Cluster–Robust Variance Estimation for Dyadic Data

Abstract

Dyadic data are common in the social sciences, although inference for such settings involves accounting for a complex clustering structure. Many analyses in the social sciences fail to account for the fact that multiple dyads share a member, and that errors are thus likely correlated across these dyads. We propose a non-parametric, sandwich-type robust variance estimator for linear regression to account for such clustering in dyadic data. We enumerate conditions for estimator consistency. We also extend our results to repeated and weighted observations, including directed dyads and longitudinal data, and provide an implementation for generalized linear models such as logistic regression. We examine empirical performance with simulations and an application to interstate disputes.

Inference With Dyadic Data: Asymptotic Behavior of the Dyadic-Robust t -Statistic

“…A special case of Proposition 3.4 for M L = M H = G − 1 appears in Aronow et al (2015), whose proof generalizes to ours. Our next result generalizes Proposition 3.4…”

“…This assumption is completely analogous to the standard assumption made on the variance in clustered data with strong dependence, and is implicitly the assumption made in all of the results in Aronow et al (2015). Note that this assumption holds under an additive common shocks error specification:…”

“…Configurations of this type can arise in empirical settings with dyadic data: as an example, the application in Aronow et al (2015) features a configuration in which most of the units are contained in approximately 10 dyads, but a handful of units are contained in upwards of 140 dyads. Model B will play an important role in the simulation study of Section 4, as well as in developing our proposed degrees of freedom adjustment.…”

“…where α g , α h , n are i.i.d, which is a specification considered in the simulations of both Cameron and Miller (2014) and Aronow et al (2015). More generally, Assumption 2.5 would be appropriate in applications where the dependence results in a positive correlation between dyads.…”

“…Cameron and Miller (2014) and Aronow et al (2015) also consider the use of the dyadic-robust variance estimator in settings with M-estimators or GMM estimators. Our results can be extended to these settings under a set of "classical" regularity conditions (see Van der Vaart, 1998, Section 5.6) which include, for example, the logit or probit models considered in Cameron …”