The regression discontinuity (RD) design is a popular approach to causalinference in non-randomized studies. This is because it can be used to identifyand estimate causal effects under mild conditions. Specifically, for eachsubject, the RD design assigns a treatment or non-treatment, depending onwhether or not an observed value of an assignment variable exceeds a fixed andknown cutoff value. In this paper, we propose a Bayesian nonparametric regression modelingapproach to RD designs, which exploits a local randomization feature. In thisapproach, the assignment variable is treated as a covariate, and ascalar-valued confounding variable is treated as a dependent variable (whichmay be a multivariate confounder score). Then, over the model's posteriordistribution of locally-randomized subjects that cluster around the cutoff ofthe assignment variable, inference for causal effects are made within thisrandom cluster, via two-group statistical comparisons of treatment outcomes andnon-treatment outcomes. We illustrate the Bayesian nonparametric approach through the analysis of areal educational data set, to investigate the causal link between basic skillsand teaching ability.
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