Here is the scenario. I have three very similarly collected datasets with very similar models. In fact, the model for 1 and 2 are identical. Dataset 3 contains all of the variables of 1 and 2, plus a few more.
I want to conduct an integrated data analysis across all datasets, in which all shared parameters across datasets are distributed according to a hierarchical prior. This is, in essence, a random effect model, on all shared parameters.
I have already estimated the models for each dataset individually, and merely wish to make a ‘mega model’ of sorts, with priors on shared parameters.
One of these parameters is the correlation matrix for some random effects.
Studies 1-2 have a cholesky corr matrix of dimension 6, and study 3 has a cholesky corr matrix of dimension 9.
Now, if all three studies had identically-sized corr matrices, then I would simply put a prior on each element of the cholesky corr matrix, and construct the respective cholesky corr matrices.
But because study 3 has a 9x9 (all of the previous cors, but a few new ones), I don’t think that would be appropriate, because the elements of a cholesky factorization changes with dimensionality (correct? or incorrect?).
Should I simply place priors on all of the shared raw correlations, then construct respective correlation matrices, rather than operating on the cholesky elements?