Im am pretty new using R and in particular trying to model BLUPs with Ime4 in R, how do I define a link function in a GLMM to relate the the proportion of a variable to a linear predictor β.
Thank you in advance.
Use the family option. You can specify the link function in the family name. See https://stat.ethz.ch/R-manual/R-devel/library/stats/html/family.html
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Thank You, I have to study a lot more to understand how to set a link function based on a variable.
I'm not certain I understand the question about a "link function based on a variable". If you give more details about the link you want to use folks may be able to help you more.
That being said, one example of a user-defined link based on an additional variable is the "logistic exposure" link. You can see an example in this RPub (see Method 2). It's also discussed in this CrossValidated answer.
This may or may not be relevant to what you are trying to do. 
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Thank you aosmith, you're very kind replying my question, I need to clarify some glmm concepts though. Will be back when I am sure what is a link function and how it can be defined in generalized linear mixed model.
Regards!