I’ve been thinking something through, but perhaps it is a nonsense, so I’d like some thoughts if possible please. I have some series of data that I wish to find the correlation matrix for, but I would also like to apply to hierarchical modelling to it. The data can be assumed to be given by a mult…

@spinkney Is fast and looks fancy but the priors over bivariate correlations differ quite a lot depending on the column index. R code showing this is below – passing in a vector of 1’s results in different correlations in each column. @mike-lawrence It might be nice for some situations, but doesn’t…

[image] Charles_Driver: Is fast and looks fancy but the priors over bivariate correlations differ quite a lot depending on the column index. R code showing this is below – passing in a vector of 1’s results in different correlations in each column. It’s guaranteeing PSD so it will almost sure…

@spinkney Well, the LKJ approach and the approach I first posted (ie years ago now) both guarantee PSD and don’t differ by column. My ‘semi fix’ also only weakly differs by column, and allows easy hierarchy with decent sampling / optimizing behaviour. The example code I posted is not just about the …

[image] Charles_Driver: but doesn’t work when you actually need a correlation matrix (as when using it for integration or non-centered parameterizations), and I’ll have to give some further thought on how this can be incorporated mid-hierarchy while permitting non-centered parameterization of…

Right, right. And now I get the issue more. Yea, I mean it guarantees it by this specific construction. This - as you said in your first post today - may take some magic to input a normal prior along each column to represent the same prior weight along each dimension.

@mike-lawrence re integration, I use subject specific covariance matrices in a kalman filtering setup, for one example. I also like to be able to fix certain values to zero or to certain others, which makes the parameter expansion approach also pretty tricky I think! Oh, and I doubt you can optimize…

On further consideration, it’s definitely trivial to achieve the shift/scaling associated with a non-centered parameterization, where scaling I understand is the core benefit of NP over CP generally (to avoid the funnel). I’m still mulling on whether the de-correlation of the typical multivariate NP…

Ok, so I flipped the problem a bit and I think this works. Let’s get a PD matrix that is as close to possible to the correlations you want. functions{ matrix angle_vec2mat (vector angle, int K) { int N = num_elements(angle); matrix[K, K] mat = add_diag(identity_matrix(K), rep_vector(-1, K…

hah ok so some kind of ‘nearest pos def’ hack. Seems a little wild but I’ll think about it!

Ok, inspired by @spinkney The idea is that you can just use a uniform LKJ_cholesky. Therefore, we really only use it to get a 1) cholesky for a 2) PSD matrix, uniformly distributed across all permissible PSD matrices. As cor matrices grow, the PSD constraint forces the volume of permissible soluti…

Hierarchical Correlation?

Modeling

mike-lawrence April 1, 2021, 5:36pm 35

Is there a succinct way to express the generative process for this solution?

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Hierarchical Correlation?

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