Probit Link Function

Probit link uses standard normal distribution to transform target values, ideal for normally distributed targets.

One approach to transforming the range of a probability to the range minus infinity to infinity is to choose a probability distribution that is defined on that range and assign the distribution value that corresponds to the probability as the target value. For example, the probabilities, 0, 0.5 and 1.0 corresponds to the value -infinity, 0 and infinity in a standard normal distribution. An inverse cumulative distribution function is a function that determines the value that corresponds to a probability. In this approach, a user matches the particular probability distribution to assumptions regarding the distribution of the target. Users often find transformation of a target using the target's known associated distribution as natural. The probit link takes this approach, using the standard normal distribution. An example use case is an analysis of high blood pressure. Blood pressure is assumed to have a normal distribution.