I'm not sure what you mean by "in my case the only one link that seems correct is the link=identity"... as you say, the default link=logit is the typical (and canonical) link most used with the binomial distribution. If you have seen someone use the identity link with the binomial distribution and are wondering why, it is probably because they think they need to do that to estimate differences of population probabilities. With the default logit link, using the DIFF option in the LSMEANS statement produces differences in log odds (logits) rather than differences in probabilities. So, some might use the identity link as a way to fix that. But, as you probably know, the identity link does not ensure that the predicted values will by valid probabilities. That is what the logit link ensures. However, you can easily fit a logistic model, using the logit link, and still estimate differences on the probability scale as shown in this note. Additionally, some want to estimate the so-called "difference in difference" on the probability scale and that is illustrated in this note.
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