I was curious about the following causal problem

Given the following DAG and asked to list the minimum conditioning sets that satisfy the back-door criterion for identifying the effect of X on Y, should I only condition on Z4, as Z1 is caused by Z4, condition on both Z1 and Z4 as they appear on different non-causal paths from X to Y or only on Z1, as this also blocks Z4.

enter image description here

Sorry if this seems a basic question, but I have some troubles understanding the intuition behind the backdoor criteria.


1 Answer 1


There are two valid sets to close the backdoor paths $\{Z_4, Z_1\}$ and $\{Z_2, Z_1\}$

To understand why, I will walk through my thought process. First, $Z_1$ requires being conditioned on, since it points to both $X$ and $Y$ directly. However, by conditioning on $Z_1$, a path between $Z_4$ and $Z_2$ is opened (because $Z_1$ is a collider on the $X \leftarrow Z_4 \rightarrow Z_1 \leftarrow Z_2 \rightarrow Y$ pathway). The now open $Z_4$ and $Z_2$ pathway now is an open backdoor path between $X$ and $Y$. As a result, either $Z_2$ or $Z_4$ must be conditioned on to close that path.

Either is a valid option to choose. You may want to consider which variable has less measurement error potential as a criteria. If you are using standardization to obtain the effect estimate, then $Z_2$ would lead to a more precise (i.e. smaller standard error) estimate because it is more predictive of the outcome.

Another easy way to find a sufficient set is to condition on everything that directly points into $X$. If all variables with arrows pointing into $X$ are conditioned on, that is a sufficient adjustment set.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.