On the implied weights of linear regression for causal inference
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线性回归用于因果推断时的隐含权重
- 研究问题
- 观察研究中的线性回归调整如何通过个体隐含权重体现协变量平衡、自加权与代表性，并影响因果效应估计的稳健性？
- 方法与思路
- 作者推导回归隐含权重的闭式表达，研究有限样本与渐近性质，建立其与凸优化的等价关系，并据此设计因果诊断。
- 材料陈述的贡献
- 摘要称该权重视角连接回归建模与因果研究设计，分析双重及多重稳健性，并覆盖多值治疗、匹配后回归和 R 诊断实现。
- 阅读关注点
- 应核对权重对应的目标效应、平衡与代表性条件，以及稳健性结论的适用范围和诊断如何揭示研究设计的问题。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未列稳健性条件，权重表达与诊断本身不能保证观察研究因果识别。
原文摘要
A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under controlled circumstances. Now, linear regression models are commonly used to analyze observational data and estimate causal effects. How do linear regression adjustments in observational studies emulate key features of randomized experiments, such as covariate balance, self-weighted sampling, and study representativeness? In this paper, we provide answers to this and related questions by analyzing the implied (individual-level data) weights of linear regression methods. We derive new closed-form expressions of the weights and examine their properties in both finite and asymptotic regimes. We show that the implied weights of general regression problems can be equivalently obtained by solving a convex optimization problem. Among others, we study doubly and multiply robust properties of regression estimators from the perspective of their implied weights. This equivalence allows us to bridge ideas from the regression modeling and causal inference literatures. As a result, we propose novel regression diagnostics for causal inference that are part of the design stage of an observational study. As special cases, we analyze the implied weights in common settings such as multi-valued treatments and regression adjustment after matching. We implement the weights and diagnostics in the new lmw package for R.