The ability to retain existing customers is a major concern for many businesses. However retention is not the only dimension of interest; the revenue stream associated with each customer is another key factor influencing customer profitability.
In most contractual situations the exact revenue that will be generated per customer is uncertain at the beginning of the contract period; customer revenue is determined by how much of the service each individual consumes. While a number of researchers have explored the problem of modeling retention in a contractual setting, the literature has been surprisingly silent on how to forecast customers' usage (and therefore future revenue) in contractual situations.
We propose a dynamic latent trait model in which usage and renewal behavior are modeled simultaneously by assuming that both behaviors are driven by the same (individual-level) underlying process that evolves over time. We capture the dynamics in the underlying latent variable (which we label "commitment") using a hidden Markov model, and then incorporate unobserved heterogeneity in the usage process.
The model parameters are estimated using hierarchical Bayesian methods. We validate the model using data from a so-called Friends scheme run by a performing arts organization. First we show how the proposed model outperforms benchmark models on both the usage and retention dimensions. In contrast to most churn models, this dynamic model is able to identify changes in behavior before the contract is close to expiring, thus providing early predictions of churn. Moreover, the model provides additional insights into the behavior of the customer base that are of interest to managers.
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Ascarza, Eva, and Bruce G. S. Hardie. "A Joint Model of Usage and Churn in Contractual Settings." Working paper, Columbia Business School, March 2009.