Customer Needs and Solutions

, Volume 3, Issue 1, pp 11–28 | Cite as

Analyzing Recurrent Customer Purchases and Unobserved Defections: a Bayesian Data Augmentation Scheme

  • Sharad Borle
  • Siddharth Shekhar Singh
  • Dipak C. Jain
  • Ashutosh Patil
Research Article

Abstract

Understanding customer purchase behavior is important for firms’ customer relationship management (CRM) efforts. In certain contexts of firm-customer relationship (e.g., retailing and catalog marketing), a firm does not observe customer defections or termination of relationship. Thus, specifying and estimating models of customer lifetime purchases is more difficult in such contexts, specifically in analyzing two key issues, viz. how often will a customer purchase from the firm (purchase frequency) and how long will the customer continue purchasing from the firm (customer lifetime). In this paper, we use a Bayesian data augmentation scheme that overcomes the estimation constraints and allows the use of all available information on customers. Using data from a direct marketing company and also an online classifieds company, we demonstrate the flexibility of this scheme by estimating existing models of lifetime purchase behavior, along with a new proposed model. We show how different types of customer heterogeneity (i.e., observed, unobserved, and time varying) can be incorporated in these models, which is made possible due to the data augmentation.

Keywords

Customer purchase behavior Customer defection Customer heterogeneity 

References

  1. 1.
    Allenby GM, Arora N, Ginter JL (1998) On the heterogeneity of demand. J Mark Res 35(3):384–389CrossRefGoogle Scholar
  2. 2.
    Allenby GM, Leone RP, Jen L (1999) A dynamic model of purchase timing with application to direct marketing. J Am Stat Assoc 94:365–374CrossRefGoogle Scholar
  3. 3.
    Bemmaor AC, Glady N (2012) Modeling purchasing behavior with sudden “Death”: a flexible customer lifetime model. Manag Sci 58:1012–1021CrossRefGoogle Scholar
  4. 4.
    Boatwright P, Borle S, Kadane JB (2003) A model of the joint distribution of purchase quantity and timing. J Am Stat Assoc 98:564–572CrossRefGoogle Scholar
  5. 5.
    Casella G, George EI (1992) Explaining the Gibbs sampler. Am Stat 46(3):167–174Google Scholar
  6. 6.
    Chib S, Greenberg E (1995) Understanding the Metropolis–Hastings algorithm. Am Stat 49(4):327–335Google Scholar
  7. 7.
    Gelfand AE, Smith AFM (1990) Sampling based approaches to calculating marginal densities. J Am Stat Assoc 85:398–409CrossRefGoogle Scholar
  8. 8.
    Hacking I (1965) Logic of statistical inference. Cambridge University Press, New YorkGoogle Scholar
  9. 9.
    Kamakura WA, Russell GJ (1989) A probabilistic choice model for market segmentation and elasticity structure. J Mark Res 26(4):379–390CrossRefGoogle Scholar
  10. 10.
    Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90:773–795CrossRefGoogle Scholar
  11. 11.
    Lazarsfeld PF, Henry NW (1968) Latent structure analysis. Houghton-Mifflin Company, BostonGoogle Scholar
  12. 12.
    Liu L, Wolfe RA, Huang X (2004) Shared frailty model for recurrent events and terminating event. Biometrics 60:747–756CrossRefGoogle Scholar
  13. 13.
    Miloslavsky M, Keles S, Van der Laan MJ, Butler S (2004) Recurrent events analysis in the presence of time-dependent covariates and dependent censoring. J R Stat Soc Ser B 66:239–257CrossRefGoogle Scholar
  14. 14.
    Newton MA, Raftery AE (1994) Approximate Bayesian inference with the weighted likelihood bootstrap. J R Stat Soc Ser B 56:3–48Google Scholar
  15. 15.
    Rossi PE, Allenby GM (2003) Bayesian statistics and marketing. Mark Sci 22(3):304–328CrossRefGoogle Scholar
  16. 16.
    Royall R (1997) Statistical evidence: a likelihood paradigm. Chapman & Hall/CRC, New YorkGoogle Scholar
  17. 17.
    Schmittlein DC, Morrison DG, Colombo R (1987) Counting your customers: who are they and what will they do next? Manag Sci 33:1–24CrossRefGoogle Scholar
  18. 18.
    Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefGoogle Scholar
  19. 19.
    Schweidel DA, Knox G (2013) Incorporating direct marketing activity into latent attrition models. Mark Sci 32(3):471–487CrossRefGoogle Scholar
  20. 20.
    Singh S, Borle S, Jain DC (2009) A generalized framework for estimating customer lifetime value when customer lifetimes are not observed. Quant Mark Econ 7:181–205CrossRefGoogle Scholar
  21. 21.
    Singh S, Jain DC (2010) Measuring customer lifetime value: model and analysis. Rev Mark Res 6:37–62CrossRefGoogle Scholar
  22. 22.
    Sinha D, Maiti T, Ibrahim JG, Ouyang B (2008) Current methods for recurrent events data with dependent termination: a Bayesian perspective. J Am Stat Assoc 103(482):866–878CrossRefGoogle Scholar
  23. 23.
    Tanner MA, Wong WH (1987) The calculation of posterior distributions by data augmentation. J Am Stat Assoc 82(398):528–540CrossRefGoogle Scholar
  24. 24.
    Van Dyk DA, Meng X-L (2001) The art of data augmentation. J Comput Graph Stat 10(1):1–50CrossRefGoogle Scholar
  25. 25.
    Wang M-C, Qin J, Chang C-T (2001) Analyzing recurrent event data with informative censoring. J Am Stat Assoc 96:1057–1065CrossRefGoogle Scholar
  26. 26.
    Wedel M, Desarbo WS, Bult JR, Ramaswamy V (1993) A latent class poisson regression model for heterogeneous count data. J Appl Econ 8:397–411CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Sharad Borle
    • 1
  • Siddharth Shekhar Singh
    • 2
  • Dipak C. Jain
    • 3
  • Ashutosh Patil
    • 4
  1. 1.Jesse H. Jones Graduate School of BusinessRice UniversityHoustonUSA
  2. 2.Indian School of BusinessHyderabadIndia
  3. 3.Sasin Graduate Institute of Business AdministrationChulalongkorn UniversityBangkokThailand
  4. 4.Robert J. Trulaske, Sr. College of BusinessUniversity of MissouriColumbiaUSA

Personalised recommendations