Adrian Raftery: Latent Space Modeling

Basing analysis on a latent Euclidean space has long been known to be useful for data in the form of dissimilarities (or of such high dimension that dissimilarities are a useful way to summarize things). This is the idea underlying multidimensional scaling, which goes back to the 1930s. We have developed a Bayesian approach to this that makes explicit inference about the latent space (Oh and Raftery 2001); this also provides a principled basis for deciding the dimension of the latent space. It also allows inference about clusters to be made at the same time (Oh and Raftery 2007).

The same idea has been extended to social networks, where the data consist of the presence or absence (or intensity) of links between actors (Hoff et al 2002). This also allows inference about clustering in social networks to be made at the same time (Handcock, Raftery and Tantrum, 2007). These methods are implemented in the latentnet software.

Papers

Krivitsky, P., Handcock, M.S., Raftery, A.E. and Hoff. P. (2007). ``Representing Degree Distributions, Clustering, and Homophily in Social Networks with Latent Cluster Random Effects Models.'' Technical Report no. 517, Department of Statistics, University of Washington. Also Working Paper no. 77, Center for Statistics and the Social Sciences, University of Washington.

Handcock, M.S., Raftery, A.E. and Tantrum, J. (2007). Model-based clustering for social networks (with Discussion). Journal of the Royal Statistical Society, Series A, 170, 301-354.

Oh, M.-S. and Raftery, A.E. (2007). Model-based Clustering with Dissimilarities: A Bayesian Approach. Journal of Computational and Graphical Statistics, 16, 559-585.

Hoff, P., Raftery, A.E. and Handcock, M.S. (2002). Latent Space Approaches to Social Network Analysis. Journal of the American Statistical Association, 97, 1090-1098.

Oh, M.-S. and Raftery, A.E. (2001). Bayesian Multidimensional Scaling and Choice of Dimension. Journal of the American Statistical Association, 96, 1031-1044.

Updated May 21, 2008