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CLV Models and More

This list contains a curated, ever-growing collection of papers and repositories about modelling and prediction of customer churn and customer lifetime value.

Contributions and feedback are more than welcome.

Table of Contents

Models and Papers

Contractual Setting Models

Probabilistic models predicting churn and CLV in scenarios where transactions happen on fixed time periods, e.g. weekly, monthly.

  • Beta-Geometric (BG) (2007) - [doi] [pdf]

    Fader, P. S., & Hardie, B. G. S. (2007). How to Project Customer Retention. Journal of Interactive Marketing, 21(1), 76–90.

  • Usage-Renewal Model (2013) - [doi] [pdf]

    Ascarza, E., & Hardie, B.G.S. (2013). A Joint Model of Usage and Churn in Contractual Settings. Marketing Science, 32(4), 570-590.

  • Beta-discrete-Weibull (BdW) (2018) - [doi] [pdf]

    Fader, P. S., Hardie, B. G. S., Liu, Y., Davin, J., & Steenburgh, T. (2018). “How to Project Customer Retention” Revisited: The Role of Duration Dependence. Journal of Interactive Marketing, 43, 1–16.

Non-Contractual Setting Models (a.k.a. Buy 'Til You Die)

Probabilistic models predicting churn and CLV in scenarios where transactions appear spontaneously at any given time.

  • Negative Binomial Distribution (NBD) (1959) - [doi] [pdf]

    Ehrenberg, A. S. (1959). The pattern of consumer purchases. Journal of the Royal Statistical Society. Series C (Applied Statistics), 8(1), 26–41.

  • Pareto/NBD (1987) - [doi] [pdf]

    Schmittlein, D. C., Morrison, D. G., & Colombo, R. (1987). Counting your customers: Who-are they and what will they do next? Management Science, 33(1), 1–24.

  • BG/NBD (2005) - [doi] [pdf]

    Fader, P. S., Hardie, B. G., & Lee, K. L. (2005). “Counting your Customers” the Easy Way: An Alternative to the Pareto/NBD Model. Marketing Science, 24(2), 275–284.

  • BG/NBD with time-invariant contextual factors (2007) - [pdf]

    Fader, P. S., & Hardie, B. G. S. (2007). Incorporating Time-Invariant Covariates into the Pareto/NBD and BG/NBD Models

  • Pareto/NBD with time-invariant contextual factors (2007) - [pdf]

    Fader, P. S., & Hardie, B. G. S. (2007). Incorporating Time-Invariant Covariates into the Pareto/NBD and BG/NBD Models

  • MBG/NBD (2007) - [doi] [pdf]

    Batislam, E. P., Denizel, M., & Filiztekin, A. (2007). Empirical validation and comparison of models for customer base analysis. International Journal of Research in Marketing, 24(3), 201–209.

  • Pareto/NBD (HB) (2007) - [doi] [pdf]

    Ma, S.-H., & Liu, J.-L. (2007). The MCMC approach for solving the pareto/NBD model and possible extensions. Third International Conference on Natural Computation (ICNC 2007).

  • Pareto/NBD (Abe) (2009) - [doi] [pdf]

    Abe, M. (2009). “Counting your Customers” One by One: A Hierarchical Bayes Extension to the Pareto/NBD Model. Marketing Science, 28(3), 541–553.

  • BG/BB (Beta-Geometric/Beta-Binomial) (2010) - [doi] [pdf]

    Fader, P. S., Hardie, B. G., & Shang, J. (2010). Customer-base analysis in a discrete-time noncontractual setting. Marketing Science, 29(6), 1086–1108.

  • Gamma/Gompertz/NBD (2012) - [doi] [pdf]

    Bemmaor, A. C., & Glady, N. (2012). Modeling purchasing behavior with sudden “death”: A flexible customer lifetime model. Management Science, 58(5), 1012–1021.

  • Pareto/GGG (GammaGammaGamma) (2016) - [doi] [pdf]

    Platzer, M., & Reutterer, T. (2016). Ticking away the moments: Timing regularity helps to better predict customer activity. Marketing Science, 35(5), 779–799.

  • **(M)BG/CNBD-k ** (2021) - [doi] [pdf]

    Reutterer, T., Platzer, M., & Schröder, N. (2021). Leveraging Purchase Regularity for Predicting Customer Behavior the Easy Way. International Journal of Research in Marketing, 38(1), 194–215.

  • Pareto/NBD with time-varying contextual factors (2021) - [doi] [pdf]

    Bachmann, P., Meierer, M., & Näf, J. (2021). The role of time-varying contextual factors in latent attrition models for customer base analysis. Marketing Science, 40(4), 783–809.

Extensions

  • RFM to RFMC (Clumpiness) (2015) - [doi] [pdf]

    Zhang, Y., Bradlow, E.T., & Small, D. S. (2015). Predicting Customer Value Using Clumpiness: From RFM to RFMC. Marketing Science, 34(2), 195-208.

Non-Probabilistic CLV Models

  • To be added (e.g. ML/DL approaches)

Additional Valuable Sources

Software Packages and Tools

List of model implemenations and software tools in various programming languages.

Python

  • Lifetimes - Python implementation of BTYD models, namely BG, BG/BB, GG, MBG and Pareto/NBD (not maintained, succeded by PyMC-Marketing)
  • PyMC-Marketing - Bayesian marketing toolbox in PyMC. Media Mix (MMM), customer lifetime value (CLV), buy-till-you-die (BTYD) models and more.

R

  • BTYD - The original R implementation of BTYD models, namely BG/BB, BG/NBD, P/NBD-GG
  • BTYDplus - Extension of the BTYD package with NBD, MBG/NBD, (M)BG/CNBD-k, Pareto/NBD (HB), Pareto/NBD (Abe) and Pareto/GGG
  • CLVTools (web) - The most recent and optimized R package for BTYD models including the newest additions to the field
  • foretell - Implementation of contractual models by Fader, Hardie et al.