Estimation of Stochastic actor-oriented models for the evolution of networks by generalized method of moments

The stochastic actor-oriented model (Snijders, Sociological Methodology, 2001) models the evolution of networks over time, given panel data in a fixed group of actors, where at each panel wave the network between these actors (a digraph structure) as well as attribute variables for these actors are observed. The parameters of this model usually are estimated by a stochastic approximation version of the method of moments. Statistics that correspond to the parameters in a natural way are used for fitting the model. Here we present an estimator based on the generalized method of moments, i.e., using more statistics than parameters, for minimizing the distance between observed statistics and their expected values. Again, the resulting equation is solved by stochastic approximation. Several algorithmic issues arise that have to be solved in order to obtain a stable procedure. For some examples we study the resulting gain in statistical efficiency.