Latent Space Approaches to Network Analysis

Network data describe social, physical, and other relations between experimental units. Analysis of such data is complicated by the possibility of non-independence of these relations. We take a latent variable approach to analyzing network data, in which the relations between two units are conditionally independent of relations with other individuals, given an unobserved set of latent positions in an underlying ``social space.'' We use such a modeling approach to analyze datasets on a monastery, a fourth-grade classroom, and a set of Florentine families. For these datasets, the latent variable approach outperforms several existing methods of analysis, and also provides a graphical, model-based representation of the network data.