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% File src/library/stats/man/SSlogis.Rd
% Part of the R package, https://www.R-project.org
% Copyright 1995-2017 R Core Team
% Distributed under GPL 2 or later

\name{SSlogis}
\title{Self-Starting \code{nls} 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}.   In \R 3.4.2 and earlier, that
  init function failed when \code{min(input)} was exactly zero.
}
\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{\enc{José}{Jose} Pinheiro and Douglas Bates}
\seealso{\code{\link{nls}}, \code{\link{selfStart}}
}
\examples{\donttest{
Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
SSlogis(Chick.1$Time, 368, 14, 6)  # response only
local({
  Asym <- 368; xmid <- 14; scal <- 6
  SSlogis(Chick.1$Time, Asym, xmid, scal) # response _and_ gradient
})
getInitial(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
## Initial values are in fact the converged one here, "Number of iter...: 0" :
fm1 <- nls(weight ~ SSlogis(Time, Asym, xmid, scal), data = Chick.1)
summary(fm1)
## but are slightly improved here:
fm2 <- update(fm1, control=nls.control(tol = 1e-9, warnOnly=TRUE), trace = TRUE)
all.equal(coef(fm1), coef(fm2)) # "Mean relative difference: 9.6e-6"
str(fm2$convInfo) # 3 iterations
}%donttest

dwlg1 <- data.frame(Prop = c(rep(0,5), 2, 5, rep(9, 9)), end = 1:16)
iPar <- getInitial(Prop ~ SSlogis(end, Asym, xmid, scal), data = dwlg1)
## failed in R <= 3.4.2 (because of the '0's in 'Prop')
stopifnot(all.equal(tolerance = 1e-6,
   iPar, c(Asym = 9.0678, xmid = 6.79331, scal = 0.499934)))

## Visualize the SSlogis()  model  parametrization :
  xx <- seq(-0.75, 5, by=1/32)
  yy <- 5 / (1 + exp((2-xx)/0.6)) # == SSlogis(xx, *):
  stopifnot( all.equal(yy, SSlogis(xx, Asym = 5, xmid = 2, scal = 0.6)) )
  require(graphics)
  op <- par(mar = c(0.5, 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")
  mtext(quote(list(phi[1] == "Asym", phi[2] == "xmid", phi[3] == "scal")))
  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 = 3)
  arrows(-0.8, c(2.1, 2.9),
         -0.8, c(0,   5  ), length = 0.1, angle = 25)
  text  (-0.8, 2.5, quote(phi[1]))
  segments(c(2,2.6,2.6), c(0,  2.5,3.5),   # NB.  SSlogis(x = xmid = 2) = 2.5
           c(2,2.6,2  ), c(2.5,3.5,2.5), lty = 2, lwd = 0.75)
  text(2, -.1, quote(phi[2]))
  arrows(c(2.2, 2.4), 2.5,
         c(2.0, 2.6), 2.5, length = 0.08, angle = 25)
  text(      2.3,     2.5, quote(phi[3])); text(2.7, 3, "1")
  par(op)
}
\keyword{models}