I’m working on a model with a nested hierarchy and it’s straightforward to apply partial-pooling over things like location and scale parameters, but is there a way to apply the partial-pooling concept to correlation matrices too? I’m guessing it would actually have to be implemented in terms of cova…

There has been some success in situations like this if you make the relevant correlation matrix a convex combination of a global correlation matrix and a deviation correlation matrix and estimate the weight on the global correlation matrix.

[image] Hierarchical Correlation? Modeling It makes sense but it requires some thought to get a sensible prior. You can see a solution I’ve used on page 10 here: https://www.researchgate.net/publication/324093594_Hierarchical_Bayesian_Continuous_Time_Dynamic_Modeling …

Posting here because it seems like my question is essentially the same, and there might have been updates in the year since this topic went cold.Is there an established way to deal with correlation matrices in nested hierarchical models? Alternatively, what are the pros and cons of the different pos…

The main update from my side is a) the approach in the paper ‘works’ but turns out to have local minima issues in higher dimensions. b) to get around this I rolled a complete hack job that looks horrendous and has no theoretical justification but produces clean results on all the tests I could imagi…

Thanks a lot! I’ll definitely try and implement that.

[image] BenH: Is there an established way to deal with correlation matrices in nested hierarchical models? I’d speculate that it is usually better to form hierarchical estimates of covariance matrices and calculate correlations only for presentational purposes, because pooling correlations ba…

[image] rmac: If in some subgroup there is little evidence of variation in one variable then it’s covariance estimates within that subgroup will be small Are you not confusing variances and covariances here?

[image] mike-lawrence: Are you not confusing variances and covariances here? I don’t think I’m making exactly that mistake because I don’t think we can have evidence for covariance without also having evidence for variance. However, I do rather regret making these comments without first runn…

Partial-pooling of correlation (or covariance) matrices?

Modeling

Charles_Driver October 8, 2020, 10:33am 3

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Partial-pooling of correlation (or covariance) matrices?

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