Bivariate zero-inflated stochastic block models for the analysis of longitudinal hospital network data

An extended stochastic block model for clustering dynamic weighted network data is introduced, where the block memberships are represented by a sequence of latent variables following a Markov chain. Motivated by the availability of original data on patient transfers within a network of Italian hospitals, we propose to rely on a bivariate zero-inflated Poisson distribution to characterize the sparse and correlated interactions of hospitals. In particular, we explicitly model the distribution of the dyad referred to each pair of nodes, conditional on the states occupied by both nodes at a given time occasion. This allows us to discover unobserved blocks of hospitals sharing the same propensity to send or receive patients and to set up reciprocated relations. Model estimation is based on an algorithm that maximizes a tempered version of a variational approximation of the likelihood to address the problem of multimodality of the target function. Selection of the number of blocks is based on the integrated classification likelihood criterion. In terms of clustering, it is possible to assign units to blocks on the basis of a local decoding procedure that exploits the variational posterior probabilities.