Dear All:
 
I have a question about lmer for GLMM that I cannot find an answer on-line for quite a bit time. Suppose the response y is from a binomial distribution. The GLMM can be written as logit(pi)=x*\beta+z1b1+z2b2+z3b3, where pi is the expectation of binomial proportion, \beta is the fixed coefficients, b1,b2 and b3 are three random effects, where b1 is from a multivariate normal MN(0, \tau1 * I_(3X3)), b2 is from a multivariate normal MN(0, \tau2 * I_(3X3)), and b3 is  from a multivariate normal MN(0, \tau3 * I_(4X4)). 
 
The question is how can I specify these three random effects in the statement since all of them have  multivariate normal distribution with variance-covariance structure as some number times an identity matrix?
 
Furthermore, how to get the conditional mean of random effects, , i.e., E(b1| y), E(b2| y), and E(b3| y) by lmer procedure?
 
 
Thanks so much in advance!
 
 Maddie Wang
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