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Logistic Network Regression for Scalable Analysis of Networks with Joint Edge/Vertex Dynamics

Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Though early studies of such processes were primarily descriptive, recent work on this topic has increasingly turned to formal statistical models. While showing great promise, many of these modern dynamic models are computationally intensive and scale very poorly in the size of the network under study and/or the number of time points considered. Likewise, currently employed models focus on edge dynamics, with little support for endogenously changing vertex sets. Here, we show how an existing approach based on logistic network regression can be extended to serve as highly scalable framework for modeling large networks with dynamic vertex sets. We place this approach within a general dynamic exponential family (ERGM) context, clarifying the assumptions underlying the framework (and providing a clear path for extensions), and show how model assessment methods for cross-sectional networks can be extended to the dynamic case. Finally, we illustrate this approach on a classic data set involving interactions among windsurfers on a California beach.