Estimation and prediction in dynamic multi-location multiplex networks

Abstract We introduce multi-location networks to model the real-world phenomena of nodes existing in multiple places simultaneously. A multi-location network contains a set of locations. Each location can have a different set of nodes, but nodes can be present in multiple locations at once. In contrast, a multiplex network contains a set of layers, where each layer shares the same set of nodes. By combining these two structures, a multi-location multiplex network (MLMN) enables nodes to appear in various locations and connect through multiple edge types. For example, in a species interaction MLMN, locations could correspond to continents, while layers represent different types of interactions, such as predation and competition. Some species may inhabit multiple continents, with interactions varying by location. Analyzing the evolution of MLMNs poses substantial challenges due to the complexity of integrating location and edge type. Traditional dynamic network logistic regression models often aggregate data across these structures, leading to information loss. In this paper, we extend dynamic network logistic regression to accommodate MLMNs, improving the estimation of factors driving changes in such networks. Our approach predicts node presence in each location and the formation of edges across different layers at each location. We provide theoretical guarantees for the model, including global optimality, consistency, asymptotic normality, and asymptotic efficiency of the estimated parameters. The model’s finite sample performance is evaluated through simulations. Additionally, a case study is conducted using a dataset from Equinix, a 2024 Fortune 500 company and one of the world’s largest data center operators. Our findings highlight the strong impact of location on node presence and link formation, showcasing the practical relevance of understanding multi-location structures to capture complex network dynamics.