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.

翻译：政治与社会研究中的许多网络属于二分网络，其边仅连接两类不同节点。共同提案网络是一个常见例子，立法者通过其支持的议案间接相连。然而，现有网络模型大多针对单分网络设计，即边可出现在任意节点对之间。我们证明，实际中常用的单分网络模型分析二分网络会导致聚合偏差。为解决这一方法论问题，我们通过扩展广受欢迎的混合成员随机块模型，提出了二分网络统计模型。该模型允许研究者识别每类节点中具有共同边形成模式的节点群体，同时纳入节点级和二元组级协变量作为边形成模式的预测因子。我们开发了高效的计算算法用于模型拟合，并将其应用于美国参议院的共同提案数据。研究发现，参议员在形成法案共同提案时，会基于党派界限和资历构建社区，而共同提案模式取决于立法的时间与内容。我们还发现了互惠规范的证据，并揭示了政策专业知识在参议员与法案之间共同提案形成中发挥的重要作用。我们提供了开源软件包用于实施所提方法。