validation of probabilistic customer base analysis models based on purchase timing

This research provides a new way to validate and compare buy-till-you-defect [BTYD] models. These models specify a customer’s transaction and defection processes in a non-contractual setting. They are typically used to identify active customers in a com- pany’s customer base and to predict the number of purchases. Surprisingly, the literature shows that models with quite different assumptions tend to have a similar predictive performance. We show that BTYD models can also be used to predict the timing of the next purchase. Such predictions are managerially relevant as they enable managers to choose appropriate promotion strategies to improve revenues. Moreover, the predictive performance on the purchase timing can be more informative on the relative quality of BTYD models. For each of the established models, we discuss the prediction of the purchase timing. Next, we compare these models across three datasets on the predictive performance on the purchase timing as well as purchase frequency. We show that while the Pareto/NBD and its Hierarchical Bayes extension [HB] models perform the best in predicting transaction frequency, the PDO and HB models predict transaction timing more accurately. Furthermore, we find that differences in a model’s predictive performance across datasets can be explained by the correlation between behavioral parameters and the proportion of customers without repeat purchases

A Statistical Significance Test for Necessary Condition Analysis

In this article, we present a statistical significance test for necessary conditions. This is an elaboration of necessary condition analysis (NCA), which is a data analysis approach that estimates the necessity effect size of a condition X for an outcome Y. NCA puts a ceiling on the data, representing the level of X that is necessary (but not sufficient) for a given level of Y. The empty space above the ceiling relative to the total empirical space characterizes the necessity effect size. We propose a statistical significance test that evaluates the evidence against the null hypothesis of an effect being due to chance. Such a randomness test helps protect researchers from making Type 1 errors and drawing false positive conclusions. The test is an “approximate permutation test.” The test is available in NCA software for R. We provide suggestions for further statistical development of NCA