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

Amati, Viviana; Schönenberger, Felix; Snijders, Tom A. B.

Journal de la société française de statistique, Tome 156 (2015) no. 3, pp. 140-165.

Le modèle stochastique orienté par l’acteur (Snijders, Sociological Methodology, 2001) modèle l’évolution temporelle des réseaux, étant donné un panel dans un ensemble fixe d’acteurs, où à chaque vague de panel le réseau entre ces acteurs (une structure de graphe orienté) ainsi que les attributs des acteurs sont observés. Les paramètres de ce modèle sont, d’habitude, estimés par une version d’approximation stochastique de la méthode des moments. Des statistiques qui correspondent aux paramètres d’une manière naturelle sont utilisés pour l’ajustement du modèle. Nous présentons ici un estimateur basé sur la méthode généralisée des moments, utilisant plus de statistiques que de paramètres, pour minimiser la distance entre les statistiques observées et leurs espérances mathématiques. Ici encore, l’équation résultante est résolue par approximation stochastique. Plusieurs questions algorithmiques surviennent qui doivent être résolues afin d’obtenir une procédure stable. Pour quelques exemples, nous étudions le gain résultant de l’efficience statistique.

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.

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