Network Autocorrelation Modeling: Bayesian Techniques for Estimating and Testing Multiple Network Autocorrelations

The network autocorrelation model has been the workhorse for estimating and testing the strength of theories of social influence in a network. In many network studies, different types of social influence are present simultaneously and can be modeled using various connectivity matrices. Often, researchers have expectations about the order of strength of these different influence mechanisms. However, currently available methods cannot be applied to test a specific order of social influence in a network. In this article, the authors first present flexible Bayesian techniques for estimating network autocorrelation models with multiple network autocorrelation parameters. Second, they develop new Bayes factors that allow researchers to test hypotheses with order constraints on the network autocorrelation parameters in a direct manner. Concomitantly, the authors give efficient algorithms for sampling from the posterior distributions and for computing the Bayes factors. Simulation results suggest that frequentist properties of Bayesian estimators on the basis of noninformative priors for the network autocorrelation parameters are overall slightly superior to those based on maximum likelihood estimation. Furthermore, when testing statistical hypotheses, the Bayes factors show consistent behavior with evidence for a true data-generating hypothesis increasing with the sample size. Finally, the authors illustrate their methods using a data set from economic growth theory.