- For all who use Bayesian hierarchical models, have a look at our new preprint, out now together with @linushof.bsky.social @nunobusch.bsky.social and @thorstenpachur.bsky.social osf.io/preprints/ps...
- If you’re estimating group-level means of constraint parameters, which are fitted with nonlinear transformations, beware that a common approach can produce biased estimates—especially with high individual variability. For constraint parameters, we often use nonlinear transformations...Sep 10, 2025 14:40
- (e.g. the standard normal CDF) and normal distributions to fit the group-level distribution. But we cannot simply apply the same transformation to the mean of the real-valued normal distribution to derive the group-level mean on the parameter scale! This ignores individual variability.
- The good news: We provide a simple, correct computation that accounts for this variability, ensuring accurate group-level inferences. This fix is crucial for reliable conclusions in all cognitive models with constrained parameters. Check out the details to improve your hierarchical analyses!
- Looks and reads great, I especially like the concise figure! This is an important issue which is often overlooked, so the contribution will be useful for many modelers. 👍
- Just a remark regarding "The same incorrect computation appears in implementations of latent-trait multinomial processing tree models": The issue has been mentioned in the literature (shorturl.at/Ajx0W), and the R package TreeBUGS has the function probitInverse as a solution (shorturl.at/mRp1S).
- Still, it is worthwile to have a paper elaborating on this in detail!
- Thanks for the kind words. Glad to see that people already account for this in some packages. Not sure whether it helps a lot, but using the direct computations instead of using numerical integration may still speed up things a bit (about 20 times on my machine)
- Unfortunately, for the variance on the probability scale, the speed up vanishes.
- That's interesting - thanks for comparing the methods and for letting me know! Analytical solutions are of course more elegant than numerical integration.
