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.