A Class of Temporal Hierarchical Exponential Random Graph Models for Longitudinal Network Data

Abstract: As a representation of relational data over time series, longitudinal networks provide opportunities to study link formation processes. However, networks at scale often exhibits community structure (i.e. clustering), which may confound local structural effects if it is not considered appropriately in statistical analysis. To infer the (possibly) evolving clusters and other network structures (e.g. degree distribution and/or transitivity) within each community, simultaneously, we propose a class of statistical models named Temporal Hierarchical Exponential Random Graph Models (THERGM). Our generative model imposes a Markovian transition matrix for nodes to change their membership, and assumes they join new community in a preferential attachment way. For those remaining in the same cluster, they follow a specific temporal ERG model (TERGM). While a direct MCMC based Bayesian estimation is computational infeasible, we propose a two-stage strategy. At the first stage, a specific dynamic latent space model will be used as the working model for clustering. At the second stage, estimated memberships are taken as given to fit a TERG model in each cluster. We evaluate our methods on simulated data in terms of the mis-clustering rate, as well as the goodness of fit and link prediction accuracy.