NIASRA, University of Wollongong
Exponential Random Graph Models for Multi-Layer Networks
Abstract: Networks with multiple layers of relationships are of increasing interdisciplinary interest. Such networks arise in a host of contexts where more than one type of relation may be observed among a common set of actors or vertices. Previously implemented approaches have been limited to dependence arising from just two layers. To address these limitations we introduce an extension to estimate a joint exponential random graph model over all separate measurement types which retains the (possibly correlated) layered nature of the data while facilitating estimation of dependence effects for arbitrary numbers of relations. Specifically, we extend the Conway--Maxwell-Binomial distribution to model the marginal dependence between layers while simultaneously modeling conditional dependence in multi-layer networks arising from cross-layer graph features. Model terms include analogs of familiar ERGM effects for arbitrary numbers of layers in the network and employ a novel "layer logic" in their specification. Our empirical example is drawn from a problem of common interest in the social and psychological sciences: multi-layer family networks of conflict and cohesion. This work is joint with Laura Koehly (National Institutes of Health) and Christopher Steven Marcum (National Institutes of Health).