[R] Canonical link for the GLM gamma model

[Serguei Kaniovski]

Hello!

When I estimate a glm gamma model using the canonical link (inverse), I 
get the opposite signs on almost all coefficients compared to the same 
model (i.e. with the same linear predictor) estimated using other suitable 
links (log, logit).

What confuses me is that most of sources quote the canonical link for the 
gamma model as 1/mu, but some quote -1/mu!

For example: 
http://support.sas.com/rnd/app/da/new/802ce/stat/chap5/sect19.htm

Which is the correct link, and can this explain the sign-flips I get in my 
models?

Thank you very much for your help / advice!
Serguei