  Longitudinal bipartite relational data characterize the evolution of
relations between pairs of actors, where actors are of two distinct types and
relations exist only between disparate types. A common goal is to understand
the temporal dependencies, specifically which actor relations incite later
actor relations. There are two existing approaches to this problem. The first
approach projects the bipartite data in each time period to a unipartite
network and uses existing unipartite network models. Unfortunately, information
is lost in calculating the projection and generative models for networks
obtained through this process are scarce. The second approach represents
dependencies using two unipartite \emph{influence networks}, corresponding to
the two actor types. Existing models taking this approach are bilinear in the
influence networks, creating challenges in computation and interpretation. We
propose a novel generative model that permits estimation of weighted, directed
influence networks and does not suffer from these shortcomings. The proposed
model is linear in the influence networks, permitting inference using
off-the-shelf software tools. We prove our estimator is consistent under cases
of model misspecification and nearly asymptotically equivalent to the bilinear
estimator. We demonstrate the performance of the proposed model in simulation
studies and an analysis of weekly international state interactions.
