Maximum likelihood estimation for social network dynamics

A model for network panel data is discussed, based on the assumption that the observed data are discrete observations of a continuous-time Markov process on the space of all directed graphs on a given node set, in which changes in tie variables are independent conditional on the current graph. The model for tie changes is parametric and designed for applications to social network analysis, where the network dynamics can be interpreted as being generated by choices made by the social actors represented by the nodes of the graph. An algorithm for calculating the Maximum Likelihood estimator is presented, based on data augmentation and stochastic approximation. An application to an evolving friendship network is given and a small simulation study is presented which suggests that for small data sets the Maximum Likelihood estimator is more efficient than the earlier proposed Method of Moments estimator.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS313 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dynamics in the European Air Transport Network, 2003-9 : an explanatory framework drawing on stochastic actor-based modeling

In this paper, we outline and test an explanatory framework drawing on stochastic actor-based modeling to understand changes in the outline of European air transport networks between 2003 and 2009. Stochastic actor-based models show their capabilities to estimate and test the effect of exogenous and endogenous drivers on network changes in this application to the air transport network. Our results reveal that endogenous structural effects, such as transitivity triads, indirect relations and betweenness effects impact the development of the European air transport network in the period under investigation. In addition, exogenous nodal and dyadic covariates also play a role, with above all the enlargement of the European Common Aviation Area having benefitted its new members to open more air routes between them. The emergence of major low-cost airline-focused airports also significantly contributed to these changes. We conclude by outlining some avenues for further research

Locally Adaptive Dynamic Networks

Our focus is on realistically modeling and forecasting dynamic networks of face-to-face contacts among individuals. Important aspects of such data that lead to problems with current methods include the tendency of the contacts to move between periods of slow and rapid changes, and the dynamic heterogeneity in the actors' connectivity behaviors. Motivated by this application, we develop a novel method for Locally Adaptive DYnamic (LADY) network inference. The proposed model relies on a dynamic latent space representation in which each actor's position evolves in time via stochastic differential equations. Using a state space representation for these stochastic processes and P\'olya-gamma data augmentation, we develop an efficient MCMC algorithm for posterior inference along with tractable procedures for online updating and forecasting of future networks. We evaluate performance in simulation studies, and consider an application to face-to-face contacts among individuals in a primary school