Exponential-Family Random Graph Models for Multi-Layer Networks

Multi-layer networks arise when more than one type of relation is observed on a common set of actors. Modeling such networks within the exponential-family random graph (ERG) framework has been previously limited to special cases and, in particular, to dependence arising from just two layers. Extensions to ERGMs are introduced to address these limitations: Conway-Maxwell-Binomial distribution to model the marginal dependence among multiple layers; a layer logic language to translate familiar ERGM effects to substantively meaningful interactions of observed layers; and nondegenerate triadic and degree effects. The developments are demonstrated on two previously published datasets.