Abstract:
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Network topology evolves through time. Modeling the evolving structure of dynamic network is critical to making valid inferences and providing interpretable summaries of the network. For unweighted networks observed in continuous time, we propose a varying-coefficient exponential random graph model (VCERGM) that characterizes the evolution of network topology through smoothly varying parameters. Our model imposes smoothness on the varying parameters through a roughness penalty on the coefficients of a basis-spline expansion. We fit the model via maximum pseudo-likelihood, which we show is equivalent to maximum likelihood estimation of penalized logistic regression. Further, we devise a computationally efficient iteratively reweighted least squares algorithm to estimate the model parameters. A hypothesis testing framework is also developed, which can be used to test for heterogeneity in any dynamic network sequence. The VCERGM is applied to a US Congress co-voting network and a resting-state brain connectivity case study, and is shown to provide relevant insights in both cases. Comprehensive simulation studies demonstrate the advantages of our proposed method over existing methods.
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