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If we condition on a descendant of 𝑇 that isn’t a mediator, it could unblock a path from 𝑇 to π‘Œ that was blocked by a collider. For example, this is the case with conditioning on 𝑍 in Figure 4.13. This induces non-causal association between 𝑇 and π‘Œ , 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: 𝑇 β†’ Β· Β· Β· β†’ 𝑍 ← Β· Β· Β· ← π‘Œ . Conditioning on 𝑍 , or any descendant of 𝑍 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 𝑍 or any of its descendants (see Section 3.6).
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owner: crocodile - (no access) - Introduction_to_Causal_Inference-Nov19_2020-Neal.pdf, p51


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