| SSasympOff | R Documentation |
This selfStart model evaluates an alternative parametrization
of the asymptotic
regression function and the gradient with respect to those parameters.
It has an initial
attribute that creates initial estimates of the parameters
Asym, lrc, and c0.
SSasympOff(input, Asym, lrc, c0)
input |
a numeric vector of values at which to evaluate the model. |
Asym |
a numeric parameter representing the horizontal asymptote on
the right side (very large values of |
lrc |
a numeric parameter representing the natural logarithm of the rate constant. |
c0 |
a numeric parameter representing the |
a numeric vector of the same length as input. It is the value of
the expression Asym*(1 - exp(-exp(lrc)*(input - c0))). If all of
the arguments Asym, lrc, and c0 are
names of objects, the gradient matrix with respect to these names is
attached as an attribute named gradient.
José Pinheiro and Douglas Bates
nls, selfStart;
example(SSasympOff) gives graph showing the SSasympOff
parametrization.
CO2.Qn1 <- CO2[CO2$Plant == "Qn1", ]
SSasympOff(CO2.Qn1$conc, 32, -4, 43) # response only
local({ Asym <- 32; lrc <- -4; c0 <- 43
SSasympOff(CO2.Qn1$conc, Asym, lrc, c0) # response and gradient
})
getInitial(uptake ~ SSasympOff(conc, Asym, lrc, c0), data = CO2.Qn1)
## Initial values are in fact the converged values
fm1 <- nls(uptake ~ SSasympOff(conc, Asym, lrc, c0), data = CO2.Qn1)
summary(fm1)
## Visualize the SSasympOff() model parametrization :
xx <- seq(0.25, 8, by=1/16)
yy <- 5 * (1 - exp(-(xx - 3/4)*0.4))
stopifnot( all.equal(yy, SSasympOff(xx, Asym = 5, lrc = log(0.4), c0 = 3/4)) )
require(graphics)
op <- par(mar = c(0, 0, 4.0, 0))
plot(xx, yy, type = "l", axes = FALSE, ylim = c(-.5,6), xlim = c(-1, 8),
xlab = "", ylab = "", lwd = 2,
main = "Parameters in the SSasympOff model")
mtext(quote(list(phi[1] == "Asym", phi[2] == "lrc", phi[3] == "c0")))
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(3/4, -.2, 3/4, 1.6, lty = 2)
text (3/4, c(-.3, 1.7), quote(phi[3]))
arrows(c(1.1, 1.4), -.15,
c(3/4, 7/4), -.15, length = 0.07, angle = 25)
text (3/4 + 1/2, -.15, quote(1))
segments(c(3/4, 7/4, 7/4), c(0, 0, 2), # 5 * exp(log(0.4)) = 2
c(7/4, 7/4, 3/4), c(0, 2, 0), lty = 2, lwd = 2)
text( 7/4 +.1, 2./2, quote(phi[1]*e^phi[2]), adj = c(0, .5))
par(op)
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