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.
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This work was partially supported by the Japan Society for the Promotion of Science (JSPS), Grant no. 15K00060.
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Kuroki, M., Nanmo, H. Variance formulas for estimated mean response and predicted response with external intervention based on the back-door criterion in linear structural equation models. AStA Adv Stat Anal (2020). https://doi.org/10.1007/s10182-020-00372-7
- Causal effect
- Path diagram
- Structural causal model