A multilayer exponential random graph modelling approach for weighted networks
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This paper introduces a new modelling approach to analyse weighted networks with ordinal/polytomous edge values. The proposed approach consists in modelling the weighted network generative process as a hierarchical multilayer ERGM process where each network layer represents a different ordinal dyadic category. Each layer is assumed to be generated by an ERGM conditional on the lower layer. A crucial advantage of the proposed method is the possibility of adopting the standard binary ERGM specification to model either the between-layer and across-layer generative processes thus facilitating the interpretation of the parameter estimates of the model. The Bayesian approach provides a natural way to estimate the uncertainty of the parameters associated to the local network effects included in the model. An extension of the approximate exchange algorithm is proposed to sample from the doubly-intractable posterior distribution of the parameters. Finally, applications of the methodology are illustrated on well-known real datasets and a goodness-of-fit diagnostic procedure for model assessment is proposed.
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