Link function

A link function connects the response mean to the linear predictor through $g({\mu }_i)={\eta }_i$.

The logit link maps a mean probability to its log odds: $g(p)=\log [p/(1-p)]$, $0<p<1$. Its inverse is $p=(1+e^{-\eta }{)}^{-1}$, used in logistic regression.

The logarithmic link maps a positive mean to $\log \mu$. It is the Poisson canonical link.