  The statistical analysis of import/export data is helpful to understand the
mechanism that determines exchanges in an economic network. The probability of
having a commercial relationship between two countries often depends on some
unobservable (or not easy-to-measure) factors, like socio-economical
conditions, political views, level of the infrastructures. To conduct inference
on this type of data, we introduce a novel class of latent variable models for
multiview networks, where a multivariate latent Gaussian variable determines
the probabilistic behavior of the edges. We label our model the Graph
Generalized Linear Latent Variable Model (GGLLVM) and we base our inference on
the maximization of the Laplace-approximated likelihood. We call the resulting
M-estimator the Graph Laplace-Approximated Maximum Likelihood Estimator
(GLAMLE) and we study its statistical properties. Numerical experiments on
simulated networks illustrate that the GLAMLE yields fast and accurate
inference. A real data application to commodities trading in Central Europe
countries unveils the import/export propensity that each node of the network
has toward other nodes, along with additional information specific to each
traded commodity.
