Gamma model with log link

[Miracle]

Dear all.

Wish you all well.

My apoloy that this's not a SAS question.

Can someone please englighten me on why log link but not others is used for Gamma models? What's the underlying theory?

Thank you very much.

[Ksharp]

Because Gamma they are all positive value , use LOG() to map it into (- infinite ,+ infinite) .

[StatDave]

Actually, the canonical link is the reciprocal and this is, in fact, the default link in PROC GENMOD when you specify the DIST=GAMMA option without the LINK= option.  But the log link is the one most commonly used.  The canonical link is the link function that naturally occurs when the distribution is written in the general exponential family form that is shown in the "Details: Generalized Linear Models Theory" section of the GENMOD or GLIMMIX documentation.  More explanation can be found in a reference text like McCullagh and Nelder's Generalized Linear Models book.

[Miracle]

Dear Xia and Dave,

Thank you both for your reply.

I think I need to do some further readings on it.