A confounder is like some backdoor paths from X to Y. To eliminate the confounder, you just need to block those backdoor paths. A randomized Controlled Trial did exactly that. But there is another way if we have a hypothesis on the causal diagram.

1. In a chain junction, A –> B –> C, controlling for B prevents information about A getting to C and vice versa.
2. In a fork (confounding junction), A <– B –> C, controlling for B prevents information about A getting to C and vice versa.
3. In a collider, A –> B <– C, controlling for B will open the gate, allowing information flowing from A to C.
4. Controlling for descendants (or proxies) of a variable is partially controlling the path.

# Some Games

Game 1: There is no backdoor path. We do not need to control anything. If you try to control for B, you will partially close gate A. Then X and Y may not be correlated which is not good.

Game 2: There is one backdoor path highlighted in Green. However, B is a collider that is already blocked. If you try to control for B, you will open this backdoor path which is not good.

Game 3: There are two potential backdoor paths highlighted in Green and Orange. A is a collider. The path is already blocked. We need to control for B to close the flow from X to Y through B.

Game 4: There is one potential backdoor path. Controlling for B will open the gate which is not good. Statisticians may consider B as a confounder and control for it since B is correlated with X and also Y. B is not on a causal path and it is not a descendant. But this graph shows that if we control for B, it is not good.

Game 5: It is a similar graph as Game 4. We already know that the Green path is not a backdoor path since B is a collider. However, there is one more backdoor path highlighted in Orange. If you try to control for B, you closed the orange path but opened the green path. It is not good. Instead of controlling for B, you need to control for C.

This article is probably the end of the discussion of confunder. It is indeed very interesting to read these chapters. In the next few articles, let’s make use of this concept and examine some puzzles together.