Hi all, I have a multivariate GLM with many columns in both X and Y. I want the matrix of parameters (W) to be low-rank, so I’m representing it as a `transformed parameter`

that depends on `parameters`

U and V:

W = U * V’

However, I’m not sure what priors to put on U and V. I’d like to do something equivalent to

W ~ normal(0, sigma),

but I’d like some help with the absolute value of the determinant of the Jacobian matrix of the transform. Alternatively, if it’s nasty to compute, I’d be interested in alternative parameterizations that are easier to work with.

Thanks in advance for any assistance!