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Signed directed acyclic graphs for causal inference

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  • Tyler J. VanderWeele
  • James M. Robins

Abstract

Summary. Formal rules governing signed edges on causal directed acyclic graphs are described and it is shown how these rules can be useful in reasoning about causality. Specifically, the notions of a monotonic effect, a weak monotonic effect and a signed edge are introduced. Results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables. The incorporation of signed edges in the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables. It is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data are missing on confounding variables.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:72:y:2010:i:1:p:111-127
    DOI: 10.1111/j.1467-9868.2009.00728.x
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    References listed on IDEAS

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    Cited by:

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    3. Sanjay Chaudhuri, 2014. "Qualitative inequalities for squared partial correlations of a Gaussian random vector," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 345-367, April.
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    7. Peña Jose M., 2020. "On the Monotonicity of a Nondifferentially Mismeasured Binary Confounder," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 150-163, January.
    8. Tyler J. VanderWeele, 2013. "Surrogate Measures and Consistent Surrogates," Biometrics, The International Biometric Society, vol. 69(3), pages 561-565, September.
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