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Covariate selection for estimating the causal effect of control plans by using causal diagrams

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  • Manabu Kuroki
  • Masami Miyakawa

Abstract

Summary. Consider a case where cause–effect relationships between variables can be described by a causal path diagram and the corresponding linear structural equation model. The paper proposes a graphical selection criterion for covariates to estimate the causal effect of a control plan. For designing the control plan, it is essential to determine both covariates that are used for control and covariates that are used for identification. The selection of covariates used for control is only constrained by the requirement that the covariates be non‐descendants of a treatment variable. However, the selection of covariates used for identification is dependent on the selection of covariates used for control and is not unique. In the paper, the difference between covariates that are used for identification is evaluated on the basis of the asymptotic variance of the estimated causal effect of an effective control plan. Furthermore, the results can be also described in terms of a graph structure.

Suggested Citation

  • Manabu Kuroki & Masami Miyakawa, 2003. "Covariate selection for estimating the causal effect of control plans by using causal diagrams," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 209-222, February.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:209-222
    DOI: 10.1111/1467-9868.00381
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    Cited by:

    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. Leonard Henckel & Emilija Perković & Marloes H. Maathuis, 2022. "Graphical criteria for efficient total effect estimation via adjustment in causal linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 579-599, April.
    3. Ryusei Shingaki & Hiroshi Kanda & Manabu Kuroki, 2021. "Selection and integration of generalized instrumental variables for estimating total effects," Statistical Papers, Springer, vol. 62(5), pages 2355-2381, October.
    4. F Richard Guo & Emilija Perković & Andrea Rotnitzky, 2023. "Variable elimination, graph reduction and the efficient g-formula," Biometrika, Biometrika Trust, vol. 110(3), pages 739-761.
    5. Tyler J. VanderWeele & James M. Robins, 2010. "Signed directed acyclic graphs for causal inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 111-127, January.
    6. Pearl Judea & Paz Azaria, 2014. "Confounding Equivalence in Causal Inference," Journal of Causal Inference, De Gruyter, vol. 2(1), pages 75-93, March.

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