The R Project SVN – R – Diff – /trunk/src/library/stats/man/SSfpl.Rd

 % File src/library/stats/man/SSfpl.Rd
 % Part of the R package, https://www.R-project.org
-% Copyright 1995-2010 R Core Team
+% Copyright 1995-2017 R Core Team
 % Distributed under GPL 2 or later
 \name{SSfpl}
-\encoding{UTF-8}
 \title{Self-Starting Nls Four-Parameter Logistic Model}
+\alias{SSfpl}
+\encoding{UTF-8}
 \usage{
 SSfpl(input, A, B, xmid, scal)
+}
-\alias{SSfpl}
 \arguments{
  \item{input}{a numeric vector of values at which to evaluate the model.}
  \item{A}{a numeric parameter representing the horizontal asymptote on
    the left side (very small values of \code{input}).}
  \item{B}{a numeric parameter representing the horizontal asymptote on
    midway between \code{A} and \code{B} at \code{xmid}.}
  \item{scal}{a numeric scale parameter on the \code{input} axis.}
+}
 \description{
   This \code{selfStart} model evaluates the four-parameter logistic
-  function and its gradient.  It has an \code{initial} attribute that
+  function and its gradient.  It has an \code{initial} attribute computing
-  will evaluate initial estimates of the parameters \code{A}, \code{B},
+  initial estimates of the parameters \code{A}, \code{B},
   \code{xmid}, and \code{scal} for a given set of data.
+}
 \value{
   a numeric vector of the same length as \code{input}.  It is the value of
   the expression \code{A+(B-A)/(1+exp((xmid-input)/scal))}.  If all of
 \seealso{\code{\link{nls}}, \code{\link{selfStart}}
+}
 \examples{
 Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
 SSfpl(Chick.1$Time, 13, 368, 14, 6)  # response only
+local({
-A <- 13; B <- 368; xmid <- 14; scal <- 6
+  A <- 13; B <- 368; xmid <- 14; scal <- 6
-SSfpl(Chick.1$Time, A, B, xmid, scal) # response and gradient
+  SSfpl(Chick.1$Time, A, B, xmid, scal) # response _and_ gradient
+})
 print(getInitial(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1),
       digits = 5)
 ## Initial values are in fact the converged values
 fm1 <- nls(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1)
 summary(fm1)
-\dontshow{
-require(graphics)
+## Visualizing the  SSfpl()  parametrization
   xx <- seq(-0.5, 5, len = 101)
-  yy <- 1 + 4 / ( 1 + exp((2-xx)))
+  yy <- 1 + 4 / (1 + exp((2-xx))) # == SSfpl(xx, *) :
+  stopifnot( all.equal(yy, SSfpl(xx, A = 1, B = 5, xmid = 2, scal = 1)) )
+  require(graphics)
-  par(mar = c(0, 0, 3.5, 0))
+  op <- 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 SSfpl model")
+  mtext(quote(list(phi[1] == "A", phi[2] == "B", phi[3] == "xmid", phi[4] == "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))
+  text(     -0.1, usr[4], "y", adj = c(1, 1))
-  abline(h = 5, lty = 2, lwd = 0)
+  abline(h = c(1, 5), lty = 3)
-  arrows(-0.8, 2.1, -0.8, 0, length = 0.1, angle = 25)
+  arrows(-0.8, c(2.1, 2.9),
-  arrows(-0.8, 2.9, -0.8, 5, length = 0.1, angle = 25)
+         -0.8, c(0,   5  ), length = 0.1, angle = 25)
-  text(-0.8, 2.5, expression(phi[1]), adj = c(0.5, 0.5))
+  text  (-0.8, 2.5, quote(phi[1]))
-  abline(h = 1, lty = 2, lwd = 0)
+  arrows(-0.3, c(1/4, 3/4),
-  arrows(-0.3, 0.25, -0.3, 0, length = 0.07, angle = 25)
+         -0.3, c(0,   1  ), length = 0.07, angle = 25)
-  arrows(-0.3, 0.75, -0.3, 1, length = 0.07, angle = 25)
+  text  (-0.3, 0.5, quote(phi[2]))
-  text(-0.3, 0.5, expression(phi[2]), adj = c(0.5, 0.5))
+  text(2, -.1, quote(phi[3]))
-  segments(2, 0, 2, 3.3, lty = 2, lwd = 0.75)
+  segments(c(2,3,3), c(0,3,4), # SSfpl(x = xmid = 2) = 3
-  text(2, 3.3, expression(phi[3]), adj = c(0.5, 0))
-  segments(3, 1+4/(1+exp(-1)) - 0.025, 3, 2.5, lty = 2, lwd = 0.75)
+           c(2,3,2), c(3,4,3),    lty = 2, lwd = 0.75)
-  arrows(2.3, 2.7, 2.0, 2.7, length = 0.08, angle = 25)
+  arrows(c(2.3, 2.7), 3,
-  arrows(2.7, 2.7, 3.0, 2.7, length = 0.08, angle = 25)
+         c(2.0, 3  ), 3, length = 0.08, angle = 25)
-  text(2.5, 2.7, expression(phi[4]), adj = c(0.5, 0.5))
+  text(      2.5,     3, quote(phi[4])); text(3.1, 3.5, "1")
-}
+  par(op)
+}
 \keyword{models}

The R Project SVN R

(root)/trunk/src/library/stats/man/SSfpl.Rd – Rev 68948 → 73628