  Dynamic multilayer networks frequently represent the structure of multiple
co-evolving relations; however, statistical models are not well-developed for
this prevalent network type. Here, we propose a new latent space model for
dynamic multilayer networks. The key feature of our model is its ability to
identify common time-varying structures shared by all layers while also
accounting for layer-wise variation and degree heterogeneity. We establish the
identifiability of the model's parameters and develop a structured mean-field
variational inference approach to estimate the model's posterior, which scales
to networks previously intractable to dynamic latent space models. We
demonstrate the estimation procedure's accuracy and scalability on simulated
networks. We apply the model to two real-world problems: discerning regional
conflicts in a data set of international relations and quantifying infectious
disease spread throughout a school based on the student's daily contact
patterns.
