Bayesian analysis of higher-order network autocorrelation models

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 chapter, we first present flexible Bayesian techniques for estimating network autocorrelation models with multiple network autocorrelation parameters. Second, we develop new Bayes factors that allow researchers to test hypotheses with order constraints on the network autocorrelation parameters in a direct manner. Concomitantly, we give efficient algorithms for sampling from the posterior distributions and for computing the Bayes factors. Simulation results suggest that frequentist properties of Bayesian estimators based on non-informative 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, we illustrate our methods using a data set from the economic growth theory.