Measuring the Graph Concordance of Locally Dependent Observations

TL;DR

This paper proposes a simple measure for assessing how outcomes are correlated along a network, and develops permutation-based confidence intervals for inference, demonstrating robustness through simulations.

Contribution

It introduces a novel graph concordance measure and a permutation-based inference method, applicable to large networks with dependent outcomes.

Findings

Permutation method is more robust than asymptotic in various graph configurations.

Confidence intervals are valid in finite samples under exchangeability.

Asymptotic validity holds under dependency graph assumptions.

Abstract

This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance measure can be generally used to quantify the empirical relevance of a network in explaining cross-sectional dependence of the outcomes, and as shown in the paper, can also be used to quantify the extent of homophily under certain conditions. When one observes a single large network, it is nontrivial to make inference about the concordance pattern. Assuming dependency graph, this paper develops a permutation-based confidence interval for the graph concordance measure. The confidence interval is valid in finite samples when the outcomes are exchangeable, and under the dependency graph assumption together with other regularity conditions, is shown to exhibit asymptotic validity. Monte Carlo simulation results show that the validity of the permutation method is more robust to various graph configurations than the asymptotic method.