2/ While the critique is intriguing, it is fundamentally flawed for three reasons. (1) the causal estimand & ID assumptions are not clearly defined. Most applied research focuses on estimating the CME, whereas the critique centers on CAPE, an estimand rarely used in applied work. - ThreadSky

2/ While the critique is intriguing, it is fundamentally flawed for three reasons. (1) the causal estimand & ID assumptions are not clearly defined.

Most applied research focuses on estimating the CME, whereas the critique centers on CAPE, an estimand rarely used in applied work.

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yiqingxu.bsky.social•15 days ago

3/ The critique compares the estimated CME to the wrong benchmark, leading to misleading conclusions. For example, in its simulation, the benchmark CME is not *zero* (as incorrectly stated) but increases with the moderator X because X and the treatment D are positively correlated.

yiqingxu.bsky.social•15 days ago

4/ (2) We show that the kernel estimator accurately recovers the true CME in the scenarios presented in the critique. The binning estimator, as a diagnostic tool, also performs reasonably well.

yiqingxu.bsky.social•15 days ago

5/ (3) We review recent advancements in the causal inference literature and highlight doubly robust and double/debiased machine learning estimators as appealing strategies for estimating the CME. Most of these methods are already supported by the *interflex* package in R.

yiqingxu.bsky.social•15 days ago

6/ In contrast, Simonsohn’s proposed implementation of GAM is not well suited for estimating the CME. The method estimates the CAPE given a specific value of the treatment D = d, and we show that the estimated CAPE varies depending on the choice of d.

yiqingxu.bsky.social•15 days ago

7/ Based on the discussion, we propose a set of recommendations, starting from clearly stating the quantity of interest and the key ID & modeling assumptions.

We provide software support for various estimation strategies: https://yiqingxu.org/packages/interflex/

yiqingxu.bsky.social•15 days ago

8/ Finally, we thank Professor Simonsohn for his thoughtful critique, which brings renewed attention to the estimation and testing of conditional relationships.

w/ Jens Hainmueller, Jiehan Liu, Ziyi Liu & Jonathan Mummolo

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