Multilevel logistic regression using lmer vs glmmPQL vs. gllamm in Stata

Dear all,

I am trying to replicate some multilevel models with binary outcomes 
using R's "lmer" and "glmmPQL" and Stata's gllmm, respectively. 

The data can be found at <http://www.uni-koeln.de/~ahf34/xerop.dta>. 

The relevant Stata output can be found at  <http://www.uni-
koeln.de/~ahf34/stataoutput.txt>. First, you will find the 
unconditional model, i.e. no level1- or 2-predictor variables. The 
second model contains some level 1-predictor variables

My R file can be found at <http://www.uni-koeln.de/~ahf34/xerop.R>.

Beside the fact that there is a difference between the estimates of 
the intercept (unconditional model: R: -2.76459 and Stata: -2.698923) 
I am especially interested in the level 2 variance. 

In Stata the level 2 variance is about 1.03, while in R it is  4.68. 

Using glmmPQL from package MASS again gives different results for the 
level 2 variance component. What is meant by "Residual"? I thought 
the level 1 variance is fixed to (pi^2)/3.  

I am a beginner in multilevel modeling so I assume I made some 
mistake either in interpreting the output or specifying the models. 

I would appreciate any help.

Bernd