Investigating network structures in recurrent event data with discrete observation times

To investigate pairwise interactions arising from recurrent event processes in a longitudinal network, the framework of the stochastic block model is followed, where every node belongs to a latent group and interactions between node pairs from two specified groups follow a conditional nonhomogeneous Poisson process. Our focus lies on discrete observation times, which are commonly encountered in reality for cost-saving purposes. The variational EM algorithm and variational maximum likelihood estimation are applied for statistical inference. A specific method based on the defined distribution function F and self-consistency algorithm for recurrent events is used when estimating the intensity functions of edges. Numerical simulations illustrate the performance of our proposed estimation procedure in uncovering the underlying structure in the longitudinal networks with recurrent event processes. The dataset of interactions between French schoolchildren for influenza monitoring is analyzed.