Varying-coefficient models for dynamic networks

Dynamic networks are commonly used to model relational data that are observed over time. Statistical models for such data should capture both the temporal variation of the relational system as well as the structural dependencies within each network. As a consequence, effectively making inference on dynamic networks is a computationally challenging task, and many models are intractable even for moderately sized systems. In light of these challenges, a family of dynamic network models known as varying-coefficient exponential random graph models (VCERGMs) is proposed to characterize the evolution of network topology through smoothly varying parameters. The VCERGM provides an interpretable dynamic network model that enables the inference of temporal heterogeneity in dynamic networks. Estimation of the VCERGM is achieved via maximum pseudo-likelihood techniques, thereby providing a computationally tractable strategy for statistical inference of complex dynamic networks. Furthermore, a bootstrap hypothesis testing framework is presented for testing the temporal heterogeneity of an observed dynamic network sequence. Application to the U.S. Senate co-voting network and comprehensive simulation studies both reveal that the VCERGM provides relevant and interpretable patterns and has significant advantages over existing methods.