% $Id: SSlogis.Rd,v 1.3.4.1 2001/08/07 14:05:15 ripley Exp $
\name{SSlogis}
\title{Logistic Model}
\usage{
SSlogis(input, Asym, xmid, scal)
}
\alias{SSlogis}
\arguments{
 \item{input}{a numeric vector of values at which to evaluate the model.}
 \item{Asym}{a numeric parameter representing the asymptote.}
 \item{xmid}{a numeric parameter representing the \code{x} value at the
   inflection point of the curve.  The value of \code{SSlogis} will be
   \code{Asym/2} at \code{xmid}.}
 \item{scal}{a numeric scale parameter on the \code{input} axis.}
}
\description{
  This \code{selfStart} model evaluates the logistic
  function and its gradient.  It has an \code{initial} attribute that
  creates initial estimates of the parameters \code{Asym},
  \code{xmid}, and \code{scal}.
}
\value{
  a numeric vector of the same length as \code{input}.  It is the value of
  the expression \code{Asym/(1+exp((xmid-input)/scal))}.  If all of
  the arguments \code{Asym}, \code{xmid}, and \code{scal} are
  names of objects the gradient matrix with respect to these names is attached as
  an attribute named \code{gradient}.
}
\author{Jose Pinheiro and Douglas Bates}
\seealso{\code{\link{nls}}, \code{\link{selfStart}}
}
\examples{
data( ChickWeight )
Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
SSlogis( Chick.1$Time, 368, 14, 6 )  # response only
Asym <- 368; xmid <- 14; scal <- 6
SSlogis( Chick.1$Time, Asym, xmid, scal ) # response and gradient
getInitial(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
## Initial values are in fact the converged values
fm1 <- nls(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
summary(fm1)
\testonly{
  xx <- seq(-0.5, 5, len = 101)
  yy <- 5 / ( 1 + exp((2-xx)))
  par(mar = c(0, 0, 3.5, 0))
  plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,6), xlim = c(-1, 5),
       xlab = "", ylab = "", lwd = 2,
       main = "Parameters in the SSlogis model")
  usr <- par("usr")
  arrows(usr[1], 0, usr[2], 0, length = 0.1, angle = 25)
  arrows(0, usr[3], 0, usr[4], length = 0.1, angle = 25)
  text(usr[2] - 0.2, 0.1, "x", adj = c(1, 0))
  text(-0.1, usr[4], "y", adj = c(1, 1))
  abline(h = 5, lty = 2, lwd = 0)
  arrows(-0.8, 2.1, -0.8, 0, length = 0.1, angle = 25)
  arrows(-0.8, 2.9, -0.8, 5, length = 0.1, angle = 25)
  text(-0.8, 2.5, expression(phi[1]), adj = c(0.5, 0.5))
  segments(2, 0, 2, 4.0, lty = 2, lwd = 0.75)
  text(2, 4.0, expression(phi[2]), adj = c(0.5, 0))
  segments(3, 5/(1+exp(-1)) + 0.025, 3, 4.0, lty = 2, lwd = 0.75)
  arrows(2.3, 3.8, 2.0, 3.8, length = 0.08, angle = 25)
  arrows(2.7, 3.8, 3.0, 3.8, length = 0.08, angle = 25)
  text(2.5, 3.8, expression(phi[3]), adj = c(0.5, 0.5))
}
}
\keyword{models}
