Editing Generalized linear model (section)

==== Probit link function as popular choice of inverse cumulative distribution function ====
Alternatively, the inverse of any continuous [[cumulative distribution function]] (CDF) can be used for the link since the CDF's range is <math>[0,1]</math>, the range of the binomial mean. The [[Normal distribution#Cumulative distribution function|normal CDF]] <math>\Phi</math> is a popular choice and yields the [[probit model]]. Its link is

:<math>g(p) = \Phi^{-1}(p).\,\!</math>

The reason for the use of the probit model is that a constant scaling of the input variable to a normal CDF (which can be absorbed through equivalent scaling of all of the parameters) yields a function that is practically identical to the logit function, but probit models are more tractable in some situations than logit models. (In a Bayesian setting in which normally distributed [[prior distribution]]s are placed on the parameters, the relationship between the normal priors and the normal CDF link function means that a [[probit model]] can be computed using [[Gibbs sampling]], while a logit model generally cannot.)