The focus of this paper is an approach to the modeling of longitudinal social
network or relational data. Such data arise from measurements on pairs of
objects or actors made at regular temporal intervals, resulting in a social
network for each point in time. In this article we represent the network and
temporal dependencies with a random effects model, resulting in a stochastic
process defined by a set of stationary covariance matrices. Our approach builds
upon the social relations models of Warner, Kenny and Stoto [Journal of
Personality and Social Psychology 37 (1979) 1742--1757] and Gill and Swartz
[Canad. J. Statist. 29 (2001) 321--331] and allows for an intra- and
inter-temporal representation of network structures. We apply the methodology
to two longitudinal data sets: international trade (continuous response) and
militarized interstate disputes (binary response).Comment: Published in at http://dx.doi.org/10.1214/10-AOAS403 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
