What is a collider and why is conditioning on it bad?

hard

Answer

$In a DAG A \to C \leftarrow B: C is a collider (both A and B point into it).$
$A and B are marginally independent, but conditioning on C creates a spurious association.$
$Classic example: 'talent and beauty are anticorrelated among Hollywood stars, because being famous (a collider caused by both) has been implicitly selected on'.$
$Same mechanism drives selection bias, sample-conditioning artifacts, restaurant-only surveys (studies that condition on 'made it to production' etc.).$

Check yourself — multiple choice

Random
In A → C ← B, conditioning on C opens a spurious A-B association → selection bias; textbook: Hollywood 'talent vs beauty' myth
Same as confounder
Not real

Collider: A → C ← B; conditioning on C creates spurious A-B association.

#causal-inference

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