Regression Analysis of Networked Data: Estimating Function Theory and Applications

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Network data are pervasive in practice such as genetic network data and social network data. Regression analysis of network data is needed to understand the relationship between a set of network-correlated outcomes and another set of covariates. Accomplishing this task requires fast and efficient estimation and inference methods for the model parameters. This motivates researchers to develop a new regression modeling framework for data arising from either networks with undirected edges or networks with directed edges. Through PI's long-term collaborations in Epidemiology, Environmental Health Sciences, and Nephrology, the studied methods can be used by local scientists who will provide valuable feedback. This new research project can also lead to substantial educational initiatives that will involve undergraduate and graduate students and expose them to the state-of-the-art research in various interdisciplinary topics related to the corresponding research. These include new courses, short courses at major conferences, summer workshops, mentoring, and software development. These and other dissemination activities will increase awareness of modern powerful methods for data analysis among scientists from other fields.Although the network analysis has been extensively studied in the literature for dependent structures, little has been studied yet in the regression analysis of response-covariate relationships. This project attempts to fill in such a gap through a few steps. Specifically, the PI proposes to study three different but related problems, including network dependence models, estimating functions methodology via the generalized method of moments, and large-sample theory. This research project includes several innovative and efficient statistical procedures based on estimating functions for estimation and inference. It is anticipated that the studied framework will allow researchers to handle a large variety of network-correlated discrete and continuous data.