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The link function is ?(?). However, both are in the form of a negative reciprocal in this case, since the negative of the reciprocal is its own inverse-function.

"The canonical link of Gamma GLM is g(x)=1/x is often not very practical. Log-link is more appropriated in most cases." One reason I can think of is that log-link makes sure ?, the mean, is always greater than zero.

Canonical Link Normal: identity link g(µi) = µi or simply write g(µ) = µ (same as below). . Poisson: log link g(µ) = log(µ). Gamma: negative inverse link g(µ) = ?1/µ.

The log-link would always be the first choice for a gamma glm because it transforms the expected values to an unconstrained linear predictor on the whole real line. A sqrt link is almost never defensible.

A link function transforms the probabilities of the levels of a categorical response variable to a continuous scale that is unbounded. Once the transformation is complete, the relationship between the predictors and the response can be modeled with linear regression.

Choosing a Link Function To choose a link function, it is helpful to examine the distribution of values for the outcome variable. ... Select the Bar gallery and choose Simple Bar. In the Element Properties tab, select Percentage as the statistic in the Statistics group.

For the linear regression model, the link function is called the identity link function, because no transformation is needed to get from the linear regression parameters on the right-hand side of the equation to the normal distribution.

The default link for Gamma() is ?inverse?. Let's try that and see how the output compares to the previous model. The dispersion parameter and residual deviance are identical, however the intercept coefficient is different. To get the estimated mean on the original scale we have to take the inverse, or the reciprocal.

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