Link Function

A link function connects the mean of the response distribution to a linear predictor. In practice, this is typically the expected value of the distribution.

For example, suppose we had $\lambda$ which is the rate parameter for a Poisson distribution.

Suppose $\lambda =(\beta x{)}^2$

Then our Link Function becomes $\sqrt{\lambda }(1)$ $⟺$ $\beta x(2)$

Note that (2) must be Linear in our Link Function