| % File src/library/stats/man/SSasymp.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2017 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{SSasymp} |
| \encoding{UTF-8} |
| \title{Self-Starting Nls Asymptotic Regression Model} |
| \usage{ |
| SSasymp(input, Asym, R0, lrc) |
| } |
| \alias{SSasymp} |
| \arguments{ |
| \item{input}{a numeric vector of values at which to evaluate the model.} |
| \item{Asym}{a numeric parameter representing the horizontal asymptote on |
| the right side (very large values of \code{input}).} |
| \item{R0}{a numeric parameter representing the response when |
| \code{input} is zero.} |
| \item{lrc}{a numeric parameter representing the natural logarithm of |
| the rate constant.} |
| } |
| \description{ |
| This \code{selfStart} model evaluates the asymptotic regression |
| function and its gradient. It has an \code{initial} attribute that |
| will evaluate initial estimates of the parameters \code{Asym}, \code{R0}, |
| and \code{lrc} for a given set of data. |
| |
| Note that \code{\link{SSweibull}()} generalizes this asymptotic model |
| with an extra parameter. |
| } |
| \value{ |
| a numeric vector of the same length as \code{input}. It is the value of |
| the expression \code{Asym+(R0-Asym)*exp(-exp(lrc)*input)}. If all of |
| the arguments \code{Asym}, \code{R0}, and \code{lrc} 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{ |
| \dontshow{options(show.nls.convergence=FALSE)} |
| Lob.329 <- Loblolly[ Loblolly$Seed == "329", ] |
| SSasymp( Lob.329$age, 100, -8.5, -3.2 ) # response only |
| local({ |
| Asym <- 100 ; resp0 <- -8.5 ; lrc <- -3.2 |
| SSasymp( Lob.329$age, Asym, resp0, lrc) # response _and_ gradient |
| }) |
| getInitial(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329) |
| ## Initial values are in fact the converged values |
| fm1 <- nls(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329) |
| summary(fm1) |
| |
| ## Visualize the SSasymp() model parametrization : |
| |
| xx <- seq(-.3, 5, length.out = 101) |
| ## Asym + (R0-Asym) * exp(-exp(lrc)* x) : |
| yy <- 5 - 4 * exp(-xx / exp(3/4)) |
| stopifnot( all.equal(yy, SSasymp(xx, Asym = 5, R0 = 1, lrc = -3/4)) ) |
| require(graphics) |
| op <- par(mar = c(0, .2, 4.1, 0)) |
| plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,5.2), xlim = c(-.3, 5), |
| xlab = "", ylab = "", lwd = 2, |
| main = quote("Parameters in the SSasymp model " ~ |
| {f[phi](x) == phi[1] + (phi[2]-phi[1])*~e^{-e^{phi[3]}*~x}})) |
| mtext(quote(list(phi[1] == "Asym", phi[2] == "R0", phi[3] == "lrc"))) |
| 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(c(0.35, 0.65), 1, |
| c(0 , 1 ), 1, length = 0.08, angle = 25); text(0.5, 1, quote(1)) |
| y0 <- 1 + 4*exp(-3/4) ; t.5 <- log(2) / exp(-3/4) ; AR2 <- 3 # (Asym + R0)/2 |
| segments(c(1, 1), c( 1, y0), |
| c(1, 0), c(y0, 1), lty = 2, lwd = 0.75) |
| text(1.1, 1/2+y0/2, quote((phi[1]-phi[2])*e^phi[3]), adj = c(0,.5)) |
| axis(2, at = c(1,AR2,5), labels= expression(phi[2], frac(phi[1]+phi[2],2), phi[1]), |
| pos=0, las=1) |
| arrows(c(.6,t.5-.6), AR2, |
| c(0, t.5 ), AR2, length = 0.08, angle = 25) |
| text( t.5/2, AR2, quote(t[0.5])) |
| text( t.5 +.4, AR2, |
| quote({f(t[0.5]) == frac(phi[1]+phi[2],2)}~{} \%=>\% {}~~ |
| {t[0.5] == frac(log(2), e^{phi[3]})}), adj = c(0, 0.5)) |
| par(op) |
| } |
| \keyword{models} |