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If we condition on a descendant of π that isnβt a mediator, it could unblock a path from π to π that was blocked by a collider. For example, this is the case with conditioning on π in Figure 4.13. This induces non-causal association between π and π , which biases the estimate of the causal effect. Consider the following general kind of path, where β Β· Β· Β· β denotes a directed path: π β Β· Β· Β· β π β Β· Β· Β· β π . Conditioning on π , or any descendant of π in a path like this, will induce collider bias. That is, the causal effect estimate will be biased by the non-causal association that we induce when we condition on π or any of its descendants (see Section 3.6).
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crocodile - (no access) - Introduction_to_Causal_Inference-Nov19_2020-Neal.pdf, p51
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