Hello again,
I am back to working on this project and have become more familiar with shrinkage priors. I am considering using the R2D2 prior (as suggested by avehtari) on b, as it allows me to retain all predictors. I am using the default mean and precision of the Beta prior (also suggested in Yanchenko et al. 2024 - The R2D2 Prior for Generalized Linear Mixed Models), but I slightly increased the concentration to imply less shrinkage.
prior(R2D2(mean_R2 = 0.5, prec_R2 = 2, cons_D2 = 1), class = "b")
However, my predictors belong to different classes (numerical [standardized], categorical, and ordinal modeled as monotonic mo()) . I came across R2D2M2 prior and monotonic predictors - #3 by Xavier_La_Rochelle but I can’t dummy-code all my categorical/ordinal covariates (for convergence purpose).
My questions :
(1) Can I still interpret coefficients and conditional effects, given that not all predictors are on the same scale?
(2) If yes, is there a general guideline on how to choose the concentration value?
(3) Regarding the interpretation of the results (see below), some coefficients are centered on 0 (b_nominalA_1) which I interpret as shrunk and thus not meaningful. However, the coefficients that seem to have an impact (b_nominalA_2 and A3) are still slightly shrunk toward 0. I would have expected the shrinkage to either lead to coefficients centered on 0 (strong shrinkage) or leave them largely unaffected (slighty encompassing 0 to far from 0). Could someone clarify what I am missing here?
Thanks!