This question is about CJS models and link functions.
I have been reading chapters 4 and 6 about link functions and design matrices and it is my understanding that with the identity design matrix, you usually use the identity link function or log link function. I also read that in this particular situation the parameters will not be constrained to [0,1].
My question is, is there anything stopping me from using a sin or logit link function with an identity design matrix? (I want the parameters to be constrained to [0,1]). Is it because the parameters may not be esteemable close to either 0 or 1 boundaries?
I ran the same CJS model using sin, logit, and identity link functions and got the same results except for the last phi and p parameters at the end.