# GLM difference between the links [duplicate]

I'd be very grateful if someone could help me understand the idea behind link functions:

I know that the idea is that we want to map the mean to the $\eta$-vector. Also, I know that the canonical link is the one that makes $\eta=\theta$, where $\theta$ is the parameter.

But why/when do we want to choose the canonical link? When do we have to consider other alternatives?

Thanks a lot!

• I think you will find the information you need in the linked thread. Please read it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. – gung - Reinstate Monica Apr 24 '18 at 12:59