= Collider =

A '''collider''' is a variable that is caused by multiple variables.

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== Description ==

Colliders are one possible failure of causal inference, although in an atypical manner. Generically a collider ''Z'' is associated with two independent variables, ''X'' and ''Y''. Therefore when controlling for the collider ''X'' and ''Y'' become associated.

In this example, controlling for ''Z'' 'creates' a correlation. (Note that in [[R]], the [[Analysis/BernoulliDistribution|Bernoulli distribution]] is handled as a special case of the [[Analysis/BinomialDistribution|Binomial distribution]]. Comparing the sum of ''X'' and ''Y'' to 0 is effectively checking if either is 1.)

{{{
> X <- rbinom(1000, 1, 0.5)
> Y <- rbinom(1000, 1, 0.5)
> Z <- rbinom(1000, 1, ifelse(X+Y>0, 0.9, 0.2))
> cor(X,Y)
[1] -0.02387166
> cor(X[Z==1], Y[Z==1])
[1] -0.3387377
> cor(X[Z==0], Y[Z==0])
[1] 0.2764379
}}}

The important consequence is that colliders should not be controlled for.



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CategoryRicottone