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A Bivariate Timing Model of Customer Acquisition and Retention

Author

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  • David A. Schweidel

    (Department of Marketing, Madison School of Business, University of Wisconsin, Madison, Wisconsin 53706)

  • Peter S. Fader

    (Department of Marketing, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Eric T. Bradlow

    (Department of Marketing, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

Abstract

Two widely recognized components, central to the calculation of customer value, are acquisition and retention propensities. However, while extant research has incorporated such components into different types of models, limited work has investigated the kinds of associations that may exist between them. In this research, we focus on the relationship between a prospective customer's time until acquisition of a particular service and the subsequent duration for which he retains it, and examine the implications of this relationship on the value of prospects and customers. To accomplish these tasks, we use a bivariate timing model to capture the relationship between acquisition and retention. Using a split-hazard model, we link the acquisition and retention processes in two distinct yet complementary ways. First, we use the Sarmonov family of bivariate distributions to allow for correlations in the observed acquisition and retention times ; next, we allow for differences customers using latent classes for the parameters that govern the two processes. We then demonstrate how the proposed methodology can be used to calculate the discounted expected value of a subscription based on the time of acquisition, and discuss possible applications of the modeling framework to problems such as customer targeting and resource allocation.

Suggested Citation

  • David A. Schweidel & Peter S. Fader & Eric T. Bradlow, 2008. "A Bivariate Timing Model of Customer Acquisition and Retention," Marketing Science, INFORMS, vol. 27(5), pages 829-843, 09-10.
    • Handle: RePEc:inm:ormksc:v:27:y:2008:i:5:p:829-843
    DOI: 10.1287/mksc.1070.0328
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    Cited by:

    1. Polo, Yolanda & Sese, F. Javier & Verhoef, Peter C., 2011. "The Effect of Pricing and Advertising on Customer Retention in a Liberalizing Market," Journal of Interactive Marketing, Elsevier, vol. 25(4), pages 201-214.
    2. David A. Schweidel & George Knox, 2013. "Incorporating Direct Marketing Activity into Latent Attrition Models," Marketing Science, INFORMS, vol. 32(3), pages 471-487, May.
    3. Peter J. Danaher & Michael S. Smith, 2011. "Modeling Multivariate Distributions Using Copulas: Applications in Marketing," Marketing Science, INFORMS, vol. 30(1), pages 4-21, 01-02.
    4. Chang, Chun-Wei & Zhang, Jonathan Z., 2016. "The Effects of Channel Experiences and Direct Marketing on Customer Retention in Multichannel Settings," Journal of Interactive Marketing, Elsevier, vol. 36(C), pages 77-90.
    5. repec:tiu:tiutis:52e91e47-4a2d-4e7b-bb23-3926b842ae30 is not listed on IDEAS
    6. Lhoest-Snoeck, Sietske & van Nierop, Erjen & Verhoef, Peter C., 2014. "For New Customers Only: A Study on the Effect of Acquisition Campaigns on a Service Company's Existing Customers' CLV," Journal of Interactive Marketing, Elsevier, vol. 28(3), pages 210-224.
    7. Philippe Aurier & Victor D. Mejía, 2021. "The differing impacts of brand-line breadth and depth on customers’ repurchasing behavior of frequently purchased packaged goods," Journal of the Academy of Marketing Science, Springer, vol. 49(6), pages 1244-1266, November.
    8. Anas Abdallah & Lan Wang, 2023. "Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves," Risks, MDPI, vol. 11(11), pages 1-37, October.
    9. Yan Dong & Yuliang Yao & Tony Haitao Cui, 2011. "When Acquisition Spoils Retention: Direct Selling vs. Delegation Under CRM," Management Science, INFORMS, vol. 57(7), pages 1288-1299, July.
    10. Agustín Hernández-Bastida & M. Fernández-Sánchez, 2012. "A Sarmanov family with beta and gamma marginal distributions: an application to the Bayes premium in a collective risk model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 391-409, November.
    11. David A. Schweidel & Eric T. Bradlow & Peter S. Fader, 2011. "Portfolio Dynamics for Customers of a Multiservice Provider," Management Science, INFORMS, vol. 57(3), pages 471-486, March.
    12. Yang, Yang & Ignatavičiūtė, Eglė & Šiaulys, Jonas, 2015. "Conditional tail expectation of randomly weighted sums with heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 20-28.
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    14. Shmargad, Yotam & Watts, Jameson K.M., 2016. "When Online Visibility Deters Social Interaction: The Case of Digital Gifts," Journal of Interactive Marketing, Elsevier, vol. 36(C), pages 1-14.
    15. Glady, Nicolas & Lemmens, Aurélie & Croux, Christophe, 2015. "Unveiling the relationship between the transaction timing, spending and dropout behavior of customers," International Journal of Research in Marketing, Elsevier, vol. 32(1), pages 78-93.
    16. Park, Chang Hee & Park, Young-Hoon & Schweidel, David A., 2014. "A multi-category customer base analysis," International Journal of Research in Marketing, Elsevier, vol. 31(3), pages 266-279.
    17. Wei, Li & Yuan, Zhongyi, 2016. "The loss given default of a low-default portfolio with weak contagion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 113-123.
    18. Ashish Sood & Gerard J. Tellis, 2011. "Demystifying Disruption: A New Model for Understanding and Predicting Disruptive Technologies," Marketing Science, INFORMS, vol. 30(2), pages 339-354, 03-04.
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    20. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2016. "Sarmanov family of multivariate distributions for bivariate dynamic claim counts model," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 120-133.
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    22. Raluca Vernic, 2016. "On the Distribution of a Sum of Sarmanov Distributed Random Variables," Journal of Theoretical Probability, Springer, vol. 29(1), pages 118-142, March.

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