A Latent Variable Model for Relational Events with Multiple Receivers

Directional relational event data, such as email data, often include multiple receivers for each event. Statistical methods for adequately modeling such data are limited however. In this article, a multiplicative latent factor model is proposed for relational event data with multiple receivers. For a given event (or message) all potential receiver actors are given a suitability score. When this score exceeds a sender-specific threshold value, the actor is added to the receiver set. The suitability score of a receiver actor for a given message can depend on observed sender and receiver specific characteristics, and on the latent variables of the sender, of the receiver, and of the message. One way to view these latent variables as the degree of specific unobserved topics on which an actor can be active as sender, as receiver, or that are relevant for a given message. Bayesian estimation of the model is relatively straightforward due to the Gaussian distribution of the latent suitability scale. The applicability of the model is illustrated on simulated data and on Enron email data for which about a third of the messages have at least two receivers.