Many networks in political and social research are naturally bipartite — with two distinct types of actors (nodes), and edges connecting exclusively across the actor types. An example of such networks is the one that results from cosponsorship decisions, in which legislators are connected to the bills they support. Typically, researchers who wish to study these networks are forced to "project" or marginalize over one node type, in an effort to form the kinds of unipartite networks that standard models can handle. This can result in aggregation bias and loss of relevant information about the node type that is averaged over. To avoid these issues, we propose an extension of the mixed-membership stochastic blockmodel that operates directly on the bipartite network structure, incorporating both node and dyad-level covariates. We design and implement a fast, scalable stochastic variational algorithm to obtain estimates latent variables and hyper-parameters, and illustrate our model using data from the 107th and 108th sessions of the U.S. Senate. We find that using our model allows us to uncover interesting groups of bills, explore the effects of individual ideology on the likelihood of bipartisan cosponsorship, and evaluate the norms of reciprocity in the legislative context.
This is joint work with Santiago Olivella and Kosuke Imai.