Specification Testing for Dyadic Regression Models

2026-07-28

AI Summary

This study addresses the lack of effective global specification tests for linear conditional mean models with undirected binary network data. By leveraging the shared-node dependence structure and applying a unified projection theorem, the authors reduce the binary process to a first-order nodal projection and develop the first unified testing framework applicable to both degenerate and non-degenerate cases. The proposed approach combines nodal multiplier bootstrap with corrected Gaussian bootstrap to construct Kolmogorov–Smirnov and Cramér–von Mises type tests suitable for both independent and dependent data. Simulations demonstrate that the corrected KS test exhibits the most stable size control and favorable local power. Applied to the Lazega law firm network data, the method successfully detects and corrects misspecifications in both additive linear and quadratic specifications.

Abstract

This paper develops omnibus specification tests for linear conditional-mean models with undirected dyadic data. We establish a uniform projection theorem that reduces the dyadic process to its latent first-order node projections under shared-node dependence. We then show that a raw first-order node-multiplier bootstrap is valid when this node component is nondegenerate but double-counts dyad-specific variation when dyads are independent. An exact covariance decomposition motivates a corrected Gaussian bootstrap that is valid in both regimes. The resulting Kolmogorov-Smirnov and Cramér-von Mises tests are consistent against fixed alternatives and have nontrivial power against rate-appropriate local alternatives. Simulations show that the corrected Kolmogorov-Smirnov test provides the most stable size control while retaining substantial local power. An application to the Lazega law-firm network rejects additive linear and quadratic specifications but finds no remaining misspecification after including an economically relevant interaction.

Problem

• dyadic data
• specification testing
• linear conditional-mean models
• shared-node dependence
• omnibus tests

Innovation

• dyadic data
• specification testing
• node-multiplier bootstrap
• covariance decomposition
• uniform projection theorem