I am working through the following paper and am wondering about the link function considered there. I am referring to Definition 7 and Example 8 in https://arxiv.org/pdf/1809.08818.pdf.
- Why is it necessary or useful for a link function to be increasing, even strictly increasing?
- I think I understand that Example 8 satisfies those conditions in definition 7. After some research by reading through other paper, it seems example 8 is a commonly used link function. Why should one use that one especially and not another one?
If I don't get the concept of link functions totally wrong, the link functions in the above paper are in principal those described on Wikipedia https://en.wikipedia.org/wiki/Generalized_linear_model#Link_function Why not use one of the link functions listed there instead?
So, you see, it may be that I do not have a deep understanding of link functions yet. Maybe someone can give me some advise and answer my questions?