I was reading through the 2nd edition preprint and took a look at your lecture and have a question regarding the treatment of pipes (in DAGs).
You use the fungal treatment example that has a DAG looking a little like this:
In the book you say that conditioning on F removes the effect of T in our model, not sure the wording is good. Essentially you want to omit F from your model to get the effect of T on H_1.
However, I would read T \rightarrow F \rightarrow H_1 as the pipe here and those are “Open unless you condition on Z [F in this DAG]”. Which I would read as “add F to your model to close the pipe”.
So now I have “omit F from your model to get the effect of T on H_1” and “add F to your model to close the pipe” which contradict each other.
Another example you give is the grandparents/parents education one:
In your lecture you list the following paths from G to C:
(1) G \rightarrow C
(2) G \rightarrow P \rightarrow C
(3) G \rightarrow P \leftarrow U \rightarrow C
And the comment: “Conditioning on P closes (2) but opens (3)”
Again, G \rightarrow P \rightarrow C looks like a pipe to me, so conditioning on P closes it, based on “Open unless you condition on Z” however if we ignore U, what is the difference to the first example?
I feel like it could be something of a direct vs indirect effect thing but am not sure how to work with that:
- For the plant example, the treatment itself has no direct effect on plant growth. Only through the hindering of fungal growth does it impact H_1.
- In the Grandparents example, there might be a direct effect of GP education on children.
The problem I have is that any kind of soil treatment could (I think) also directly influence plant growth.
Sso one could rewrite the first DAG as such:
Which makes it the same as the GP graph if we ignore U.
Conditioning on P in the GP graph closes (2) so using that on the fungal graph, we should condition on F to close the same path T \rightarrow F \rightarrow H_1.
Could you maybe give me a helping hand here (or anyone else who got DAGs)?