= Collider = A '''collider''' is a variable that is caused by multiple variables. <> ---- == Description == Colliders are closely related to [[Statistics/Confounder|confounders]], but in the 'opposite' way. Generically, consider a variable ''Z'' that is associated with two independent variables, ''X'' and ''Y''. If ''Z'' is controlled for, ''X'' and ''Y'' become associated. The presence of a collider causes '''collider bias''' or '''Berkson's paradox'''. [[https://statmodeling.stat.columbia.edu/2026/05/13/recent-discoveries-on-the-persistence-of-statistical-fallacies/|Alex Dimakis]] provides a more concrete example: "Assume that to be a successful actor you have to be either extremely good looking or extremely talented. Assume also that talent and looks are independent in the population. However, among sucessful [sic] actors you will observe a negative correlation between looks and talent." See in the following demo that controlling for ''Z'' 'creates' a [[Statistics/Correlation|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 }}} ---- CategoryRicottone