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Model-based clustering for social networks

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

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series A (Statistics in Society).

    Volume (Year): 170 (2007)
    Issue (Month): 2 ()
    Pages: 301-354

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    Handle: RePEc:bla:jorssa:v:170:y:2007:i:2:p:301-354

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    Cited by:
    1. 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.
    2. Doppelhofer, G. & Cuaresma, J.C., 2007. "Nonlinearities in Cross-Country Growth Regressions: A Bayesian Averaging of Thresholds (BAT) Approach," Cambridge Working Papers in Economics 0706, Faculty of Economics, University of Cambridge.
    3. 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.
    4. Vincent Labatut & Jean-Michel Balasque, 2012. "Detection and Interpretation of Communities in Complex Networks: Methods and Practical Application," Post-Print hal-00633653, HAL.
    5. 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.
    6. 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.
    7. García Muñiz, Ana Salomé, 2013. "Input–output research in structural equivalence: Extracting paths and similarities," Economic Modelling, Elsevier, vol. 31(C), pages 796-803.
    8. 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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