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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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  • Nanmo, Hisayoshi
  • Kuroki, Manabu

Abstract

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.

Suggested Citation

  • Nanmo, Hisayoshi & Kuroki, Manabu, 2021. "Exact variance formula for the estimated mean outcome with external intervention based on the front-door criterion in Gaussian linear structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:jmvana:v:185:y:2021:i:c:s0047259x21000440
    DOI: 10.1016/j.jmva.2021.104766
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    References listed on IDEAS

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    1. Manabu Kuroki & Hisayoshi Nanmo, 2020. "Variance formulas for estimated mean response and predicted response with external intervention based on the back-door criterion in linear structural equation models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 667-685, December.
    2. Manabu Kuroki, 2012. "Optimizing a control plan using a structural equation model with an application to statistical process analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 673-694, August.
    3. Manabu Kuroki & Takahiro Hayashi, 2016. "On the Estimation Accuracy of Causal Effects using Supplementary Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 505-519, June.
    4. Elena Stanghellini & Eduwin Pakpahan, 2015. "Identification of causal effects in linear models: beyond instrumental variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 489-509, September.
    5. Manabu Kuroki & Judea Pearl, 2014. "Measurement bias and effect restoration in causal inference," Biometrika, Biometrika Trust, vol. 101(2), pages 423-437.
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