  Dynamic network data analysis requires joint modelling individual snapshots
and time dynamics. This paper proposes a new two-way heterogeneity model
towards this goal. The new model equips each node of the network with two
heterogeneity parameters, one to characterize the propensity of forming ties
with other nodes and the other to differentiate the tendency of retaining
existing ties over time. Though the negative log-likelihood function is
non-convex, it is locally convex in a neighbourhood of the true value of the
parameter vector. By using a novel method of moments estimator as the initial
value, the consistent local maximum likelihood estimator (MLE) can be obtained
by a gradient descent algorithm. To establish the upper bound for the
estimation error of the MLE, we derive a new uniform deviation bound, which is
of independent interest. The usefulness of the model and the associated theory
are further supported by extensive simulation and the analysis of some real
network data sets.
