[R] how to incorporate prior base probabilities into binomial glmm

[sprocket]

Hi,

I am modeling a gen linear mixed model with binomial repeated measures
responses (y=cbind(correct/not correct)) of some individuals (id).
I have a 2X2 design (effort and costs) and another continuous independent
variable (scr). This will lead to something like this:

mod.1<-lmer(y~effort+costs+scr+(1|id),family=binomial)
 so far so good. In my experiment the probability to score a correct depends
also on a probability based on random choice. Short example: Individual 1
has to choose 5 times before a correct can happen in the high effort
condition while in the low effort condition Ind 1 only has to choose 3
times. So there is a different probability associated to the low and high
effort condition that an individual will choose correct.
How can I incorporate this into a model or does anybody know of paper where
a similar case has occurred?

Ulf

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