The grass is not always greener in the neighbor's yard: Bayesian and frequentist inference methods for network autocorrelated data

People do not live in isolation. Instead, we constantly interact with others, which affects our actions, opinions, or well-being. Throughout the last decades, the network autocorrelation model has been the workhorse for modeling network influence on individual behavior. In the network autocorrelation model, actor observations for a variable of interest are allowed to be correlated, where a network autocorrelation parameter represents and quantifies the strength of a network influence on the variable of interest. More precisely, an actor’s observation is assumed to be a function not only of a set of explanatory variables but also of the observations for the actor's neighbors, i.e., other actors in the network this actor is tied to. In this thesis, we develop a fully Bayesian framework to estimate the network autocorrelation model and to test multiple hypotheses on the network autocorrelation parameter(s) against each other. Taking the Bayesian route hereto has at least three attractive features that are not shared by classical statistical methods such as maximum likelihood estimation and null hypothesis significance testing. First, the Bayesian approach enables researchers to include previous empirical information about the network autocorrelation parameter through a prior distribution, which may attenuate the underestimation of the network autocorrelation parameter associated with maximum likelihood estimation of the model. Concomitantly, we also derive Bayesian default procedures for situations in which such prior information is completely unavailable. Second, Bayesian techniques do not rely on asymptotic approximations when estimating uncertainty and performing inference about the network autocorrelation parameter but yield accurate results even in case of small networks. Third, using Bayes factors as opposed to null hypothesis significance testing, researchers can test any number of hypotheses on the network autocorrelation parameter and quantify the amount of relative evidence in the data for each tested hypothesis. We provide several such Bayes factors and generalize the presented methodology to test order hypotheses on multiple network autocorrelation parameters, representing the strength of multiple influence mechanisms that may have some connection to the variable of interest. Furthermore, we introduce a discrete exponential family model to analyze network autocorrelated count data for which the network autocorrelation model itself is not well-suited. This novel model permits principled statistical inference without making any potentially limiting distributional assumptions on the marginal or conditional counts but is flexible enough to accommodate a wide range of count patterns. In sum, the methods developed in this thesis allow researchers studying network influence to quantify and test the strength of network influence(s) on a variable of interest in ways that go beyond the current state of the art