Influence of multiple network structures on bayesian estimation of peer effects and statistical power for generalized linear network autocorrelation models.

Abstract

The recent published literature on linear network autocorrelation models of actor behaviors or other mutable attributes has revealed a curious finding. Irrespective of the size of the network and the status of other network features, likelihood-based estimators (e.g., maximum likelihood and Bayesian) of the autocorrelation parameter ([Formula: see text]) are negatively biased and become increasingly so as the density of the network increases. In this paper we investigate the pattern of bias of estimators of [Formula: see text] when analyzing multiple mutually exclusive sub-networks and directed networks with various levels of reciprocity. In addition to considering the case of a linear network autocorrelation model applied to a binary-valued network, the edges may be weighted and the attribute whose actor-interdependence (or peer-effect) we are interested in may be an event (i.e., a binary outcome), a count, or a rate outcome motivating the use of generalized linear network autocorrelation models. We perform a simulation study that reveals that bias reduces substantially as either the number of sub-networks increases or with increased variation across the network in the edge weights but this pattern is not observed with reciprocity. The findings for generalized linear network autocorrelation models are in general similar to those for linear network autocorrelation models. Finally, we perform a statistical power analysis based on these findings for use in designing future studies whose goal is to estimate or to detect peer-effects.