| % File src/library/stats/man/SSfpl.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2017 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{SSfpl} |
| \title{Self-Starting Nls Four-Parameter Logistic Model} |
| \alias{SSfpl} |
| \encoding{UTF-8} |
| \usage{ |
| SSfpl(input, A, B, xmid, scal) |
| } |
| \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 |
| the right side (very large values of \code{input}).} |
| \item{xmid}{a numeric parameter representing the \code{input} value at the |
| inflection point of the curve. The value of \code{SSfpl} will be |
| 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 computing |
| 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 |
| the arguments \code{A}, \code{B}, \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{ |
| 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 |
| 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) |
| |
| ## Visualizing the SSfpl() parametrization |
| xx <- seq(-0.5, 5, len = 101) |
| 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) |
| 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)) |
| abline(h = c(1, 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])) |
| arrows(-0.3, c(1/4, 3/4), |
| -0.3, c(0, 1 ), length = 0.07, angle = 25) |
| text (-0.3, 0.5, quote(phi[2])) |
| text(2, -.1, quote(phi[3])) |
| segments(c(2,3,3), c(0,3,4), # SSfpl(x = xmid = 2) = 3 |
| c(2,3,2), c(3,4,3), lty = 2, lwd = 0.75) |
| arrows(c(2.3, 2.7), 3, |
| c(2.0, 3 ), 3, length = 0.08, angle = 25) |
| text( 2.5, 3, quote(phi[4])); text(3.1, 3.5, "1") |
| par(op) |
| } |
| \keyword{models} |