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. However, using a unipartite network model to analyze bipartite networks, as often done in practice, can result in aggregation bias and artificially high-clustering -- a particularly insidious problem when studying the role groups play in network formation. To address these methodological problems, we develop a statistical model of bipartite networks theorized to be generated through group interactions by extending the popular mixed-membership stochastic blockmodel. Our model allows researchers to identify the groups of nodes, within each node type in the bipartite structure, that share common patterns of edge formation. The model also incorporates both node and dyad-level covariates as the predictors of group membership and of observed dyadic relations. We develop an efficient computational algorithm for fitting the model, and apply it to cosponsorship data from the United States Senate. We show that legislators in a Senate that was perfectly split along party lines were able to remain productive and pass major legislation by forming non-partisan, power-brokering coalitions that found common ground through their collaboration on low-stakes bills. 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. We make an open-source software package available that makes it possible for other researchers to uncover similar insights from bipartite networks.

翻译：政治学与社会学研究中的许多网络属于二分结构，其边仅连接两种不同类型的节点。一个典型例子是共同提案网络，其中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，允许任意节点对之间产生连接。若采用单分网络模型分析二分网络（实践中常见做法），可能导致聚合偏差与人为高聚类现象——在研究群体在网络形成中的作用时，这一问题尤为隐蔽。为解决这些方法论缺陷，我们通过扩展流行的混合成员随机块模型，构建了一个基于群体交互生成机制的二分网络统计模型。该模型使研究者能够识别二分结构中每种节点类型内部具有相似连边模式的节点群体。模型同时纳入节点层面与二元组层面的协变量，分别作为群体归属和观测二元关系的预测因子。我们开发了拟合该模型的高效计算算法，并将其应用于美国参议院的共同提案数据。研究表明，在政党界限泾渭分明的参议院中，立法者通过形成跨党派权力协调联盟，在低风险议案合作中寻求共识，从而保持立法生产力并通过重要法案。我们还发现了互惠规范存在的证据，并揭示了政策专长在参议员与立法提案间共同提案关系形成中的重要作用。我们开源了软件工具包，使其他研究者能够从二分网络中发掘类似洞见。