Generalized logit and inverse logit function

Compute generalized logit and generalized inverse logit functions.

logit(x, min = 0, max = 1)
inv.logit(x, min = 0, max = 1)

Arguments

x

value(s) to be transformed

min

Lower end of logit interval

max

Upper end of logit interval

Details

The generalized logit function takes values on [min, max] and transforms them to span [-Inf,Inf] it is defined as:

$$y = log(\frac{p}{(1-p)})$$

where

$$p=\frac{(x-min)}{(max-min)}$$

The generized inverse logit function provides the inverse transformation:

$$x = p' (max-min) + min$$

where

$$p'=\frac{exp(y)}{(1+exp(y))}$$

Value

Transformed value(s).

Author

Gregory R. Warnes <greg@warnes.net>

Examples

if (FALSE) {
  x <- seq(0,10, by=0.25)
  xt <- logit(x, min=0, max=10)
  cbind(x,xt)

  y <- inv.logit(xt, min=0, max=10)
  cbind(x,xt,y)  
}