In nested multilevel models we model variability between experimental units within rather than across groups of interest, hence nested. In the simplest case one group is known a priori to have much lower variability between experimental units than another and estimating this variability across both …

Here’s why that Jacobian adjustment is needed when using s2z in the centered model. Let’s start at why the sqrt(N / (N - 1)) thing comes up and then what adding \sigma does. Why \sqrt{N / (N - 1)}? The sum-to-zero constraint is effectively pre-multiplying x by an orthogonal basis. The basis used i…

[image] lukaseamus: In nested multilevel models we model variability between experimental units within rather than across groups of interest, hence nested. The two terms of art are “hierarchical” for when things are properly nested (e.g., students in classes in schools in school districts in …

Thanks for the thorough reply @Bob_Carpenter ! [image] Bob_Carpenter: “hierarchical” for when things are properly nested … and “multilevel” when they’re not I did not know this. I always assumed the terms to be interchangeable. There seems to be some confusion on this, e.g. This results in …

[image] lukaseamus: I noticed that there is a Stan File option in the New File dropdown, but I thought it was only to be used with rstan. I would be grateful for an easy solution for cmdstanr in RStudio. It would definitely make my R code more readable. You can use the same files with cmdstan…

Not related to original post. But this info about RStudio using rstan to parse Stan files explains some odd things I’ve noticed for a while, like std_normal_lpdf() not getting highlighted “appropriately”. I am glad to know this now. Is this factoid publically documented anywhere? If not, should …

Hmm, I guess it’s not documented. It’s just that it’s always used rstan since way before cmdstanr existed, but you’re right that we should put this information somewhere. Where do you think would be a helpful place to document this? Maybe in the main vignette for cmdstanr? Somewhere else? If I reca…

You an also install rstan from the develop branch for reasonably up-to-date syntax highlighting.

Since using Stan files in RStudio was just an aside, I’d like move this thread back to its original question, which remains unresolved for me. I have now tried centred and non-centred sum-to-zero parameterisations for various likelihoods and data and the centred sum-to-zero parametrisation never sa…

In the centered zero sum case you’re doing z \sim \mathcal{N} \bigg(0, \sigma \sqrt{ \frac{N}{N - 1} } \bigg) z \in \mathbb{R}^N,\quad \text{subject to } \sum_{i=1}^N z_i = 0. The issue here is that both z and \sigma are parameters. The sum to zero constraint has a Jacobian correction of 0 b…

Not sure if the previous argument is right. As we have -N * log(sigma) from the N calls to the normal distribution. We add a log(sigma) and now we have (N - 1) * log(sigma). Now, it results in the same thing but is a bit clearer. We have a singular covariance on z from the sum to zero constraint a…

Proper use of sum_to_zero_vector in nested multilevel models

Modeling

ssp3nc3r May 24, 2025, 4:52pm 7

I think this is what your referring to: Rstudio Stan syntax checker is outdated

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Proper use of sum_to_zero_vector in nested multilevel models

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