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

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...

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Bibliographic Details
Published in:Advances in statistical analysis : AStA : a journal of the German Statistical Society 2020-12, Vol.104 (4), p.667-685
Main Authors: Kuroki, Manabu, Nanmo, Hisayoshi
Format: Article
Language:English
Subjects:
Criteria
Econometrics
Economics
Finance
Insurance
Management
Mathematics and Statistics
Mean
Multivariate statistical analysis
Original Paper
Probability Theory and Stochastic Processes
Quality control
Regression models
Statistical analysis
Statistics
Statistics for Business
Structural equation modeling
Variance
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Summary: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.
ISSN:1863-8171
1863-818X
DOI:10.1007/s10182-020-00372-7