Recover correlation between random effects from posterior samples

Modeling
1

Dear all,

question: in a linear mixed effects model (LME, also known as hierarchical model), can the correlation coefficient between the random effects be recovered from the posterior samples?

Thanks to your previous help (here), I managed to fit a LME for the sleep study, with random intercept and slope for each subject ( Reaction ~ Days + (Days | Subject). In the STAN code (generated with the help of brms) the correlation between the random effects was explicitly modeled via the Cholesky decomposition, and the model fit gives a correlation coefficient between intercepts and slopes of about 0.09 [-0.48, 0.68].

Next, I tried to recover the correlation coefficient from the posterior samples. I was expecting to be able to recover the correlation coefficients accurately. However, the estimation I got is not correct and slightly (?) off (i.e., 0.10 [-0.28, 0.62]). They way I did was to compute the correlation between the intercepts and slopes across participants for each step in the MCMC trace.

Any ideas?

Thank you

2

Your way would match the print output if you had many, many draws from the posterior distribution, but it is a noisy measure of the correlation with only 18 subjects or whatever.

3

I understand, so in theory (let’s say with infinite samples) I can recover the correlation from the posterior samples. Thank you!