  A new modeling framework for bipartite social networks arising from a
sequence of partially time-ordered relational events is proposed. We directly
model the joint distribution of the binary variables indicating if each single
actor is involved or not in an event. The adopted parametrization is based on
first- and second-order effects, formulated as in marginal models for
categorical data and free higher order effects. In particular, second-order
effects are log-odds ratios with meaningful interpretation from the social
perspective in terms of tendency to cooperate, in contrast to first-order
effects interpreted in terms of tendency of each single actor to participate in
an event. These effects are parametrized on the basis of the event times, so
that suitable latent trajectories of individual behaviors may be represented.
Inference is based on a composite likelihood function, maximized by an
algorithm with numerical complexity proportional to the square of the number of
units in the network. A classification composite likelihood is used to cluster
the actors, simplifying the interpretation of the data structure. The proposed
approach is illustrated on a dataset of scientific articles published in four
top statistical journals from 2003 to 2012.
