Conditional independence in dynamic networks

Abstract

Given a longitudinal network observed at time points t1<⋯<tT, tie changes that happen in the interval (th,th+1) typically depend on the networks at t1,…,th. In this article we deal with the question whether changes within one interval mutually depend on each other or whether they are conditionally independent, given the previously observed networks. Answering this question for given data is of high practical relevance since, if the conditional independence assumption is valid, network dynamics can be modeled with simple and computationally efficient statistical techniques for independent observations. Consequently, we propose a framework to systematically compare conditional independence models with more general models that are specifically designed for social network data. Our results suggest that conditional independence models are inappropriate as a general model for network evolution and can lead to distorted substantive findings on structural network effects, such as transitivity. On the other hand, the conditional independence assumption becomes less severe when inter-observation times are relatively short.