I am a stats & R beginner and am trying to understand GLMs. I have a very basic question on the link function which is the following
If I understand correctly the mean of the response variable Y is getting mapped to eta through the link function g(.)
My question is, why the mean? Is it that we are calculating a single value, namely the mean of Yi's? Why not use the Yi's themselves? A related question to the above is, that if we consider linear regression (which is a special case of GLM with link=identity), the response variable is NOT mean(Yi), but Yi. But according to GLM theory we should be using mean(yi) for the link function mapping.
Sorry if the question is very basic, and thanks in advance.
I have gone through many enlightening posts such as Meaning of link functions (GLM)
but I couldn't find the answer, no doubt my limitation.