All simulators
Selecting on the Middle Variable
Keep only the top of the middle variable and watch chains and forks lose their correlation while colliders gain one.
Day 48: Chains, Forks & Colliderscorr, everyone
0.01
corr, kept group
-0.50
partial corr | middle
-0.91
kept (selected on the middle variable)dropped
1,500 simulated people. Keep only those with the highest values of the middle variable (selection), and compare the correlation of the two outer variables in the kept group with the full population and with the partial correlation from regression. Chains and forks lose their association; colliders gain one.