Annals of Applied Statistics

E-loyalty networks in online auctions

Wolfgang Jank and Inbal Yahav

Full-text: Open access


Creating a loyal customer base is one of the most important, and at the same time, most difficult tasks a company faces. Creating loyalty online (e-loyalty) is especially difficult since customers can “switch” to a competitor with the click of a mouse. In this paper we investigate e-loyalty in online auctions. Using a unique data set of over 30,000 auctions from one of the main consumer-to-consumer online auction houses, we propose a novel measure of e-loyalty via the associated network of transactions between bidders and sellers. Using a bipartite network of bidder and seller nodes, two nodes are linked when a bidder purchases from a seller and the number of repeat-purchases determines the strength of that link. We employ ideas from functional principal component analysis to derive, from this network, the loyalty distribution which measures the perceived loyalty of every individual seller, and associated loyalty scores which summarize this distribution in a parsimonious way. We then investigate the effect of loyalty on the outcome of an auction. In doing so, we are confronted with several statistical challenges in that standard statistical models lead to a misrepresentation of the data and a violation of the model assumptions. The reason is that loyalty networks result in an extreme clustering of the data, with few high-volume sellers accounting for most of the individual transactions. We investigate several remedies to the clustering problem and conclude that loyalty networks consist of very distinct segments that can best be understood individually.

Article information

Ann. Appl. Stat., Volume 4, Number 1 (2010), 151-178.

First available in Project Euclid: 11 May 2010

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Online auction electronic commerce functional data principal component analysis model assumptions random effects model weighted least squares clustering


Jank, Wolfgang; Yahav, Inbal. E-loyalty networks in online auctions. Ann. Appl. Stat. 4 (2010), no. 1, 151--178. doi:10.1214/09-AOAS310.

Export citation


  • Agresti, A., Booth, J., Hobert, J. and Caffo, C. (2000). Random effects modeling of categorical response data. Sociological Methodology 30 27–80.
  • Ba, S. and Pavlou, P. (2002). Evidence of the effect of trust building technology in electronic markets: Price premiums and buyer behavior. MIS Quarterly 26 243–268.
  • Bailey, J., Gao, G., Jank, W., Lin, M., Lucas, H. C. and Viswanathan, S. (2008). The long tail is longer than you think: The surprisingly large extent of online sales by small volume sellers. Technical report, RH Smith School of Business, University of Maryland. Available at SSRN:
  • Bajari, P. and Hortacsu, A. (2004). Economic insights from internet auctions. Journal of Economic Literature 42 457–486.
  • Bapna, R., Jank, W. and Shmueli, G. (2008). Consumer surplus in online auctions. Inform. Syst. Res. 19 400–416.
  • Brown, J. and Morgan, J. (2006). Reputation in online auctions: The market for trust. California Management Review 49 61–81.
  • Donkers, B., Verhoef, P. C. and De Jong, M. (2003). Predicting customer lifetime value in multi-service industries. Technical report, ERIM Report Series Reference No. ERS-2003-038-MKT. Available at SSRN:
  • Fader, P. and Hardie, B. (2006). How to project customer retention. Technical report. Available at SSRN:
  • Fader, P., Hardie, B. and Lee, K. L. (2006). CLV: More than meets the eye. Technical report, Available at SSRN:
  • Greene, W. H. (2003). Econometric Analysis, 4th ed. Prentice Hall, Upper Saddle River, NJ.
  • Haruvy, E., Popkowski Leszczyc, P., Carare, O., Cox, J., Greenleaf, E., Jap, S., Jank, W., Park, Y. and Rothkopf, M. (2008). Competition between auctions. Marketing Letters 19 431–448.
  • Jank, W. and Shmueli, G. (2007). Modeling concurrency of events in online auctions via spatio-temporal semiparametric models. J. Roy. Statist. Soc. Ser. C 56 1–27.
  • Jank, W. and Zhang, S. (2008). An automated and data-driven bidding strategy for online auctions. Technical report, RH Smith School of Business, Univ. Maryland. Available at SSRN:
  • Kneip, A. and Utikal, K. J. (2001). Inference for density families using functional principal component analysis. J. Amer. Statist. Assoc. 96 519–542.
  • Lingfang, L. (2006). Reputation, trust and rebates: How online auction markets can improve their feedback systems. Journal of Economics and Management Strategies. To appear.
  • Livingston, J. (2005). How valuable is a good reputation? A sample selection model of internet auctions. Rev. Econ. Statist. 87 453–465.
  • Lucking-Reiley, D., Bryan, D., Prasad, N. and Reeves, D. (2007). Pennies from Ebay: The determinants of price in online auctions. The Journal of Industrial Economics 55 223–233.
  • Ramsay, J. and Silverman, B. (2005). Functional Data Analysis. Springer, New York.
  • Reddy, S. K. and Dass, M. (2006). Modeling online art auction dynamics using functional data analysis. Statist. Sci. 21 179–193.