I’m trying to fit a linear regression with the regularized horseshoe as the prior on my coefficients. n is a few hundred, p is around a thousand in my full dataset.

Here is a github repo documenting this attempt, including code, figures, and data. I’m using rstanarm and following Aki’s slides.

My trouble is that I don’t see the shrinkage that I expected. Oddly when I specify the prior on the coefficients as gaussian, the coefficients seem to shrink more to 0 with a few staying quite large. I think I’ve either made an error in my code, or maybe I’m expecting too much from the horseshoe prior.

I’m at the boundary of my knowledge and lack good intuition about what is happening, hence my post here. There is extreme correlation among predictors in my model and perhaps it’s difficult to pick the few “truly” non-zero coefficients. Any suggestions for how to continue would be much appreciated. I’d love to try this method out with our datasets.

I can also post code here too if that’s more helpful.

Thanks for your help.