Regression-based causal inference with factorial experiments: estimands, model specifications and design-based properties
Regression-based causal inference with factorial experiments: estimands, model specifications and design-based properties
复制标题
基于回归的因果推理与阶乘实验：估计值、模型规范和基于设计的属性
DOI：
10.1093/biomet/asab051
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发表时间：
2021
期刊：
影响因子：
2.7
通讯作者：
Ding, Peng
中科院分区：
文献类型：
--
作者：
Zhao, Anqi;Ding, Peng
析因设计因其能够同时适应多个因素而被广泛使用。具有主效应和一些交互作用的基于因子的回归是下游分析的主要策略，通过一次最小二乘拟合同时提供点估计量和标准误差。从设计为基础的角度来看，这些方便的估计的理由需要量化的分配机制下的抽样性能，同时条件的潜在结果。为此，我们推导出的回归估计的抽样性质下的一个广泛的规格，并建立相应的稳健的标准误的适当性Wald型推断。这些结果有助于澄清这些基于因子的回归中系数的因果解释，并激发一般因子效应的定义，以统一各领域的因子效应定义。我们还量化的偏差方差之间的权衡饱和和不饱和回归从设计为基础的角度。
Factorial designs are widely used because of their ability to accommodate multiple factors simultaneously. Factor-based regression with main effects and some interactions is the dominant strategy for downstream analysis, delivering point estimators and standard errors simultaneously via one least-squares fit. Justification of these convenient estimators from the design-based perspective requires quantifying their sampling properties under the assignment mechanism while conditioning on the potential outcomes. To this end, we derive the sampling properties of the regression estimators under a wide range of specifications, and establish the appropriateness of the corresponding robust standard errors for Wald-type inference. The results help to clarify the causal interpretation of the coefficients in these factor-based regressions, and motivate the definition of general factorial effects to unify the definitions of factorial effects in various fields. We also quantify the bias-variance trade-off between the saturated and unsaturated regressions from the design-based perspective.