How to specify prior for within-study correlation?

Modeling
, , ,
1

I am working on a model as the one indicated here based on Burke et al 2016.

image

Let’s suppose that I use the following or similar brms specification:

res <- brm(yi ~ outcome - 1 + (outcome - 1 | trial), data = dat, autocor = fcor(V))

Let’s assume that I have data on V: a fixed value of s_{i} exists for each i, but \rho_{w_{i}} is available as a distribution of likely values, with location (i.e., concentrates around) 0.5. Now, I can use this value of 0.5 in V via fcor:

V = vcalc(vi, cluster=author, type=outcome, rho=0.5, data=dat)

But I would like to take into account the full distribution and variability of \rho_{w_{i}}, for example by specifying an informative prior on \rho_{w_{i}} based on external sources of data.

Since \rho are skewed to the right and mostly around 0.5 (not symmetric around 0), I found that using the approach recommended here (i.e., LKJ prior) perhaps might not be straightforward.

How can I specify a prior on \rho skewed to the right around 0.5 in brms?

Edit: I found that similar questions have been posted here and there has been some debate elsewhere:

  1. Why LKJ prior for correlation between random effects? Can we set asymmetrical priors? e.g. nonnegative;

  2. Underestimating correlation coefficients with LKJ prior;

  3. Informative priors for correlation matrices: An easy approach | Stephen R. Martin, PhD;

  4. Prior distributions for covariance matrices | Statistical Modeling, Causal Inference, and Social Science.

So perhaps my question would be: Is there any substantive progress on this matter? How can these solutions be implemented in brms?

Thanks.

1 Like
2

Great question. Looking forward for upcoming replies.

1 Like