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% File src/library/stats/man/SSasympOff.Rd
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% File src/library/stats/man/SSasympOff.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{SSasympOff}
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\name{SSasympOff}
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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 with an Offset}
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\title{Self-Starting Nls Asymptotic Regression Model with an Offset}
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attached as an attribute named \code{gradient}.
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attached as an attribute named \code{gradient}.
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}
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}
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\author{\enc{José}{Jose} Pinheiro and Douglas Bates}
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\author{\enc{José}{Jose} Pinheiro and Douglas Bates}
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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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\code{example(SSasympOff)} gives graph showing the \code{SSasympOff}
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\code{example(SSasympOff)} gives graph showing the \code{SSasympOff}
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parametrization, where \eqn{\phi_1}{phi_1} is \code{Asymp},
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parametrization.
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\eqn{\phi_3}{phi_3} is \code{c0}.% , and \eqn{t_{0.5}} is FIXME
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}
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}
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\examples{
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\examples{
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CO2.Qn1 <- CO2[CO2$Plant == "Qn1", ]
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CO2.Qn1 <- CO2[CO2$Plant == "Qn1", ]
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SSasympOff(CO2.Qn1$conc, 32, -4, 43) # response only
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SSasympOff(CO2.Qn1$conc, 32, -4, 43) # response only
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Asym <- 32; lrc <- -4; c0 <- 43
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local({ Asym <- 32; lrc <- -4; c0 <- 43
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SSasympOff(CO2.Qn1$conc, Asym, lrc, c0) # response and gradient
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SSasympOff(CO2.Qn1$conc, Asym, lrc, c0) # response and gradient
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})
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getInitial(uptake ~ SSasympOff(conc, Asym, lrc, c0), data = CO2.Qn1)
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getInitial(uptake ~ SSasympOff(conc, Asym, lrc, c0), data = CO2.Qn1)
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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(uptake ~ SSasympOff(conc, Asym, lrc, c0), data = CO2.Qn1)
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fm1 <- nls(uptake ~ SSasympOff(conc, Asym, lrc, c0), data = CO2.Qn1)
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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 SSasympOff() model parametrization :
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xx <- seq(0.5, 5, len = 101)
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xx <- seq(0.25, 8, by=1/16)
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yy <- 5 * (1 - exp(-(xx - 0.5)/(2*log(2))))
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yy <- 5 * (1 - exp(-(xx - 3/4)*0.4))
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stopifnot( all.equal(yy, SSasympOff(xx, Asym = 5, lrc = log(0.4), c0 = 3/4)) )
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require(graphics)
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par(mar = c(0, 0, 4.0, 0))
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op <- par(mar = c(0, 0, 4.0, 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(-.5,6), xlim = c(-1, 8),
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xlab = "", ylab = "", lwd = 2,
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xlab = "", ylab = "", lwd = 2,
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main = "Parameters in the SSasympOff model")
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main = "Parameters in the SSasympOff model")
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mtext(quote(list(phi[1] == "Asym", phi[2] == "lrc", phi[3] == "c0")))
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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(-0.8, c(2.1, 2.9),
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arrows(-0.8, 2.9, -0.8, 5, length = 0.1, angle = 25)
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-0.8, c(0 , 5 ), length = 0.1, angle = 25)
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text(-0.8, 2.5, expression(phi[1]), adj = c(0.5, 0.5))
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text (-0.8, 2.5, quote(phi[1]))
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segments(0.5, 0, 0.5, 3, lty = 2, lwd = 0.75)
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segments(3/4, -.2, 3/4, 1.6, lty = 2)
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text(0.5, 3.1, expression(phi[3]), adj = c(0.5, 0))
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text (3/4, c(-.3, 1.7), quote(phi[3]))
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segments(1.5, 2.525, 1.5, 3, lty = 2, lwd = 0.75)
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arrows(c(1.1, 1.4), -.15,
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arrows(0.7, 2.65, 0.5, 2.65, length = 0.08, angle = 25)
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c(3/4, 7/4), -.15, length = 0.07, angle = 25)
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text (3/4 + 1/2, -.15, quote(1))
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segments(c(3/4, 7/4, 7/4), c(0, 0, 2), # 5 * exp(log(0.4)) = 2
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arrows(1.3, 2.65, 1.5, 2.65, length = 0.08, angle = 25)
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c(7/4, 7/4, 3/4), c(0, 2, 0), lty = 2, lwd = 2)
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text(1.0, 2.65, expression(t[0.5]), adj = c(0.5, 0.5))
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text( 7/4 +.1, 2./2, quote(phi[1]*e^phi[2]), adj = c(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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