Hi Stan folk,

I have a question about the covariance prior in stanarm. I’m running the following model: stan_lmer(Y~K+(1|Subject)), where Y is continuous, K represents up to 20 discrete, independent treatment groups that I’m screening, and Subject represents the fact that I test the treatment on multiple subjects. I want to find coefficients for each group as part of a screening study to figure out which Ks will give me the lowest Y values on the population, and then expand my study to get more data on the most promising K candidates. I think I have this running pretty well, and as far as I can tell the default priors seem to be working reasonably well. However, in reality, the K’s are not actually independent: each K consists of a combination of 5 or so design choices covering a relatively large space. It might be cumbersome to model this space explicitly, especially since some of these factors are probably non-linear, and my dataset is small. However, I do have scientific intuitions about what some of the relationships will be, for example I believe that K1 is likely to be more “similar” to K8 than it is to K3. Is there a way to express these intuitions in the covariance prior to potentially improve my estimates? Do you know off hand if this can done within stan_lmer or does this kind of thing require full-on stan?