Network Cluster-Robust Inference

Network data commonly consists of observations on a single large network. Accordingly, researchers often partition the network into clusters in order to apply cluster-robust inference methods. All existing such methods require clusters to be asymptotically independent. We show that for this requirement to hold, under certain conditions, it is necessary and sufficient for clusters to have small "conductance," which is the ratio of edge boundary size to volume. This yields a quantitative measure of cluster quality. Unfortunately, there are important classes of networks for which small-conductance clusters appear not to exist. Our simulation results show that for such networks, cluster-robust methods can exhibit substantial size distortion. Based on well-known results in spectral graph theory, we suggest using the eigenvalues of the graph Laplacian to determine the existence and number of small-conductance clusters. We also discuss the use of spectral clustering for constructing clusters in practice