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% File src/library/stats/man/SSasymp.Rd
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% File src/library/stats/man/SSasymp.Rd
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% Part of the R package, https://www.R-project.org
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2010 R Core Team
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% Copyright 1995-2017 R Core Team
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% Distributed under GPL 2 or later
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% Distributed under GPL 2 or later
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\name{SSasymp}
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\name{SSasymp}
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\encoding{UTF-8}
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\encoding{UTF-8}
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\title{Self-Starting Nls Asymptotic Regression Model}
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\title{Self-Starting Nls Asymptotic Regression Model}
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\description{
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\description{
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This \code{selfStart} model evaluates the asymptotic regression
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This \code{selfStart} model evaluates the asymptotic regression
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function and its gradient. It has an \code{initial} attribute that
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function and its gradient. It has an \code{initial} attribute that
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will evaluate initial estimates of the parameters \code{Asym}, \code{R0},
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will evaluate initial estimates of the parameters \code{Asym}, \code{R0},
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and \code{lrc} for a given set of data.
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and \code{lrc} for a given set of data.
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Note that \code{\link{SSweibull}()} generalizes this asymptotic model
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with an extra parameter.
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}
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}
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\value{
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\value{
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a numeric vector of the same length as \code{input}. It is the value of
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a numeric vector of the same length as \code{input}. It is the value of
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the expression \code{Asym+(R0-Asym)*exp(-exp(lrc)*input)}. If all of
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the expression \code{Asym+(R0-Asym)*exp(-exp(lrc)*input)}. If all of
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the arguments \code{Asym}, \code{R0}, and \code{lrc} are
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the arguments \code{Asym}, \code{R0}, and \code{lrc} are
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\code{\link{nls}}, \code{\link{selfStart}}
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\code{\link{nls}}, \code{\link{selfStart}}
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}
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}
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\examples{
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\examples{
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\dontshow{options(show.nls.convergence=FALSE)}
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\dontshow{options(show.nls.convergence=FALSE)}
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Lob.329 <- Loblolly[ Loblolly$Seed == "329", ]
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Lob.329 <- Loblolly[ Loblolly$Seed == "329", ]
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SSasymp( Lob.329$age, 100, -8.5, -3.2 ) # response only
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SSasymp( Lob.329$age, 100, -8.5, -3.2 ) # response only
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Asym <- 100
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local({
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resp0 <- -8.5
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Asym <- 100 ; resp0 <- -8.5 ; lrc <- -3.2
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lrc <- -3.2
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SSasymp( Lob.329$age, Asym, resp0, lrc ) # response and gradient
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SSasymp( Lob.329$age, Asym, resp0, lrc) # response _and_ gradient
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})
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getInitial(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
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getInitial(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
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## Initial values are in fact the converged values
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## Initial values are in fact the converged values
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fm1 <- nls(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
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fm1 <- nls(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
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summary(fm1)
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summary(fm1)
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\dontshow{
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require(graphics)
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## Visualize the SSasymp() model parametrization :
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xx <- seq(0, 5, len = 101)
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xx <- seq(-.3, 5, len = 101)
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## Asym + (R0-Asym) * exp(-exp(lrc)* x) :
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yy <- 5 - 4 * exp(-xx/(2*log(2)))
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yy <- 5 - 4 * exp(-xx / exp(3/4))
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stopifnot( all.equal(yy, SSasymp(xx, Asym = 5, R0 = 1, lrc = -3/4)) )
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require(graphics)
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par(mar = c(0, 0, 4.1, 0))
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op <- par(mar = c(0, .2, 4.1, 0))
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plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,6), xlim = c(-1, 5),
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plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,5.2), xlim = c(-.3, 5),
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xlab = "", ylab = "", lwd = 2,
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xlab = "", ylab = "", lwd = 2,
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main = "Parameters in the SSasymp model")
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main = quote("Parameters in the SSasymp model " ~
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{f[phi](x) == phi[1] + (phi[2]-phi[1])*~e^{-e^{phi[3]}*~x}}))
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mtext(quote(list(phi[1] == "Asym", phi[2] == "R0", phi[3] == "lrc")))
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usr <- par("usr")
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usr <- par("usr")
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arrows(usr[1], 0, usr[2], 0, length = 0.1, angle = 25)
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arrows(usr[1], 0, usr[2], 0, length = 0.1, angle = 25)
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arrows(0, usr[3], 0, usr[4], length = 0.1, angle = 25)
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arrows(0, usr[3], 0, usr[4], length = 0.1, angle = 25)
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text(usr[2] - 0.2, 0.1, "x", adj = c(1, 0))
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text(usr[2] - 0.2, 0.1, "x", adj = c(1, 0))
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text(-0.1, usr[4], "y", adj = c(1, 1))
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text( -0.1, usr[4], "y", adj = c(1, 1))
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abline(h = 5, lty = 2, lwd = 0)
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abline(h = 5, lty = 3)
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arrows(-0.8, 2.1, -0.8, 0, length = 0.1, angle = 25)
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arrows(c(0.35, 0.65), 1,
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arrows(-0.8, 2.9, -0.8, 5, length = 0.1, angle = 25)
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c(0 , 1 ), 1, length = 0.08, angle = 25); text(0.5, 1, quote(1))
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text(-0.8, 2.5, expression(phi[1]), adj = c(0.5, 0.5))
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y0 <- 1 + 4*exp(-3/4) ; t.5 <- log(2) / exp(-3/4) ; AR2 <- 3 # (Asym + R0)/2
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segments(-0.4, 1, 0, 1, lty = 2, lwd = 0.75)
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segments(c(1, 1), c( 1, y0),
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arrows(-0.3, 0.25, -0.3, 0, length = 0.07, angle = 25)
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c(1, 0), c(y0, 1), lty = 2, lwd = 0.75)
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arrows(-0.3, 0.75, -0.3, 1, length = 0.07, angle = 25)
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text(1.1, 1/2+y0/2, quote((phi[1]-phi[2])*e^phi[3]), adj = c(0,.5))
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text(-0.3, 0.5, expression(phi[2]), adj = c(0.5, 0.5))
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axis(2, at = c(1,AR2,5), labels= expression(phi[2], frac(phi[1]+phi[2],2), phi[1]),
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pos=0, las=1)
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segments(1, 3.025, 1, 4, lty = 2, lwd = 0.75)
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arrows(c(.6,t.5-.6), AR2,
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arrows(0.2, 3.5, 0, 3.5, length = 0.08, angle = 25)
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c(0, t.5 ), AR2, length = 0.08, angle = 25)
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arrows(0.8, 3.5, 1, 3.5, length = 0.08, angle = 25)
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text( t.5/2, AR2, quote(t[0.5]))
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text( t.5 +.4, AR2,
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quote({f(t[0.5]) == frac(phi[1]+phi[2],2)}~{} \%=>\% {}~~
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text(0.5, 3.5, expression(t[0.5]), adj = c(0.5, 0.5))
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{t[0.5] == frac(log(2), e^{phi[3]})}), adj = c(0, 0.5))
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}
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par(op)
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}
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}
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\keyword{models}
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\keyword{models}
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