Model-Based Clustering for Social Networks

• Activity Number: 81
• Type: Invited
• Date/Time: Monday, August 8, 2005 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Mark S. Handcock*+ and Adrian E. Raftery and Jeremy M. Tantrum
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: graph modeling ; latent space

Abstract

Network models are widely used to represent relational information among interacting units and the implications of these relations. In studies of social networks, recent emphasis has been on random graph models where the nodes usually represent individual social actors and the edges represent a specified relationship between the actors. One substantive theory postulates the existence of a latent "social space" where the probability of relational ties depends on the relative positions of the actors within this space. We extend models of this form to incorporate clustering information using ideas drawn from model-based clustering. We also consider an alternative form of clustering based on spatial point process ideas. Inference for the clustering within the social space is developed within a likelihood and Bayesian framework. We extend the Markov Chain Monte Carlo algorithm from the latent space models to our latent clustering models and present the analyses of real networks of social relations where the true clustering is known.