What's the difference between terms 'link function' and 'canonical link function'? Also, are there any (theoretical) advantages of using one over the other?

e.g. A binary response variable can be modeled using many link functions such as 'logit', 'probit' etc. But, 'logit' here is considered the 'canonical' link.

What's the difference between terms 'link function' and 'canonical link function'? Also, are there any (theoretical) advantages of using one over the other?

For example, a binary response variable can be modeled using many link functions such as logit, probit, etc. But, logit here is considered the "canonical" link function.

What's the difference between terms 'link function' and 'canonical link function'?

e.g. A binary response variable can be modeled using many link functions such as 'logit', 'probit' etc. But, 'logit' here is considered the 'canonical' link.

What's the difference between terms 'link function' and 'canonical link function'? Also, are there any (theoretical) advantages of using one over the other?

e.g. A binary response variable can be modeled using many link functions such as 'logit', 'probit' etc. But, 'logit' here is considered the 'canonical' link.