Beginner question: getting CATE estimations & confidence intervalls

[darjooling86]

Hi,

based on the attached graph, I would like to estimate the CATE for the variable 'komplex' (discret) on 'dlz_implementierung' (continuous) based on the treatment 'spm' (binary). From the data generation process I know, that 'komplex' does not affect the assignment of 'spm' (in terms if it is 1 or 0). But 'komplex' is used to determine the effect of the treatment (if 'komplex' > 5 then -10 else 0). Therefore, I would like the retrieve the treatment effect for the different levels 'komplex' together with its confidence intervals. By using the econml estimation methods (e.g. T-Learner, CausalForestDML) with X=['komplex', 'team'], I get the effect and confidence interval on this exact level. Since I have to control for 'team', is there any way in this setup to get the treatment effect and confidence intervals on the 'komplex'-level from the estimator? Any help is appreciated!

Thank you very much!

[kbattocchi]

Just to make completely sure I understand the question, you state that you

would like to estimate the CATE for the variable 'komplex' (discret) on 'dlz_implementierung' (continuous) based on the treatment 'spm' (binary)

I assume this means that you want to assess the effect of the treatment spm on the outcome dlz_implementierung conditional on the feature komplex - is that right? If so, then I think this actually should work fine with CausalForestDML - just use only komplex in your features X, put team in your controls W, spm as your treatment T, and dlz_implementierung as your outcome Y. In the first stage, we'll fit models for T and Y based on X and W (in the case of the treatment model, given a sufficiently rich model we should be able to learn that the treatment depends on W but not directly on X, while both directly affect Y). Then in the second stage, we'll learn the treatment effect conditional on komplex as desired.