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Model‐based clustering of semiparametric temporal exponential‐family random graph models

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.