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I have several questions regarding the link function of generalized linear regression. I know how link function changes range of the distribution function's mean to the complete real line. But is that the only purpose of it? What is the negative inverse link for exponential distribution doing then ?

Also how exactly does the link function LINK the linear predictor and the mean of the distribution function? Why is that after using the link function, there's the linear relationship between the mean and the linear predictor? I've been searching around for awhile and still couldn't find a satisfying answer ... so can someone help please.

kjetil b halvorsen
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Eva Li
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  • This is very broad, you might be better off reading an introductory text on glm's. But see https://stats.stackexchange.com/questions/259683/understand-link-function-in-generalized-linear-model, https://stats.stackexchange.com/questions/63978/do-statisticians-assume-one-cant-over-water-a-plant-or-am-i-just-using-the-wro/64039#64039 and search this site. – kjetil b halvorsen Oct 31 '20 at 14:46

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