Florian Pargent
florianpargent.bsky.social
Florian Pargent
@florianpargent.bsky.social
Psychologist and statistician at LMU Munich.

https://florianpargent.github.io/
I do not know any literature that handles that exact case. Before I did the simulation, it was not really obvious to me what would happen.
November 25, 2025 at 1:55 PM
In the extended example, it is often better to control only for measurement-invariant indicators, but not always. If you find it interesting, you can reopen the comments on your blog, and I will also post the link there.
November 25, 2025 at 7:06 AM
I know I'm a little late, but I was inspired to look at your example from the perspective of measurement invariance. I extended your scenario so that one measure of the confounder is also influenced by the treatment:

florianpargent.github.io/posts/003_mi...
If you have two measures of the same confounder, it might be better to only control for the measurement-invariant one. – Florian Pargent
Response to ‘The 100% CI’ blog post: ‘If you have two measures of the same confounder, you can just include both of them in your regression model.’
florianpargent.github.io
November 25, 2025 at 7:06 AM