TY - JOUR

T1 - Discussion on the paper by Handcock, Raftery and Tantrum.

AU - Snijders, T. A. B.

AU - Robinson, T.

AU - Atkinson, A. C.

AU - Riani, M.

AU - Gormley, I. C.

AU - Murphy, T. B.

AU - Sweeting, T.

AU - Leslie, D. S.

AU - Longford, N. T.

AU - Kent, J. T.

AU - Lawrance, T.

AU - Airoldi, E. M.

AU - Besag, J.

AU - Blei, D.

AU - Fienberg, S. E.

AU - Breiger, R.

AU - Butts, C. T.

AU - Doreian, P.

AU - Batagelj, V.

AU - Ferligoj, A.

AU - Draper, D.

AU - Van Duijn, M. A. J.

AU - Faust, K.

AU - Petrescu-Prahova, M.

AU - Forster, J. J.

AU - Gelman, A.

AU - Goodreau, S. M.

AU - Greenwood, P. E.

AU - Gruenberg, Katharina Tatjana

AU - Francis, Brian J.

AU - Hennig, C.

AU - Hoff, P. D.

AU - Hunter, D. R.

AU - Husmeier, D.

AU - Glasbey, C.

AU - Krackhardt, D.

AU - Kuha, J.

AU - Skrondal, A.

AU - Lawson, A.

AU - Liao, T. F.

AU - Mendes, B.

AU - Draper, D.

AU - Reinert, G.

AU - Richardson, S.

AU - Lewin, A.

AU - Titterington, D. M.

AU - Wasserman, S.

AU - Werhli, A. V.

AU - Ghazal, P.

PY - 2007/3

Y1 - 2007/3

N2 - 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.

AB - 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.

KW - Bayes factor • Dyad • Latent space • Markov chain Monte Carlo methods • Mixture model • Transitivity

U2 - 10.1111/j.1467-985X.2007.00471.x

DO - 10.1111/j.1467-985X.2007.00471.x

M3 - Comment/debate

VL - 170

SP - 322

EP - 354

JO - Journal of the Royal Statistical Society: Series A Statistics in Society

JF - Journal of the Royal Statistical Society: Series A Statistics in Society

SN - 0964-1998

IS - 2

ER -