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The statistical analysis of import/export data is helpful to understand themechanism that determines exchanges in an economic network. The probability ofhaving a commercial relationship between two countries often depends on someunobservable (or not easy-to-measure) factors, like socio-economicalconditions, political views, level of the infrastructures. To conduct inferenceon this type of data, we introduce a novel class of latent variable models formultiview networks, where a multivariate latent Gaussian variable determinesthe probabilistic behavior of the edges. We label our model the GraphGeneralized Linear Latent Variable Model (GGLLVM) and we base our inference onthe maximization of the Laplace-approximated likelihood. We call the resultingM-estimator the Graph Laplace-Approximated Maximum Likelihood Estimator(GLAMLE) and we study its statistical properties. Numerical experiments onsimulated networks illustrate that the GLAMLE yields fast and accurateinference. A real data application to commodities trading in Central Europecountries unveils the import/export propensity that each node of the networkhas toward other nodes, along with additional information specific to eachtraded commodity.

GLAMLE: inference for multiview network data in the presence of latent variables, with application to commodities trading