[R] lme4 and incomplete block design

[Christian Lerch]

Dear list members,

I try to simulate an incomplete block design in which every participants 
receives 3 out of 4 possible treatment. The outcome in binary.

Assigning a binary outcome to the BIB or PBIB dataset of the package 
SASmixed gives the appropriate output.
With the code below, fixed treatment estimates are not given for each of 
the 4 possible treatments, instead a kind of summary measure(?) for 
'treatment' is given.

block<-rep(1:24,each=3)
treatment<-c(1, 2, 3, 2, 1, 4, 3, 4, 1, 4, 3, 2, 1, 3, 4, 2, 4, 3, 3, 1, 
2, 4, 2, 1, 1, 4, 2, 2, 3, 1, 3, 2, 4, 4, 1, 3, 1, 2, 3, 2, 1, 4, 3, 4, 
1, 4, 3, 2, 1, 3, 4, 2, 4, 3, 3, 1, 2, 4, 2, 1, 1, 4, 2, 2, 3, 1, 3, 2, 
4, 4, 1, 3)
outcome<-c(0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 
0, 0, 1, 0)
data<-data.frame(block,treatment,outcome)
lmer(outcome~treatment +(1|block), family=binomial, data=data)

Is this a problem with the recovery of interblock estimates? Are there 
special rules how incomplete block designs should look like to enable 
this recovery?

Any help is appreciated!

Regards,
Christian