****REMINDER - THIS WEDNESDAY****
Ordinary meeting of the Royal Statistical Society organized by the
Research Section
Wednesday, October 11th, 2006 at 5pm (tea from 4:30pm)
Venue: Royal Statistical Society, 12 Errol St, London EC1Y 8LX
M. S. Handcock and A. E. Raftery (University of Washington, Seattle) and
J. M. Tantrum (Microsoft adCenter Laboratories)
Model-based clustering for social networks
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.
You can download/view a PDF copy of this paper at
http://www.rss.org.uk/main.asp?page=1836#1076
Trevor Sweeting
Chair, RSS Research Section Committee
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