Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 72, Issue -, Pages 111-127Publisher
WILEY
DOI: 10.1111/j.1467-9868.2009.00728.x
Keywords
Bias; Causal inference; Confounding; Directed acyclic graphs; Structural equations
Categories
Funding
- National Institutes of Health [AI032475]
- NATIONAL INSTITUTE OF ALLERGY AND INFECTIOUS DISEASES [R37AI032475] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES [R01ES017876] Funding Source: NIH RePORTER
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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.
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