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Distortion of effects caused by indirect confounding

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  • Nanny Wermuth
  • D. R. Cox

Abstract

Undetected confounding may severely distort the effect of an explanatory variable on a response variable, as defined by a stepwise data-generating process. The best known type of distortion, which we call direct confounding, arises from an unobserved explanatory variable common to a response and its main explanatory variable of interest. It is relevant mainly for observational studies, since it is avoided by successful randomization. By contrast, indirect confounding, which we identify in this paper, is an issue also for intervention studies. For general stepwise-generating processes, we provide matrix and graphical criteria to decide which types of distortion may be present, when they are absent and how they are avoided. We then turn to linear systems without other types of distortion, but with indirect confounding. For such systems, the magnitude of distortion in a least-squares regression coefficient is derived and shown to be estimable, so that it becomes possible to recover the effect of the generating process from the distorted coefficient. Copyright 2008, Oxford University Press.

Suggested Citation

  • Nanny Wermuth & D. R. Cox, 2008. "Distortion of effects caused by indirect confounding," Biometrika, Biometrika Trust, vol. 95(1), pages 17-33.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:1:p:17-33
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    File URL: http://hdl.handle.net/10.1093/biomet/asm092
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    Cited by:

    1. 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.
    2. Pearl Judea, 2017. "A Linear “Microscope” for Interventions and Counterfactuals," Journal of Causal Inference, De Gruyter, vol. 5(1), pages 1-15, March.
    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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