Many networks in political and social research are bipartite, with edges connecting exclusively across two distinct types of nodes. A common example includes cosponsorship networks, in which legislators are connected indirectly through the bills they support. Yet most existing network models are designed for unipartite networks, where edges can arise between any pair of nodes. We show that using a unipartite network model to analyze bipartite networks, as often done in practice, can result in aggregation bias. To address this methodological problem, we develop a statistical model of bipartite networks by extending the popular mixed-membership stochastic blockmodel. Our model allows researchers to identify the groups of nodes, within each node type, that share common patterns of edge formation. The model also incorporates both node and dyad-level covariates as the predictors of the edge formation patterns. We develop an efficient computational algorithm for fitting the model, and apply it to cosponsorship data from the United States Senate. We show that senators tapped into communities defined by party lines and seniority when forming cosponsorships on bills, while the pattern of cosponsorships depends on the timing and substance of legislations. We also find evidence for norms of reciprocity, and uncover the substantial role played by policy expertise in the formation of cosponsorships between senators and legislation. An open-source software package is available for implementing the proposed methodology.

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