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A new modelling approach for the analysis of weighted networks withordinal/polytomous dyadic values is introduced. Specifically, it is proposed tomodel the weighted network connectivity structure using a hierarchicalmultilayer exponential random graph model (ERGM) generative process where eachnetwork layer represents a different ordinal dyadic category. The networklayers are assumed to be generated by an ERGM process conditional on theirclosest lower network layers. A crucial advantage of the proposed method is thepossibility of adopting the binary network statistics specification to describeboth the between-layer and across-layer network processes and thus facilitatingthe interpretation of the parameter estimates associated to the network effectsincluded in the model. The Bayesian approach provides a natural way to quantifythe uncertainty associated to the model parameters. From a computational pointof view, an extension of the approximate exchange algorithm is proposed tosample from the doubly-intractable parameter posterior distribution. Asimulation study is carried out on artificial data and applications of themethodology are illustrated on well-known datasets. Finally, a goodness-of-fitdiagnostic procedure for model assessment is proposed.

A multilayer exponential random graph modelling approach for weighted networks