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# 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

Liu, B., Lubold, S., Raftery, A.E. and McCormick, T.H. (2024).
Bayesian hyperbolic multidimensional scaling.
*Journal of Computational and Graphical Statistics*, advance publication.
Preprint.
Kaur, H., Rastelli, R., Friel, N. and Raftery, A.E. (2023).
Latent Position Network Models.
Chapter 36 in
Sage Handbook of Social Network Analysis (2nd Edition), edited by J. McLevey, P. Carrington and J. Scott, Sage Publications.
Preprint.

Rastelli, R., Friel, N. and Raftery, A.E. (2016).
Properties of latent variable network models.
*Network Science* 4:407--432.
Earlier version.

Friel, N., Wyse, J. and Raftery, A.E. (2016).
Interlocking directorates in Irish companies using bipartite
networks: a latent space approach.
*Proceedings of the National Academy of Sciences*, 113: 6629-6634.

Raftery, A.E., Niu, X., Hoff, P.D. and Yeung, K.Y. (2012).
Fast Inference for the
Latent Space Network Model Using a Case-Control Approximate Likelihood.
*Journal of Computational and Graphical Statistics*, 21:909-919.

Krivitsky, P., Handcock, M.S., Raftery, A.E. and Hoff, P. (2009).
Representing Degree Distributions, Clustering, and Homophily in
Social Networks With Latent Cluster Random Effects Models.
*Social Networks* 31:204-213.

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.

These papers are being made available here to facilitate the timely
dissemination of scholarly work; copyright and all related rights are
retained by the copyright holders.

Updated May 7, 2024.

Copyright 2005-2024 by Adrian E. Raftery; all rights reserved.