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Variance formulas for estimated mean response and predicted response with external intervention based on the back-door criterion in linear structural equation models

机译:基于线性结构方程模型后门标准的基于外部干预的估计平均响应和预测响应的方差公式

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This paper considers a situation in which cause-effect relationships among variables can be described by a linear structural equation model (linear SEM) and the corresponding directed acyclic graph (DAG). By considering a set of covariates that satisfies the back-door criterion, we formulate (1) the variances of the estimated mean response and (2) the mean squared error (MSE) of the predicted response, with external intervention in which a treatment variable is set to be a certain constant value. The variance and MSE formulas proposed in this paper are exact, unlike those in most previous studies regarding the problem of estimating total effects. In addition, we compare the performance of the simple regression model with that of the predicted response with the external intervention. Furthermore, we apply the present results to statistical quality control.
机译:本文考虑了可以通过线性结构方程模型(线性SEM)和相应的定向非循环图(DAG)来描述变量之间的原因关系的情况。通过考虑一组满足后门标准的协调因子,我们制定(1)估计平均响应的差异和(2)预测响应的平均平方误差(MSE),具有治疗变量的外部干预被设置为一定的恒定值。本文提出的方差和MSE公式是精确的,与估算总效果的问题的最先前研究中的方差和MSE公式是精确的。此外,我们将简单回归模型的性能与外部干预的预测响应的性能进行比较。此外,我们将目前的结果应用于统计质量控制。

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