  We propose a new Bayesian Markov switching regression model for
multidimensional arrays (tensors) of binary time series. We assume a
zero-inflated logit regression with time-varying parameters and apply it to
multilayer temporal networks. The original contribution is threefold. First, to
avoid over-fitting we propose a parsimonious parametrization based on a
low-rank decomposition of the tensor of regression coefficients. Second, we
assume the parameters are driven by a hidden Markov chain, thus allowing for
structural changes in the network topology. We follow a Bayesian approach to
inference and provide an efficient Gibbs sampler for posterior approximation.
We apply the methodology to a real dataset of financial networks to study the
impact of several risk factors on the edge probability. Supplementary materials
for this article are available online.
