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Model-based clustering for social networks

Author

Listed:
  • Mark S. Handcock
  • Adrian E. Raftery
  • Jeremy M. Tantrum

Abstract

Network models are widely used to represent relations between interacting units or actors. Network data often exhibit transitivity, meaning that two actors that have ties to a third actor are more likely to be tied than actors that do not, homophily by attributes of the actors or dyads, and clustering. Interest often focuses on finding clusters of actors or ties, and the number of groups in the data is typically unknown. We propose a new model, the "latent position cluster model", under which the probability of a tie between two actors depends on the distance between them in an unobserved Euclidean 'social space', and the actors' locations in the latent social space arise from a mixture of distributions, each corresponding to a cluster. We propose two estimation methods: a two-stage maximum likelihood method and a fully Bayesian method that uses Markov chain Monte Carlo sampling. The former is quicker and simpler, but the latter performs better. We also propose a Bayesian way of determining the number of clusters that are present by using approximate conditional Bayes factors. Our model represents transitivity, homophily by attributes and clustering simultaneously and does not require the number of clusters to be known. The model makes it easy to simulate realistic networks with clustering, which are potentially useful as inputs to models of more complex systems of which the network is part, such as epidemic models of infectious disease. We apply the model to two networks of social relations. A free software package in the R statistical language, latentnet, is available to analyse data by using the model. Copyright 2007 Royal Statistical Society.

Suggested Citation

  • Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model-based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354.
  • Handle: RePEc:bla:jorssa:v:170:y:2007:i:2:p:301-354
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-985X.2007.00471.x
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    Cited by:

    1. Peter J. Bickel & Purnamrita Sarkar, 2016. "Hypothesis testing for automated community detection in networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 253-273, January.
    2. N. Lee & C. Priebe, 2011. "A latent process model for time series of attributed random graphs," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 231-253, October.
    3. Jean-Jacques Daudin & Laurent Pierre & Corinne Vacher, 2010. "Model for Heterogeneous Random Networks Using Continuous Latent Variables and an Application to a Tree–Fungus Network," Biometrics, The International Biometric Society, vol. 66(4), pages 1043-1051, December.
    4. repec:eee:econom:v:201:y:2017:i:2:p:176-197 is not listed on IDEAS
    5. Aßmann, Christian & Boysen-Hogrefe, Jens, 2011. "A Bayesian approach to model-based clustering for binary panel probit models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 261-279, January.
    6. Michael Braun & André Bonfrer, 2011. "Scalable Inference of Customer Similarities from Interactions Data Using Dirichlet Processes," Marketing Science, INFORMS, vol. 30(3), pages 513-531, 05-06.
    7. Crespo Cuaresma, Jesus & Doppelhofer, Gernot, 2007. "Nonlinearities in cross-country growth regressions: A Bayesian Averaging of Thresholds (BAT) approach," Journal of Macroeconomics, Elsevier, vol. 29(3), pages 541-554, September.
    8. Charles Bouveyron, 2014. "Adaptive Mixture Discriminant Analysis for Supervised Learning with Unobserved Classes," Journal of Classification, Springer;The Classification Society, vol. 31(1), pages 49-84, April.
    9. Cai, Haiyan, 2017. "A note on jointly modeling edges and node attributes of a network," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 54-60.
    10. Prasad Naik & Michel Wedel & Lynd Bacon & Anand Bodapati & Eric Bradlow & Wagner Kamakura & Jeffrey Kreulen & Peter Lenk & David Madigan & Alan Montgomery, 2008. "Challenges and opportunities in high-dimensional choice data analyses," Marketing Letters, Springer, vol. 19(3), pages 201-213, December.
    11. Irene Crimaldi & Michela Del Vicario & Greg Morrison & Walter Quattrociocchi & Massimo Riccaboni, 2015. "Homophily and Triadic Closure in Evolving Social Networks," Working Papers 3/2015, IMT Institute for Advanced Studies Lucca, revised May 2015.
    12. Vincent Labatut & Jean-Michel Balasque, 2012. "Detection and Interpretation of Communities in Complex Networks: Methods and Practical Application," Post-Print hal-00633653, HAL.
    13. repec:jss:jstsof:v:074:i09 is not listed on IDEAS
    14. West, Robert M. & House, Allan O. & Keen, Justin & Ward, Vicky L., 2015. "Using the structure of social networks to map inter-agency relationships in public health services," Social Science & Medicine, Elsevier, vol. 145(C), pages 107-114.
    15. McDaid, Aaron F. & Murphy, Thomas Brendan & Friel, Nial & Hurley, Neil J., 2013. "Improved Bayesian inference for the stochastic block model with application to large networks," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 12-31.
    16. repec:eee:regeco:v:67:y:2017:i:c:p:135-147 is not listed on IDEAS
    17. Aßmann, Christian & Boysen-Hogrefe, Jens, 2009. "A bayesian approach to model-based clustering for panel probit models," Economics Working Papers 2009-03, Christian-Albrechts-University of Kiel, Department of Economics.
    18. repec:spr:compst:v:32:y:2017:i:2:d:10.1007_s00180-016-0655-5 is not listed on IDEAS
    19. Jianxi Gao & Xueming Liu & Daqing Li & Shlomo Havlin, 2015. "Recent Progress on the Resilience of Complex Networks," Energies, MDPI, Open Access Journal, vol. 8(10), pages 1-24, October.
    20. Wang, Tai-Chi & Phoa, Frederick Kin Hing, 2016. "A scanning method for detecting clustering pattern of both attribute and structure in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 295-309.
    21. Daniel Felix Ahelegbey, 2015. "The Econometrics of Networks: A Review," Working Papers 2015:13, Department of Economics, University of Venice "Ca' Foscari".
    22. García Muñiz, Ana Salomé, 2013. "Input–output research in structural equivalence: Extracting paths and similarities," Economic Modelling, Elsevier, vol. 31(C), pages 796-803.
    23. Chih-Sheng Hsieh & Hans van Kippersluis, 2015. "Smoking Initiation: Peers and Personality," Tinbergen Institute Discussion Papers 15-093/V, Tinbergen Institute.
    24. Salter-Townshend, Michael & Murphy, Thomas Brendan, 2013. "Variational Bayesian inference for the Latent Position Cluster Model for network data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 661-671.

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