I am trying to estimate a latent factor model. I looked at the examples here by RIck Farouni and here by Joseph Sakaya (which is based on the paper by Bishop 1999).
The problem is that in both examples I often get different factor loadings when reordering the variables in the data matrix. I looked around and found some work addressing this issue in the Bayesian context (e.g. here by Chan et al), but I don’t think I would understand the theoretical work well enough to implement it myself in Stan.
Does anyone know how to do latent factor models in Stan such that the factor loadings are invariant to the order of the variables in the data matrix?
Basically what I want is a latent factor model where the associations between the variables X and the factors F remain the same after changing the order of the variables. I am not worried about permutation of the signs (i.e. X1(+),X2(-) → F vs X1(+),X2(-) → F) or the ordering of the factors (i.e. X1,X2 → F1 and X3,X4 → F2 vs X1,X2 → F2 and X2,X3 → F1) being affected by the ordering of the variables.
Thank you very much for your help, even if it means that this is not yet possible or implemented in Stan.