How to estimate the standard error of every single random intercept in a mixed linear model?

Dear all,


I am running a mixed linear model with group (a_i) as random intercept:


y_ij=mu + a_i + e_ij


By using lmer() function, the model outputs an estimated variance of a_i (i.e. var_hat(a)), and it is the sum of (1) the variance of the estimated group mean (i.e. between group variance) and (2) the sum of variance for each estimated group mean a_i_hat,   (i.e. sum of within group variance).


for (1) I can compute it as var(ranef(model)$group). However, I dont know how to compute (2), which is the SE of the estimated random intercept for each group. I know that using se.ranef() function in arm package can help me to extract such variance. But I would like to know how these variance are computed? it's relations to residuals and number of observations per group?


Thanks


 Chen