Bipartite network influence analysis of a two-mode network

Abstract

A two-mode network contains two types of nodes, and edges exist only between any two nodes that are associated with different entities. Owing to the network connections (i.e., edges) between the two types of network nodes, nodal responses are unlikely to be independently and identically distributed, resulting in possible nodal heterogeneity across the two types of nodes. This study proposes a novel bipartite network influence model (BNIM) to evaluate nodal heterogeneity from the perspective of nodal influence. To make the model estimable, we parameterize the influence indices with a set of nodal attributes through a prespecified link function, and employ the quasi-maximum likelihood approach to estimate the unknown parameters. Score tests are presented to examine the heterogeneity of nodal influences across the two types of nodes. To assess the adequacy of the link function, we carry out a quasi-likelihood ratio test and establish its asymptotic properties under the appropriate conditions. Simulation studies and the real data analysis of a fund-stock network are studied to assess the finite-sample performance of BNIM.