  We introduce a simple and extendable coevolution model for the analysis of
longitudinal network and nodal attribute data. The model features parameters
that describe three phenomena: homophily, contagion and autocorrelation of the
network and nodal attribute process. Homophily here describes how changes to
the network may be associated with between-node similarities in terms of their
nodal attributes. Contagion refers to how node-level attributes may change
depending on the network. The model we present is based upon a pair of
intertwined autoregressive processes. We obtain least-squares parameter
estimates for continuous-valued fully-observed network and attribute data. We
also provide methods for Bayesian inference in several other cases, including
ordinal network and attribute data, and models involving latent nodal
attributes. These model extensions are applied to an analysis of international
relations data and to data from a study of teen delinquency and friendship
networks.
