Horseshoe priors and random slope/intercept regressions

I’m interested in using the horseshoe prior (or the related hierarchical-shrinkage family of priors) for regression coefficients of a traditional multilevel regression (e.g., random slopes/intercepts). Horseshoe priors are similar to lasso and other regularization techniques, but have been found to have better performance in many situations. A regression coefficient βi, where i{1,D} predictors, has a horseshoe prior if its standard deviation is the product of a local (λi) and global (τ) scaling parameter.

I am uncertain as to the best way to expand this to a random intercept framework. For example, group j‘s ith coefficient is often normally distributed around a group-level mean (γi) with a group level standard deviation (σi).


This tends to shrink estimates of βi,j towards γi based on the average dispersion around the coefficient mean. However, if only a small number of groups are substantially different from the mean, I’m concerned that the predictive or explanatory ability of the model may decrease. If I wanted to add a horseshoe prior to these coefficients, would it be appropriate to give each group’s coefficient it’s own independent λ?


Would it be better for the λi,j‘s to have an extra level of hierarchy that controls for dispersion around γi?


I’ve played around with modeling some of these options in Stan, but I would appreciate thoughts or advice on whether or not these formulations make statistical sense.


Source : Link , Question Author : C.R. Peterson , Answer Author : Community

Leave a Comment