Hey @ignacio!

Thanks for linking the paper! I havenâ€™t used factor models in Stan, but thought this paper would give me an excuse to look into it.

I played around with it a bit. Tbh, I thought the paper could have been a bit clearer on some of the things (naming conventions, simulation codeâ€¦), but I guess they are still working on it.

I think the main point is that they just combine a multilevel regression with a factor structure. For model selection (and identification) they rely on the Bayesian Lasso, using the mixture of normals to re-parameterize the Laplace/DoubleExponentials.

The way they conceptualize the varying intercept/slopes (on the regressors) could have been better in my opinion. I guess it is conventional wisdom by now to use multivariate normal priors to model the correlations between intercepts and slopes (using cholseky decomposed correlation matrices for the non-centered parameterization). But they donâ€™t do that.

Regarding the factor part: What they do might work in a Gibbs sampling scheme, but youâ€™d need to put a lot more effort in it with HMC (or NUTS). There is literature about identification restriction, but they donâ€™t really discuss that. The multi-modality issues would not work out fine in Stanâ€¦

They rely on the Bayesian Lasso for â€śmodel searchâ€ť (and partly identificationâ€¦?). I could see that this make sense if youâ€™re interested in MAPs, but for full Bayes the â€śBaysian Lassoâ€ť is not really doing selection, right? You could maybe think about using some Horseshoe variant, but Iâ€™m afraid this would still be hard to fit.

They are not using any MCMC diagnostics, which is kind of disappointing. It says they are building an R package with the sample (built in C++), which I couldnâ€™t find with a quick google search. I think it would be much butter if they had tried to implement their model in a more general framework (like Stan, but really anything more â€śopenâ€ť).

Whatâ€™s your take on this paper?

Cheers,

Max