A Mixture of Experts Latent Position Cluster Model for Social Network Data

0 I.C. Gormley* T.B. Murphy 2009 A Mixture of Experts Latent Position Cluster Model for Social Network Data Statistical Methodology (Special Issue on Statistics in the Social Sciences) 7 3 385-405 Social network data represent the interactions between a group of social actors. Interactions between colleagues and friendship networks are typical examples of such data. The latent space model for social network data locates each actor in a network in a latent (social) space and models the probability of an interaction between two actors as a function of their locations. The latent position cluster model extends the latent space model to deal with network data in which clusters of actors exist — actor locations are drawn from a finite mixture model, each component of which represents a cluster of actors. A mixture of experts model builds on the structure of a mixture model by taking account of both observations and associated covariates when modeling a heterogeneous population. Herein, a mixture of experts extension of the latent position cluster model is developed. The mixture of experts framework allows covariates to enter the latent position cluster model in a number of ways, yielding different model interpretations. Estimates of the model parameters are derived in a Bayesian framework using a Markov Chain Monte Carlo algorithm. The algorithm is generally computationally expensive — surrogate proposal distributions which shadow the target distributions are derived, reducing the computational burden. The methodology is demonstrated through an illustrative example detailing relationships between a group of lawyers in the USA.

* Non-Clique Members

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B7CRS-4Y968K0-1&_user=10&_coverDate=05%2F31%2F2010&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1633455712&_rerunOrigin=google&_acct=C000050221&_version=1&_u