Marginally Specified Hierarchical Models for Relational Data

We present a unified approach to modelling dyadic relational data, namely that seen in social, biological and technological networks, without restriction to the binary format. The approach involves three principles: considering the marginal specification of any edge as the fundamental unit, embedding as much dependence as possible in latent structural forms, and using distributional forms that favour high-throughput computational methods for their solution. We show that this approach allows for an extremely flexible and generalizable way of describing the structural properties of relational systems; namely, we offer alternate explanations for two approaches popular in the networks literature, the “small-world” and “scale-free” mechanisms, and demonstrate the ability of marginal hierarchical modelling to expand beyond them.