Latent Space Approaches to Social Network Analysis

• Activity Number: 45
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Social Statistics Section*
• Author(s): Peter Hoff*+
• Affiliation(s): University of Washington
• Keywords: network data ; conditional independence model ; multidimensional scaling

Abstract

Network models are widely used to represent relational information among interacting units. In studies of social networks, recent emphasis has been placed on random graph models where the nodes usually represent individual social actors and the edges represent the presence of a specified relation between actors. We develop a class of models where the probability of a relation between actors depends on the locations of individuals in some unobserved "social space." Inference for the social space is developed within a likelihood and Bayesian framework, and Markov chain Monte Carlo procedures are proposed for making inference on latent locations and the effects of observed covariates. We present analyses of three real social networks, and compare the method to an alternative stochastic blockmodeling approach. In addition to improving upon model fit, our method provides a visual and interpretable model-based spatial representation of social relationships, and improves upon existing methods by allowing the statistical uncertainty in the social space to be quantified and graphically represented.