This is just a sum-up of what we should do when we try to estimate the group-level variances and correlations but the software failed to do so. As a R and lmer() user, I found this happens often.
If this is the case, there are three potential problems:
(1) sd is 0
(2) some correlations are -1 or 1
(3) covariance matrix is singular
If the problem is of (1), then we might as well forget about the group level.
If the probem is of (2) and (3), we can rescale the X's so that the correlation between intercepts and slopes will be altered. For instance,
y = a + bx --> y = a + bz where z = x - x.bar
Nonetheless, in the end day, as Andy suggests, we should stick priors to estimating group-level variances and correlations. This ensures computational stability.
15 hours ago