A Statistical Model of Bipartite Networks: Application to Cosponsorship in the United States Senate

Many networks in political and social research are bipartite, connecting two distinct node types. A common example is cosponsorship networks, where legislators are linked through the bills they support. However, most bipartite network analyses in political science rely on statistical models fitted to a “projected” unipartite network. This approach can lead to aggregation bias and an artificially high degree of clustering, invalidating the study of group roles in network formation. To address these issues, we develop a statistical model of bipartite networks theorized to arise from group interactions, extending the mixed-membership stochastic blockmodel. Our model identifies groups within each node type that exhibit common edge formation patterns and incorporates node and dyad-level covariates as predictors of group membership and observed dyadic relations. We derive an efficient computational algorithm to fit the model and apply it to cosponsorship data from the United States Senate. We show that senators who were perfectly split along party lines remained productive and pass major legislation by forming non-partisan, power-brokering coalitions that found common ground through low-stakes bills. We also find evidence of reciprocity norms and policy expertise impacting cosponsorships. An open-source software package is available for researchers to replicate these insights.