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

TL;DR

This paper introduces a multilevel mixture model for clustering nodes in multi-layer bipartite networks, accounting for hierarchical data structure and covariate effects, demonstrated through simulations and real social survey data.

Contribution

It extends the Mixture of Latent Trait Analyzers to handle multilevel bipartite networks with covariates, enabling hierarchical clustering and analysis of complex network data.

Findings

Effective parameter and cluster recovery in simulations.

Successful clustering of individuals based on digital skills.

Identification of country clusters by digitalization attitudes.

Abstract

Within network data analysis, bipartite networks represent a particular type of network where relationships occur between two disjoint sets of nodes, formally called sending and receiving nodes. In this context, sending nodes may be organized into layers on the basis of some defined characteristics, resulting in a special case of multilayer bipartite network, where each layer includes a specific set of sending nodes. To perform a clustering of sending nodes in multi-layer bipartite network, we extend the Mixture of Latent Trait Analyzers (MLTA), also taking into account the influence of concomitant variables on clustering formation and the multi-layer structure of the data. To this aim, a multilevel approach offers a useful methodological tool to properly account for the hierarchical structure of the data and for the unobserved sources of heterogeneity at multiple levels. A simulation study is conducted to test the performance of the proposal in terms of parameters' and clustering recovery. Furthermore, the model is applied to the European Social Survey data (ESS) to i) perform a clustering of individuals (sending nodes) based on their digital skills (receiving nodes); ii) understand how socio-economic and demographic characteristics influence the individual digitalization level; iii) account for the multilevel structure of the data; iv) obtain a clustering of countries in terms of the base-line attitude to digital technologies of their residents.