DR score construction for lm_forest in a RDD setting

[JFLmkt]

Hello all, I wonder if there's any way to constructing DR score for lm_forest when applying it to RDD heterogeneity analysis.

Considering such a target RDD specification $Y = h(x)D + g(x)Z + f(x)$ ($D$: treatment indicator; $Z$: running score cut off at 0; $X$: covariates), the CATE of interests is $E[Y(1) - Y(0)|Z=0, X]$.

I notice that in the output of predict(lm_forest), we have predicted values of each treatment function together with the variance estimates.It looks like we can interpret $\hat{h}(x)$ as the plug-in prediction of $E[Y(1) - Y(0)|Z=0, X]$. If this is true, $\hat{h}(x)$ should be similar to $\hat{\tau}(x)$ in causal forest and thus can apply some similar DR score construction strategy to it, although the difficulty is we don't observe the true values for the conditional mean.

There have been some literature such as Reguly (2025) and Semenova and Chernozhukov (2021). But since I'm not a specialist of relevant theories, I would be grateful for comments from the authors and the community.

Many thanks

[erikcs]

Hi @JFLmkt,

The RD treatment effect is a very different animal from the treatment effect under unconfoundedness that the AIPW scores target. The latter makes no assumptions on the conditional potential outcome mean functions, while the former typically makes boundedness/curvature assumptions, then tailors inference methods for this setup. These inference methods look very different from simply averaging AIPW-type scores; for example, plrd solves a convex optimization problem.

If you want to apply lm/rd forest and retain inferential guarantees, an appropriate approach would be to use it to discover potential subgroups with HTEs, which you validate (on a held out test set) with an RD inference method like above, such as plrd / RDHonest / rdrobust. See #1259 (comment)