aargh. "nb" should be "a" for each of the model formulae. This is not the source of 
the error. sorry for any confusion.

Simon.

> 
> fit <- glm(cbind(success, failure) ~ c + b + nb -1, 
> family=binomial, data=dat)
> 
> which works fine. I can also include the age factor, which 
> also seems to work ok:
> 
> fit2 <- glm(cbind(success, failure) ~ c + b + nb + 
> as.factor(age) -1, family=binomial, data=dat)
> 
> Now, since each rater performs ratings on each of the 3 
> treatment combinations, I was interested in including rater 
> as a random factor. My naive method was to use glmmPQL from 
> library MASS:
> 
> fit3 <- glmmPQL(cbind(success, failure) ~ c + b + nb -1, 
> random = ~1|rater, family=binomial, data=dat)
> 
> However, I get the following error:
> 
> iteration 1 
> Error in MEEM(object, conLin, control$niterEM) : 
>         Singularity in backsolve at level 0, block 1

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