Latent Space Models for Aggregated Relational Data in Social Sciences


Tian Zheng
Professor of Statistics; Chair, Department of Statistics
Andrew Gelman
Higgins Professor of Statistics and Professor of Political Science


How does the understanding of social networks contribute to social science? In particular, (1) which network features or observable characteristics encode social structure; (2) how do these features contribute to the formation of connections or social ties; and (3) how does network structure impacts diffusion, specifically the spread of influences, opinions, and diseases? A key difficulty in studying these questions is that most contributions to current understanding in this area come from a small number of applications where full network data are readily available. Collecting complete network data is typically financially and practically impossible, while sampled network data are hard to collect and usually require special statistical modeling considerations. In this project, latent space approaches will be applied to aggregated relational data (questions of the form, "How many X?s do you know?") collected using surveys on non-network samples.

The project's methods development and data analysis should make information about more complicated network structure available to the multitude of researchers who cannot in practice collect data from complete networks. By analyzing existing data using this framework, the project will estimate aspects of social structure in personal acquaintances networks, variation of social structure across different sub-networks (family, friends, coworkers, etc), estimate homogeneity of groups, and estimate individual and population gregariousness, all of which could benefit social science researchers interested in understanding relationships between groups of individuals in the population. The methods also are potentially useful for research on groups that are difficult to reach with traditional surveys, such as those with HIV/AIDS, the homeless, or injection drug users. The project is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.