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For a project, we have been trying to fit different models. When we used a Poisson regression, so a glm with a Poisson family, initially our fit was quite bad. But once we used the identity link instead of the canonical one, results were very promising. My question is, are we entitled to use the link we prefer? Why? I'm asking it because we found out by trials that the identity function gives out a good fit, but how can we justify it?

kjetil b halvorsen
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Davide Trono
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    look through this search – kjetil b halvorsen Jan 30 '21 at 19:34
  • Thank you for the suggestion. Do you know if there's any text I can look forward abou such topics? – Davide Trono Jan 30 '21 at 22:15
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    Many advanced texts about generalized linear models should have information ... but I have not one in particular. If you can augment your post with context, and goals of the analysis we can find out what link function you need. – kjetil b halvorsen Jan 30 '21 at 22:27
  • We are modelling data about covid infections in Italy. In particular we are modelling new intensive care cases, so we thought a Poisson reg could be reasonable. The canonical link didn't give us good results whereas the identity function was quite an improvement, so now I'm searching for theoretical reasons to explain why it is okay to use such link and why it gives a better fit. – Davide Trono Jan 30 '21 at 23:20
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    Hardin: Generalized Linear Models and Extensions : Fourth Edition is very detailed and seems to give a better case-by-case coverage of varios link functions than other books. See also https://stats.stackexchange.com/questions/142338/goodness-of-fit-and-which-model-to-choose-linear-regression-or-poisson/142353#142353 – kjetil b halvorsen Jan 31 '21 at 20:09

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