Exponential random graph models for multilevel networks

Modern multilevel analysis, whereby outcomes of individuals within groups take into account group membership, has been accompanied by impressive theoretical development (e.g. Kozlowski and Klein, 2000) and sophisticated methodology (e.g. Snijders and Bosker, 2012). But typically the approach assumes that links between groups are non-existent, and interdependence among the individuals derives solely from common group membership. It is not plausible that such groups have no internal structure nor they have no links between each other. Networks provide a more complex representation of interdependence. Drawing on a small but crucial body of existing work, we present a general formulation of a multilevel network structure. We extend exponential random graph models (ERGMs) to multilevel networks, and investigate the properties of the proposed models using simulations which show that even very simple meso effects can create structure at one or both levels. We use an empirical example of a collaboration network about French cancer research elites and their affiliations (0125 and 0120) to demonstrate that a full understanding of the network structure requires the cross-level parameters. We see these as the first steps in a full elaboration for general multilevel network analysis using ERGMs.