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

Manabu Kuroki () and Hisayoshi Nanmo ()
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Manabu Kuroki: Yokohama National University
Hisayoshi Nanmo: Yokohama National University

AStA Advances in Statistical Analysis, 2020, vol. 104, issue 4, No 6, 667-685

Abstract: Abstract 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.

Keywords: Causal effect; Identification; Path diagram; Structural causal model (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10182-020-00372-7

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