Exact variance formula for the estimated mean outcome with external intervention based on the front-door criterion in Gaussian linear structural equation models
Exact variance formula for the estimated mean outcome with external intervention based on the front-door criterion in Gaussian linear structural equation models
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DOI：
10.1016/j.jmva.2021.104766
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Hisayoshi Nanmo;Manabu Kuroki
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文献类型：
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作者：
Hisayoshi Nanmo;Manabu Kuroki
本文假设变量之间的因果关系可以用高斯线性结构方程模型和相应的有向无环图来表示。对于满足前门标准的一组中间变量，我们给出了外部干预下治疗变量设置为指定常量时估计的平均结果的方差公式。与以往大多数估计总体效应的研究相比，本文提出的方差公式是准确的。此外，基于方差公式，我们推导出未来样本与外部干预下估计平均结果之间的均方误差。
In this paper, we assume that cause–effect relationships among variables can be represented by a Gaussian linear structural equation model and a corresponding directed acyclic graph. For a set of intermediate variables that satisfies the front-door criterion, we provide the variance formula of the estimated mean outcome under an external intervention in which a treatment variable is set to a specified constant value. The variance formula proposed in this paper is exact, in contrast to those in most previous studies on estimating total effects. In addition, based on the variance formula, we formulate the mean squared error between a future sample and the estimated mean outcome with the external intervention.