Specification Testing for Dyadic Regression Models

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 Cram\'er-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.