Two-Mode Network Autoregressive Model

 A two-mode network refers to a network where the nodes are classified into two distinct types and edges can only exist between nodes of different types. In analysis of two-mode networks, one important objective is to explore the relationship between responses of two types of nodes. To this end, we propose a network autoregressive model for two-mode networks. Different network autocorrelation coefficients are allowed. To estimate the model, a quasi-maximum likelihood estimator is developed with high computational cost. To alleviate the computational burden, a least squares estimator is proposed, which is applicable in large-scale network. The theoretical properties of both estimators are investigated. The finite sample performances are assessed through simulations and a real data example.