A multilayer exponential random graph modelling approach for weighted networks

A new modelling approach for the analysis of weighted networks with ordinal/ polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer exponential random graph model (ERGM) generative process where each network layer represents a different ordinal dyadic category. The network layers are assumed to be generated by an ERGM process conditional on their closest lower network layers. A crucial advantage of the proposed method is the possibility of adopting the binary network statistics specification to describe both the between-layer and across-layer network processes and thus facilitating the interpretation of the parameter estimates associated to the network effects included in the model. The Bayesian approach provides a natural way to quantify the uncertainty associated to the model parameters. From a computational point of view, an extension of the approximate exchange algorithm is proposed to sample from the doubly-intractable parameter posterior distribution. A simulation study is carried out on artificial data and applications of the methodology are illustrated on well-known datasets. Finally, a goodness-of-fit diagnostic procedure for model assessment is proposed.