  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.
