  Dynamic network data have become ubiquitous in social network analysis, with
new information becoming available that captures when friendships form, when
corporate transactions happen and when countries interact with each other.
Flexible and interpretable models are needed in order to properly capture the
behavior of individuals in such networks. In this paper, we focus on study the
underlying latent space that describes the social properties of a dynamic and
directed international relations network of countries. We extend the directed
additive and multiplicative effects network model to the continuous time
setting by treating the time-evolution of model parameters using Gaussian
processes. Importantly we incorporate both time-varying covariates and
node-level additive random effects that aid in increasing model realism. We
demonstrate the usefulness and flexibility of this model on a longitudinal
dataset of formal state visits between the world's 18 largest economies. Not
only does the model offer high quality predictive accuracy, but the latent
parameters naturally map onto world events that are not directly measured in
the data.
