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Modeling E-mail Networks and Inferring Leadership Using Self-Exciting Point Processes

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  • Eric W. Fox
  • Martin B. Short
  • Frederic P. Schoenberg
  • Kathryn D. Coronges
  • Andrea L. Bertozzi

Abstract

We propose various self-exciting point process models for the times when e-mails are sent between individuals in a social network. Using an expectation–maximization (EM)-type approach, we fit these models to an e-mail network dataset from West Point Military Academy and the Enron e-mail dataset. We argue that the self-exciting models adequately capture major temporal clustering features in the data and perform better than traditional stationary Poisson models. We also investigate how accounting for diurnal and weekly trends in e-mail activity improves the overall fit to the observed network data. A motivation and application for fitting these self-exciting models is to use parameter estimates to characterize important e-mail communication behaviors such as the baseline sending rates, average reply rates, and average response times. A primary goal is to use these features, estimated from the self-exciting models, to infer the underlying leadership status of users in the West Point and Enron networks. Supplementary materials for this article are available online.

Suggested Citation

  • Eric W. Fox & Martin B. Short & Frederic P. Schoenberg & Kathryn D. Coronges & Andrea L. Bertozzi, 2016. "Modeling E-mail Networks and Inferring Leadership Using Self-Exciting Point Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 564-584, April.
  • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:514:p:564-584
    DOI: 10.1080/01621459.2015.1135802
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    References listed on IDEAS

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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    2. Mohler, G. O. & Short, M. B. & Brantingham, P. J. & Schoenberg, F. P. & Tita, G. E., 2011. "Self-Exciting Point Process Modeling of Crime," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 100-108.
    3. Patrick O. Perry & Patrick J. Wolfe, 2013. "Point process modelling for directed interaction networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 821-849, November.
    4. Veen, Alejandro & Schoenberg, Frederic P., 2008. "Estimation of SpaceTime Branching Process Models in Seismology Using an EMType Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 614-624, June.
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    Cited by:

    1. Chenlong Li & Zhanjie Song & Wenjun Wang, 2020. "Space–time inhomogeneous background intensity estimators for semi-parametric space–time self-exciting point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 945-967, August.
    2. Baichuan Yuan & Frederic P. Schoenberg & Andrea L. Bertozzi, 2021. "Fast estimation of multivariate spatiotemporal Hawkes processes and network reconstruction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1127-1152, December.
    3. Santitissadeekorn, Naratip & Lloyd, David J.B. & Short, Martin B. & Delahaies, Sylvain, 2020. "Approximate filtering of conditional intensity process for Poisson count data: Application to urban crime," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    4. C Matias & T Rebafka & F Villers, 2018. "A semiparametric extension of the stochastic block model for longitudinal networks," Biometrika, Biometrika Trust, vol. 105(3), pages 665-680.
    5. Li, Zhongping & Cui, Lirong & Chen, Jianhui, 2018. "Traffic accident modelling via self-exciting point processes," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 312-320.
    6. Simon Clinet & Yoann Potiron, 2016. "Statistical inference for the doubly stochastic self-exciting process," Papers 1607.05831, arXiv.org, revised Jun 2017.

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