Selecting balanced splits in instrumental forests

[JeGemm]

Hi grf team,

I am currently trying to follow how instrumental forests select balanced splits. I have read the corresponding section in the algorithm reference for causal forests, but I suppose that this does not fully apply to instrumental forests.

In particular, I'm interested in:

1. how min.node.size is determined
2. what the node size measure is which is used together with alpha and imbalance.penalty
3. what changes in 1. and 2. if stabilize.splits is set to FALSE

Thank you for your support & best regards,
Jens

[erikcs]

Hi @JeGemm, instrumental forest does balanced splits the same way, just replace treatment with instrument. min.node.size is a tuning parameter and stabilize.splits=FALSE is just plain regression splits with the corresponding constraint a standard regression forest would have.

[JeGemm]

Hi @erikcs, thank you!

I have one remaining question: In this commit, min.node.size for instrumental forests is described as:

"For instrumental splitting, use a tailored interpretation of min.node.size. Now, there can be no fewer than min.node.size samples in each leaf with instrument less than the parent's mean instrument, and no fewer with a greater instrument. In the case of causal estimation with binary treatment, this rule enforces that there are no fewer than min.node.size
treatment and control samples in each leaf."

Following the code in InstrumentalSplittingRule.cpp, I can't see how min.node.size puts a requirement on the number of treatment and control samples in a leaf?

Best,
Jens

[erikcs]

Hi Jens, in that code, when used by causal forest, then the instrument is set to the treatment.