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

• CLV Models and More
  • Table of Contents
  • Models and Papers
    • Contractual Setting Models
    • Non-Contractual Setting Models (a.k.a. Buy 'Til You Die)
    • Extensions
    • Non-Probabilistic CLV Models
    • Additional Valuable Sources
  • Software Packages and Tools
    • Python
    • R

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

• Bruce Hardie's Notes

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.