| % 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} |
| \encoding{UTF-8} |
| \title{Self-Starting 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(tol = 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} |