Models of dynamic networks—networks that evolve over time—have manifold applications. We develop a discrete time generative model for social network evolution that inherits the richness and flexibility of the class of exponential family random-graph models. The model—a separable temporal exponential family random-graph model—facilitates separable modelling of the tie duration distributions and the structural dynamics of tie formation. We develop likelihood-based inference for the model and provide computational algorithms for maximum likelihood estimation. We illustrate the interpretability of the model in analysing a longitudinal network of friendship ties within a school.
Model‐based clustering of time‐evolving networks has emerged as one of the important research topics in statistical network analysis. It is a fundamental research question to model time‐varying network parameters. However, due to difficulties in modelling functional network parameters, there is little progress in the current literature to model time‐varying network parameters effectively. In this work, we model network parameters as univariate nonparametric functions instead of constants. We effectively estimate those functional network parameters in temporal exponential‐family random graph models using a kernel regression technique and a local likelihood approach. Furthermore, we propose a semiparametric finite mixture of temporal exponential‐family random graph models by adopting finite mixture models, which simultaneously allows both modelling and detecting groups in time‐evolving networks. Also, we use a conditional likelihood to construct an effective model selection criterion and network cross‐validation to choose an optimal bandwidth. The power of our method is demonstrated in simulation studies and real‐world applications to dynamic international trade networks and dynamic arm trade networks.more » « less
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- Wiley Blackwell (John Wiley & Sons)
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- National Science Foundation
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