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% File src/library/stats/man/SSasympOrig.Rd
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% File src/library/stats/man/SSasympOrig.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{SSasympOrig}
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\name{SSasympOrig}
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\encoding{UTF-8}
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\alias{SSasympOrig}
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\title{Self-Starting Nls Asymptotic Regression Model through the Origin}
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\title{Self-Starting Nls Asymptotic Regression Model through the Origin}
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\encoding{UTF-8}
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\usage{
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\usage{
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SSasympOrig(input, Asym, lrc)
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SSasympOrig(input, Asym, lrc)
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}
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}
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\alias{SSasympOrig}
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\arguments{
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\arguments{
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\item{input}{a numeric vector of values at which to evaluate the model.}
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\item{input}{a numeric vector of values at which to evaluate the model.}
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\item{Asym}{a numeric parameter representing the horizontal asymptote.}
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\item{Asym}{a numeric parameter representing the horizontal asymptote.}
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\item{lrc}{a numeric parameter representing the natural logarithm of
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\item{lrc}{a numeric parameter representing the natural logarithm of
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the rate constant.}
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the rate constant.}
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}
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}
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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{\link{selfStart}} model evaluates the asymptotic regression
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function through the origin and its gradient. It has an
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function through the origin and its gradient. It has an
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\code{initial} attribute that will evaluate initial estimates of the
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\code{initial} attribute that will evaluate initial estimates of the
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parameters \code{Asym} and \code{lrc} for a given set of data.
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parameters \code{Asym} and \code{lrc} for a given set of data.
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}
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}
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\value{
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\value{
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\seealso{\code{\link{nls}}, \code{\link{selfStart}}
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\seealso{\code{\link{nls}}, \code{\link{selfStart}}
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}
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}
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\examples{\donttest{
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\examples{\donttest{
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Lob.329 <- Loblolly[ Loblolly$Seed == "329", ]
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Lob.329 <- Loblolly[ Loblolly$Seed == "329", ]
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SSasympOrig(Lob.329$age, 100, -3.2) # response only
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SSasympOrig(Lob.329$age, 100, -3.2) # response only
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Asym <- 100; lrc <- -3.2
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local({ Asym <- 100; lrc <- -3.2
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SSasympOrig(Lob.329$age, Asym, lrc) # response and gradient
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SSasympOrig(Lob.329$age, Asym, lrc) # response and gradient
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})
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getInitial(height ~ SSasympOrig(age, Asym, lrc), data = Lob.329)
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getInitial(height ~ SSasympOrig(age, Asym, 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 ~ SSasympOrig(age, Asym, lrc), data = Lob.329)
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fm1 <- nls(height ~ SSasympOrig(age, Asym, lrc), data = Lob.329)
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summary(fm1)
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summary(fm1)
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}
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}
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\dontshow{
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require(graphics)
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## Visualize the SSasympOrig() model parametrization :
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xx <- seq(0, 5, len = 101)
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xx <- seq(0, 5, len = 101)
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yy <- 5 * (1- exp(-xx/(2*log(2))))
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yy <- 5 * (1- exp(-xx * log(2)))
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stopifnot( all.equal(yy, SSasympOrig(xx, Asym = 5, lrc = log(log(2)))) )
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require(graphics)
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par(mar = c(0, 0, 3.5, 0))
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op <- par(mar = c(0, 0, 3.5, 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), xlim = c(-1/4, 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 SSasympOrig model")
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main = quote("Parameters in the SSasympOrig model"~~ f[phi](x)))
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mtext(quote(list(phi[1] == "Asym", phi[2] == "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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axis(2, at = 5*c(1/2,1), labels= expression(frac(phi[1],2), phi[1]), pos=0, las=1)
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arrows(-0.8, 2.9, -0.8, 5, length = 0.1, angle = 25)
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arrows(c(.3,.7), 5/2,
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text(-0.8, 2.5, expression(phi[1]), adj = c(0.5, 0.5))
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c(0, 1 ), 5/2, length = 0.08, angle = 25)
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segments(1, 2.525, 1, 3.5, lty = 2, lwd = 0.75)
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text( 0.5, 5/2, quote(t[0.5]))
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arrows(0.2, 3.0, 0, 3.0, length = 0.08, angle = 25)
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text( 1 +.4, 5/2,
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arrows(0.8, 3.0, 1, 3.0, length = 0.08, angle = 25)
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quote({f(t[0.5]) == frac(phi[1],2)}~{} \%=>\% {}~~{t[0.5] == frac(log(2), e^{phi[2]})}),
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text(0.5, 3.0, expression(t[0.5]), adj = c(0.5, 0.5))
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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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