Explaining Association with RIF Regression

• In Event: Causal Inference for Sociology

Abstract

Many questions in quantitative social science concern the strength of association between two variables and how that association would change as population composition shifts. Standard regressions with an interaction term capture how conditional associations vary by a moderator, but not how the unconditional association would change under compositional change in that moderator. This paper develops an easy-to-implement method targeting compositional effects. Building on recentered influence function (RIF) regression, it treats an association measure as a functional of the joint distribution of two variables and regresses an observation-level RIF pseudo-outcome on covariates. The resulting coefficients summarize marginal policy effects of the covariates on the association statistics. We derive RIFs for common association measures, including covariance, correlation, the unconditional OLS slope, and the Altham index for contingency tables. We also clarify the causal interpretation of our RIF regression. Simulations and an application to income and class mobility in the NLSY79 illustrate performance and provide practical guidance for applied research. We show that, unbeknownst to many, compositional effect and conditional heterogeneity easily contradict each other.

Author

• Lai Wei, The University of Hong Kong