Institute for Policy Research, Northwestern University.
Department of Psychology, Koç University.
Psychol Methods. 2018 Mar;23(1):150-168. doi: 10.1037/met0000118. Epub 2017 Mar 16.
In the "sharp" regression discontinuity design (RD), all units scoring on one side of a designated score on an assignment variable receive treatment, whereas those scoring on the other side become controls. Thus the continuous assignment variable and binary treatment indicator are measured on the same scale. Because each must be in the impact model, the resulting multi-collinearity reduces the efficiency of the RD design. However, untreated comparison data can be added along the assignment variable, and a comparative regression discontinuity design (CRD) is then created. When the untreated data come from a non-equivalent comparison group, we call this CRD-CG. Assuming linear functional forms, we show that power in CRD-CG is (a) greater than in basic RD; (b) less sensitive to the location of the cutoff and the distribution of the assignment variable; and that (c) fewer treated units are needed in the basic RD component within the CRD-CG so that savings can result from having fewer treated cases. The theory we develop is used to make numerical predictions about the efficiency of basic RD and CRD-CG relative to each other and to a randomized control trial. Data from the National Head Start Impact study are used to test these predictions. The obtained estimates are closer to the predicted parameters for CRD-CG than for basic RD and are generally quite close to the parameter predictions, supporting the emerging argument that CRD should be the design of choice in many applications for which basic RD is now used. (PsycINFO Database Record
在“尖锐”回归不连续设计（RD）中，所有在指定分配变量得分一侧得分的单位都接受治疗，而在另一侧得分的单位则成为对照组。因此，连续分配变量和二进制治疗指标是在同一尺度上测量的。由于每个都必须在影响模型中，因此由此产生的多重共线性会降低 RD 设计的效率。但是，可以沿分配变量添加未经处理的比较数据，并创建比较回归不连续设计（CRD）。当未经处理的数据来自非等效对照组时，我们称此为 CRD-CG。假设线性函数形式，我们表明 CRD-CG 中的功效为：（a）大于基本 RD；（b）对截止值的位置和分配变量的分布不敏感；（c）在 CRD-CG 内的基本 RD 组件中需要更少的治疗单位，从而可以通过减少治疗病例数来节省成本。我们开发的理论用于对基本 RD 和 CRD-CG 之间的效率进行数值预测，并与随机对照试验进行比较。国家学前教育影响研究的数据用于检验这些预测。获得的估计值更接近 CRD-CG 的预测参数，而不是基本 RD 的预测参数，并且通常与参数预测非常接近，支持了这样一种观点，即在许多现在使用基本 RD 的应用中，CRD 应该是首选设计。
