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.