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.