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...
(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!
