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Multivariate Weibull mixtures with proportional hazard restrictions for dwell-time-based session clustering with incomplete data


  • Patrick Mair
  • Marcus Hudec


Emanating from classical Weibull mixture models we propose a framework for clustering survival data with various more parsimonious models by imposing restrictions on the distributional parameters. We show that these restrictions on the Weibull mixtures correspond to different proportional hazard restrictions across mixture components and Web page areas. A parametric cluster approach based on the EM algorithm is carried out on a multivariate data set. Our model set-up encompasses incomplete-data structures as well as censoring observations. We apply the methodology on retail data stemming from a global e-commerce company. Sessions are clustered with respect to the dwell times that a user spends on certain page areas. The cluster solution that is found allows for a detailed examination of the navigation behaviour in terms of the hazard and survivor functions within each component. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • Patrick Mair & Marcus Hudec, 2009. "Multivariate Weibull mixtures with proportional hazard restrictions for dwell-time-based session clustering with incomplete data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(5), pages 619-639.
  • Handle: RePEc:bla:jorssc:v:58:y:2009:i:5:p:619-639

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    References listed on IDEAS

    1. Wendy W. Moe & Peter S. Fader, 2004. "Dynamic Conversion Behavior at E-Commerce Sites," Management Science, INFORMS, vol. 50(3), pages 326-335, March.
    2. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    3. Eric J. Johnson & Wendy W. Moe & Peter S. Fader & Steven Bellman & Gerald L. Lohse, 2004. "On the Depth and Dynamics of Online Search Behavior," Management Science, INFORMS, vol. 50(3), pages 299-308, March.
    4. Makoto Abe, 2003. "A Two-Stage Prediction Model for Web Page Transition," CIRJE F-Series CIRJE-F-194, CIRJE, Faculty of Economics, University of Tokyo.
    5. Young-Hoon Park & Peter S. Fader, 2004. "Modeling Browsing Behavior at Multiple Websites," Marketing Science, INFORMS, vol. 23(3), pages 280-303, May.
    6. Alan L. Montgomery & Shibo Li & Kannan Srinivasan & John C. Liechty, 2004. "Modeling Online Browsing and Path Analysis Using Clickstream Data," Marketing Science, INFORMS, vol. 23(4), pages 579-595, November.
    7. Zeileis, Achim, 2006. "Object-oriented Computation of Sandwich Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(i09).
    8. Patra, Kaushik & Dey, Dipak K., 1999. "A multivariate mixture of Weibull distributions in reliability modeling," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 225-235, November.
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