Generalized Latent Position Models for Network Data

This research project will develop a new class of latent variable models for network data capable of capturing essential characteristics observed in applications from various disciplines, including the social and life sciences. Existing latent variable models for network data can capture the structural features of networks; however, they make the unrealistic assumption that connections within the network do not depend on each other. In contrast, for networks from the social and life sciences, the processes that lead to network formation and structure inherently induce fundamental dependencies among the connections within the network. This project will introduce a new class of latent variable models for network data that can model both network structure and important dependence patterns that affect how the networks of our world materialize. The research project provides an opportunity for the involvement of undergraduate and graduate students with a broad range of backgrounds and interests. Furthermore, the methods developed in this project will be introduced into relevant courses. Together with Florida State University, the project will support the formation of a K-12 educational outreach program. The program will establish a data science summer camp aimed at early exposure to statistics and data science disciplines, including an introduction to network analysis. Latent variable models for network data typically assume that connections within the network are conditionally independent given the latent variables. This assumption may be too strong for many applications of interest, especially those in the social and life sciences, as the social processes that give rise to a network may induce dependence patterns among the connections within the network that cannot be explained solely by latent variables. This project will introduce a new class of latent variable models for network data that do not adopt the almost ubiquitous conditional independence assumptions of the current state-of-the-art by integrating and extending two existing approaches to modeling network data, that of the exponential-family random graph model and the latent space literature, utilizing the strengths of each literature to compensate for known deficiencies of the other. The project will develop accompanying methodology for fitting models to observed network data and theory for establishing the statistical foundations for estimation and inference. The new methods will be applied to real network data from the social and life sciences. Freely distributed open-source software will be produced to allow practitioners to utilize the developed class of models in applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.