A comparison of estimators for the network autocorrelation model based on observed social networks

Abstract

Network autocorrelation models (NAMs) are widely used to study a response variable of interest among subjects embedded within a network. Although the NAM is highly useful for studying such networked observational units, several simulation studies have raised concerns about point estimation. Specifically, these studies have consistently demonstrated a negative bias of maximum likelihood estimators (MLEs) of the network effect parameter. However, in order to gain a practical understanding of point estimation in the NAM, these findings need to be expanded in three important ways. First, these simulation studies are based on relatively simple network generative models rather than observed networks, thereby leaving as an open question how realistic network topologies may affect point estimation in practice. Second, although there has been strong work done in developing two-stage least squares estimators as well as Bayesian estimators, only the MLE has received extensive attention in the literature, thus leaving practitioners in question as to best practices. Third, the performance of these estimators need to be compared using both bias and variance, as well as the coverage rate of each estimator's corresponding confidence or credible interval. In this paper we describe a simulation study which aims to overcome these shortcomings in the following way. We first fit real social networks using the exponential random graph model and used the Bayesian predictive posterior distribution to generate networks with realistic topologies. We then compared the performance of the three different estimators mentioned above.