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Title: Network regression and supervised centrality estimation Authors:  Junhui Jeffrey Cai - University of Pennsylvania (United States) [presenting]
Dan Yang - The University of Hong Kong (Hong Kong)
Wu Zhu - Tsinghua University (China)
Haipeng Shen - The University of Hong Kong (Hong Kong)
Linda Zhao - University of Pennsylvania (United States)
Abstract: Directed networks play a crucial role in our lives and have implications for individuals' behavior. The node's position in the network, usually captured by the centrality, is an important intermediary of network effects, and is often incorporated in a regression model to elucidate the network effect on the outcome variable of interest. In empirical studies, researchers often adopt a two-stage procedure -- first estimate the centrality from the observed network and then employ the estimated centrality in regression. Despite the prevalent adoption of such a two-stage procedure, it fails to incorporate the errors from the observed network and lacks valid inference. We first propose a unified inferential framework that combines the network error model and the regression on centrality model, under which we prove the shortcoming of the two-stage in estimating the centrality and demonstrate the consequent undesirable effect in the outcome regression. We then propose a novel supervised network centrality estimation (SuperCENT) methodology that simultaneously combines the information from the two essential models. The proposed method always provides superior estimates of the centrality and the true underlying network over the two-stage procedure, and produces better network effect estimation when the observational error of the network is severe. We further derive the distribution of the centrality and network effect, which can be used to construct valid confidence intervals.