% $Id: logit.Rd 1695 2013-07-05 23:33:15Z warnes $
%
\name{logit}
\alias{logit}
\alias{inv.logit}
\title{Generalized logit and inverse logit function}
\description{
  Compute generalized logit and generalized inverse logit functions.
}
\usage{
logit(x, min = 0, max = 1)
inv.logit(x, min = 0, max = 1)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
  \item{x}{value(s) to be transformed}
  \item{min}{Lower end of logit interval}
  \item{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:

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

  where
    
    \deqn{p=\frac{(x-min)}{(max-min)}}{p=(x-min)/(max-min)}

  The generized inverse logit function provides the inverse
  transformation:
    
    \deqn{x = p' (max-min) + min}{x = p * (max-min) + min}

  where

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


}
\value{
  Transformed value(s).
}
\author{ Gregory R. Warnes \email{greg@warnes.net} }
\seealso{ \code{\link[car]{logit}} }
\examples{

  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)  

}
\keyword{math}
