  While logistic regression models are easily accessible to researchers, when
applied to network data there are unrealistic assumptions made about the
dependence structure of the data. For temporal networks measured in discrete
time, recent work has made good advances \citep{almquist2014logistic}, but
there is still the assumption that the dyads are conditionally independent
given the edge histories. This assumption can be quite strong and is sometimes
difficult to justify. If time steps are rather large, one would typically
expect not only the existence of temporal dependencies among the dyads across
observed time points but also the existence of simultaneous dependencies
affecting how the dyads of the network co-evolve. We propose a general
observation driven model for dynamic networks which overcomes this problem by
modeling both the mean and the covariance structures as functions of the edge
histories using a flexible autoregressive approach. This approach can be shown
to fit into a generalized linear mixed model framework. We propose a
visualization method which provides evidence concerning the existence of
simultaneous dependence. We describe a simulation study to determine the
method's performance in the presence and absence of simultaneous dependence,
and we analyze both a proximity network from conference attendees and a world
trade network. We also use this last data set to illustrate how simultaneous
dependencies become more prominent as the time intervals become coarser.
