Thank you @dingdingpeng.the100.ci, very helpful! 😀

But yes, your point about inferring that X --> Y is zero seems correct to me!

Hence why I am now wondering if I can use Z as an instrumental variable to estimate the causal effect of X on Y.

For context, this is a survey-based experimental design.

We designed Z as a way to exogenously manipulate X. We found support for that in a pilot study - there was a total effect of Z on X.

In our main study, we found no total effect of Z on Y. In a larger path model, we also found no direct effect of Z on Y - but found an indirect effect through X.

Although Z could in theory influence Y, our experiment showed no total/direct effect of Z on Y. Can we then use this null result to justify using Z as an instrumental variable in a follow-up analysis? @rmcelreath.bsky.social @dominikdeffner.bsky.social @dingdingpeng.the100.ci

YES! So happy to see this finally out. I can't wait to read it. Congrats!

🎵 zotero, zo-te-ro... zotero, zo-te-ro!

Not technically misuse, but I read a paper recently where they wrote "p < 0.000000000001". It's not just significant, but really _really_ significant!

I had no idea that's where it came from!

Yep. I'd be curious to see what you come up with! This seems like a nice case of a biologically-inspired model where you can get immediate feedback on whether it makes good predictions or not.

Right. You could also see it the other way though: I set the amount of reps and see the max weight I can lift. Then what's the max weight when I set reps to 1?

Cool question! Wouldn't you want to do it the other way round though? And allow for a non-linear effect? Something like:

maxWeight ~ LogNormal(mu, sigma)
mu = a + b*log(reps)

Then exp(a) will give you your expected one rep max.

It is indeed! Thank you for your work on the package. I am now just realising that we did not cite the package in the paper! So sorry! I will do better next time.