Network Cluster-Robust Inference

TL;DR

This paper investigates conditions under which cluster-robust inference is valid for network data, introducing conductance as a key measure and proposing spectral methods to identify suitable clusters for reliable inference.

Contribution

It establishes that low conductance clusters are necessary and sufficient for valid cluster-robust inference in network data, and proposes spectral clustering techniques to find such clusters.

Findings

Low conductance clusters improve size control in cluster-robust methods.

Spectral clustering effectively identifies low-conductance clusters.

High conductance clusters can cause size distortions in inference.

Abstract

Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster-robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network-dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster-robust methods control size better than HAC estimators. However, for important classes of networks lacking low-conductance clusters, the former can exhibit substantial size distortion. To determine the number of low-conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low-conductance clusters and spectral clustering to construct them.