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| In this example, controlling for ''Z'' reveals the 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.) | 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.) |
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| The important consequence is that colliders should not be controlled for. |
Collider
A collider is a variable that is caused by multiple variables.
Contents
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 Bernoulli distribution is handled as a special case of the 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.