The R Book

Canonical Link Functions

The canonical link functions are the default options employed when a particular error structure is specified in the family directive in the model formula. Omission of a link directive means that the following settings are used:

You should try to memorize these canonical links and to understand why each is appropriate to its associated error distribution. Note that only gamma errors have a capital initial letter in R.

Choosing between using a link function (e.g. log link) and transforming the response variable (i.e. having log(y) as the response variable rather than y) takes a certain amount of experience. The decision is usually based on whether the variance is constant on the original scale of measurement. If the variance was constant, you would use a link function. If the variance increased with the mean, you would be more likely to log transform the response.