Thanks for linking the paper! I haven’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 code…), 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 don’t do that.
Regarding the factor part: What they do might work in a Gibbs sampling scheme, but you’d need to put a lot more effort in it with HMC (or NUTS). There is literature about identification restriction, but they don’t really discuss that. The multi-modality issues would not work out fine in Stan…
They rely on the Bayesian Lasso for “model search” (and partly identification…?). I could see that this make sense if you’re interested in MAPs, but for full Bayes the “Baysian Lasso” is not really doing selection, right? You could maybe think about using some Horseshoe variant, but I’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 couldn’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 “open”).
What’s your take on this paper?