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Within network data analysis, bipartite networks represent a particular typeof network where relationships occur between two disjoint sets of nodes,formally called sending and receiving nodes. In this context, sending nodes maybe organized into layers on the basis of some defined characteristics,resulting in a special case of multilayer bipartite network, where each layerincludes a specific set of sending nodes. To perform a clustering of sendingnodes in multi-layer bipartite network, we extend the Mixture of Latent TraitAnalyzers (MLTA), also taking into account the influence of concomitantvariables on clustering formation and the multi-layer structure of the data. Tothis aim, a multilevel approach offers a useful methodological tool to properlyaccount for the hierarchical structure of the data and for the unobservedsources of heterogeneity at multiple levels. A simulation study is conducted totest the performance of the proposal in terms of parameters' and clusteringrecovery. Furthermore, the model is applied to the European Social Survey data(ESS) to i) perform a clustering of individuals (sending nodes) based on theirdigital skills (receiving nodes); ii) understand how socio-economic anddemographic characteristics influence the individual digitalization level; iii)account for the multilevel structure of the data; iv) obtain a clustering ofcountries in terms of the base-line attitude to digital technologies of theirresidents.

Multilevel mixtures of latent trait analyzers for clustering multi-layer bipartite networks