[R-sig-ME] some questions about "lmer" in GLMM

[David Duffy]

On Tue, 8 May 2012, Maddie Wang wrote:

Hi.

> 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)).

I'm having trouble understanding your setup.  Why is b3 4X4 - are these 
crossed indicator variables with 3,3,4 levels?  And if so, what design and 
how much data?  Are the taus prespecified somehow?

Cheers, David Duffy.