Accounting for Edge Uncertainty in Stochastic Actor-Oriented Models for Dynamic Network Analysis

Stochastic Actor-Oriented Models (SAOMs) were designed in the social network setting to capture network dynamics representing a variety of influences on network change. The standard framework assumes the observed networks are free of false positive and false negative edges, which may be an unrealistic assumption. We propose a hidden Markov model (HMM) extension to these models, consisting of two components: 1) a latent model, which assumes that the unobserved, true networks evolve according to a Markov process as they do in the SAOM framework; and 2) a measurement model, which describes the conditional distribution of the observed networks given the true networks. An expectation-maximization algorithm is developed for parameter estimation. We address the computational challenge posed by a massive discrete state space, of a size exponentially increasing in the number of vertices, through the use of the missing information principle and particle filtering. We present results from a simulation study, demonstrating our approach offers improvement in accuracy of estimation, in contrast to the standard SAOM, when the underlying networks are observed with noise. We apply our method to functional brain networks inferred from electroencephalogram data, revealing larger effect sizes when compared to the naive approach of fitting the standard SAOM.