A Cross-Cohort Changepoint Model for Customer-Base Analysis

Abstract

We introduce a new methodology that can capture and explain differences across a series of cohorts of new customers in a repeat-transaction setting. More specifically, this new framework, which we call a vector changepoint model, exploits the underlying regime structure in a sequence of acquired customer cohorts to make predictive statements about new cohorts for which the firm has little or no longitudinal transaction data. To accomplish this, we develop our model within a hierarchical Bayesian framework to uncover evidence of (latent) regime changes for each cohort-level parameter separately, while disentangling cross-cohort changes from calendar-time changes. Calibrating the model using multicohort donation data from a nonprofit organization, we find that holdout predictions for new cohorts using this model have greater accuracy-and greater diagnostic value-compared to a variety of strong benchmarks. Our modeling approach also highlights the perils of pooling data across cohorts without accounting for cross-cohort shifts, thus enabling managers to quantify their uncertainty about potential regime changes and avoid "old data" aggregation bias.

Valuing Subscription-Based Businesses Using Publicly Disclosed Customer Data

“…For instance, it may be the case that individual-level acquisition and retention propensities are correlated (i.e., customers who take longer to acquire may have a lower propensity to churn after they have been acquired or vice versa; see Schweidel, Fader, and Bradlow 2008a), but our ability to empirically identify such a correlation is very limited, which increases the risk that we overburden the limited data we have available. Many other theoretically reasonable extensions (e.g., allowing for cross-cohort effects [Gopalakrishnan, Bradlow, and Fader 2016]), specifying a more complicated market potential model) will likely suffer from similar issues. Bodapati and Gupta (2004) warn that when data are highly aggregated, even identifying heterogeneity (in their setting, using a finite mixture model) can be challenging.…”

Valuing Subscription-Based Businesses Using Publicly Disclosed Customer Data

“…For instance, it may be the case that individual-level acquisition and retention propensities are correlated (i.e., customers who take longer to acquire may have a lower propensity to churn once they have been acquired or vice versa -see Schweidel, Fader, and Bradlow (2008a) -but our ability to empirically identify such a correlation is very limited, increasing the risk that we over-burden the limited data we have available. Many other theoretically reasonable extensions (e.g., allowing for cross-cohort effects (Gopalakrishnan, Bradlow, and Fader 2016), or specifying a more complicated market potential model) will likely suffer from similar issues. Bodapati and Gupta (2004) warn us that when data is highly aggregated, even identifying heterogeneity (in their setting, using a finite mixture model) can be challenging.…”

The Role of Time-Varying Contextual Factors in Latent Attrition Models for Customer Base Analysis

“…Although it is possible to use a pooled model and to account for cohort-specific differences by including fixed effects in the extended Pareto/NBD model, this is not an optimal solution. Leveraging the commonalities between cohorts, similar to the cross-cohort model introduced by Gopalakrishnan et al (2017), could possibly improve the predictions, especially for cohorts that have been observed for only a relatively short period of time. Fifth, future research may add further benchmarks.…”

“…The authors focus on time-discrete transactions in a charity setting, that is, whether a person has donated in a certain year. Gopalakrishnan et al (2017) present a vector changepoint model in a hierarchical Bayesian framework to capture differences across a series of customer cohorts. Their approach allows for the probability of purchase and attrition to vary by individual and time.…”

“…Extensions to the Pareto/NBD model or related models mainly focus on the computational complexity of the estimation procedure (Fader et al 2005a), the correlation between the modeled processes (Glady et al 2015), or the integration of timeinvariant contextual factors (Fader and Hardie 2007, Abe 2009, Singh et al 2009. Recent studies illustrate how regularity patterns (Platzer and Reutterer 2016) and stationary transaction attributes can be included in the customer's purchase process (Braun et al 2015) or how differences across customer cohorts may be captured in latent attrition models (Gopalakrishnan et al 2017). An approach by Schweidel and Knox (2013) goes one step further and provides the possibility of including other time-varying contextual factors (i.e.…”