Abstract:
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Factor analysis is widely used in many scientific fields, including psychology, economics, sociology and so on. At the same time, observations connected by a network are becoming increasingly common, and incorporating the network structure in factor analysis remains an open question. In this work, we propose a generalized factor model to capture both the dependence structure among the high-dimensional variables and the network structure. The latent factors are allowed to be shared by both high-dimensional variables and the network, or individual to either. We have developed a computationally efficient estimation procedure and established asymptotic inferential theories. In particular, we show that by borrowing information from the network, the proposed estimator of the factor loading matrix achieves the optimal asymptotic variance under much milder identifiability constraints than the existing literature. Further, we have also developed a hypothesis testing procedure to address the challenge of identifying the structure of shared and individual latent factors. The proposed model has been applied to a statistician co-authorship network data and meaningful results have been obtained.
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