The Hyperedge Event Model

We introduce the hyperedge event model (HEM)---a generative model for events that can be represented as directed edges with one sender and one or more receivers or one receiver and one or more senders. We integrate a dynamic version of the exponential random graph model (ERGM) of edge structure with a survival model for event timing to jointly understand who interacts with whom, and when. The HEM offers three innovations with respect to the literature---first, it extends a growing class of dynamic network models to model hyperedges. The current state-of-the-art approach to dealing with hyperedges is to inappropriately break them into separate edges/events. Second, our model involves a novel receiver selection distribution that is based on established edge formation models, but assures non-empty receiver lists. Third, the HEM integrates separate, but interacting, equations governing edge formation and event timing. We use the HEM to analyze emails sent among department managers in Montgomery County government in North Carolina. Our application demonstrates that the model is effective at predicting and explaining time-stamped network data involving edges with multiple receivers. We present an out-of-sample prediction experiment to illustrate how researchers can select between different specifications of the model.