DescTools (version 0.99.19)

Logit: Generalized Logit and Inverse Logit Function

Description

Compute generalized logit and generalized inverse logit functions.

Usage

Logit(x, min = 0, max = 1)
LogitInv(x, min = 0, max = 1)

Arguments

x

value(s) to be transformed

min

lower end of logit interval

max

upper end of logit interval

Value

Transformed value(s).

Details

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

$$y = log\left (\frac{p}{1-p} \right ) \;\;\; \; \textup{where} \; \;\; p=\frac{x-min}{max-min}$$

The generalized inverse logit function provides the inverse transformation:

$$x = p' \cdot (max-min) + min \;\;\; \; \textup{where} \; \;\; p'=\frac{exp(y)}{1+exp(y)}$$

See Also

logit

Examples

  x <- seq(0,10, by=0.25)
  xt <- Logit(x, min=0, max=10)
  cbind(x,xt)

  y <- LogitInv(xt, min=0, max=10)
  cbind(x, xt, y)