Collaborative Research: Specification and Estimation of Exponential Family Random Graph Models for Weighted Networks

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Understanding the effect of network synergies on dynamic relational processes plays an important role in a number of real-world research settings. Examples include understanding what forms of monetary and social policy reduce the instance of international financial contagion, and the role of different physiological conditions on the activity levels of different interconnected regions in the human brain. Statistical insights into areas such as these require analytical methods which deal with both the presence and absence of ties as well as tie strengths between units in networks. This project focuses on the development and implementation of statistical methods and software for the analysis of weighted (i.e., tie strength) network data. The generalized exponential random graph model (GERGM) is a powerful tool for formulating and testing hypotheses about networks. The project will advance the current state of development of the GERGM by (1) developing a better understanding of the space of network probability distributions that can be formulated with the GERGM; developing Markov Chain Monte Carlo methods for estimation, which will broaden the class of GERGM specifications for which estimation is feasible; (3) developing special-case GERGM constraints that facilitate the study of correlation matrices as networks; and (4) developing asymptotic theory regarding the properties of the GERGM family. As part of this research, two illustrative applications of the GERGM will be developed. The first one involves the analysis of global environmental public policy networks, which offers insight into the network properties of global environmental faction and cooperation. The second application involves the analysis of neural activity networks in humans, which aims to understand complex dependencies connecting regions of the brain. Given the recent explosion in the application of statistical network models in fields as diverse as sociology, genetics, neuroscience, political science, physics, finance, linguistics, and ecology, it is expected that the statistical methods developed in this project will be relevant to a number of different fields. One of the leading fields, in terms of the prominence of weighted network data, is neuroscience. One of the aims of this project is to contribute to the multi-agency initiative on Brain Research through Advancing Innovative Neurotechnologies. This project offers two additional contributions that will facilitate the statistical study of weighted networks. First, this project will contribute and disseminate free and open-source statistical software that permits user-friendly applications. Second, the material developed in this project will be incorporated into graduate-level research methods coursework and workshops.