Assessing Cross-Level Interactions in Clustered Data Using CATE Estimation Methods

Treatment effect heterogeneity is a critical issue in causal inference, as a one-size-fits-all approach is not sufficient and can even be detrimental for many treatments and interventions. In environments where individuals are clustered within communities, effect heterogeneity is commonplace rather than an exception, as characteristics of communities often interact with a treatment implemented on members within the communities, and such interactions result in treatment effect heterogeneity. This chapter demonstrates how various nonparametric methods for estimating conditional average treatment effects (CATEs) can be used to examine cross-level interaction effects between cluster-level variables and treatments implemented at the individual level. The pool of considered methods includes causal forests, Bayesian additive regression trees (BARTs), and X-Learners (using random forests and BART as base learners). We apply these methods to the Trends in International Mathematics and Science Study data, a widely recognized large-scale assessment dataset in education. In educational settings, cross-level interactions have garnered significant attention, as they can address the moderating effects of school-level resources and actions on student outcomes. Understanding these interactions is crucial for making informed policy decisions to enhance educational effectiveness. This chapter concludes by discussing remaining issues and future directions in employing CATE with clustered observational data.