Resources for Causal Reasoning in Health Services Research

d-separation

variables X and Y are said to be d-separated, if all paths from X to Y are blocked. A path may be blocked by a set of variables S, if the path contains at least one arrow-emitting variable that is in S or if the path contains at least one collider that is not in S and has no descendent in S. A collider is defined as a variable on a path such that the path enters and leaves via arrow heads. X and Y are, therefore, d-separated conditional on S, if S blocks all paths between X and Y. X and Y are marginally independent when S contains the null set

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