Covariate adjustment in multi-armed, possibly factorial experiments
多处理臂及析因实验中的协变量调整AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确针对随机实验中的平均治疗效应、协变量调整和设计型推断，并覆盖多处理臂及析因设计，属于因果推断。
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多处理臂及析因实验中的协变量调整
- 研究问题
- 在多处理臂或析因实验中，如何利用协变量提高平均治疗效应估计效率，并平衡完全交互回归的有限样本波动与约束误设？
- 方法与思路
- 作者从设计型视角比较加性与完全交互 OLS 调整，再建立约束最小二乘的推断性质，并通过理论和模拟讨论析因实验。
- 材料陈述的贡献
- 摘要称约束正确时具有渐近效率；治疗系数约束正确且与交互系数约束分离时保持一致，适度误设时仍可能改善有限样本表现。
- 阅读关注点
- 核对系数约束的具体形式与分离要求、效率比较基准，以及多协变量多处理臂下的样本条件和误设程度如何界定。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出完整渐近条件或模拟数值，不能将部分误设下的一致性扩展至任意约束。
原文摘要
Randomized experiments are the gold standard for causal inference, and justify simple comparisons across treatment groups. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This article provides a unified account of its utility for improving estimation efficiency in multi-armed experiments. We start with the commonly used additive and fully interacted models for regression adjustment, and clarify the trade-offs between the resulting ordinary least-squares (OLS) estimators for estimating average treatment effects in terms of finite-sample performance and asymptotic efficiency. We then move on to regression adjustment based on restricted least squares (RLS), and establish for the first time its properties for inferring average treatment effects from the design-based perspective. The resulting inference has multiple guarantees. First, it is asymptotically efficient when the restriction is correctly specified. Second, it remains consistent as long as the restriction on the coefficients of the treatment indicators, if any, is correctly specified and separate from that on the coefficients of the treatment-covariates interactions. Third, it can have better finite-sample performance than its unrestricted counterpart even if the restriction is moderately misspecified. It is thus our recommendation for covariate adjustment in multi-armed experiments when the OLS fit of the fully interacted regression risks large finite-sample variability in case of many covariates, many treatments, yet a moderate sample size. In addition, the proposed theory of RLS also provides a powerful tool for studying OLS-based inference from general regression specifications. As an illustration, we demonstrate its unique value for studying OLS-based regression adjustment in factorial experiments via both theory and simulation.