| SSasympOrig {stats} | R Documentation |
This selfStart model evaluates the asymptotic regression
function through the origin and its gradient. It has an
initial attribute that will evaluate initial estimates of the
parameters Asym and lrc for a given set of data.
SSasympOrig(input, Asym, lrc)
input |
a numeric vector of values at which to evaluate the model. |
Asym |
a numeric parameter representing the horizontal asymptote. |
lrc |
a numeric parameter representing the natural logarithm of the rate constant. |
a numeric vector of the same length as input. It is the value of
the expression Asym*(1 - exp(-exp(lrc)*input)). If all of
the arguments Asym and lrc are
names of objects, the gradient matrix with respect to these names is
attached as an attribute named gradient.
José Pinheiro and Douglas Bates
Lob.329 <- Loblolly[ Loblolly$Seed == "329", ]
SSasympOrig(Lob.329$age, 100, -3.2) # response only
local({ Asym <- 100; lrc <- -3.2
SSasympOrig(Lob.329$age, Asym, lrc) # response and gradient
})
getInitial(height ~ SSasympOrig(age, Asym, lrc), data = Lob.329)
## Initial values are in fact the converged values
fm1 <- nls(height ~ SSasympOrig(age, Asym, lrc), data = Lob.329)
summary(fm1)
## Visualize the SSasympOrig() model parametrization :
xx <- seq(0, 5, len = 101)
yy <- 5 * (1- exp(-xx * log(2)))
stopifnot( all.equal(yy, SSasympOrig(xx, Asym = 5, lrc = log(log(2)))) )
require(graphics)
op <- par(mar = c(0, 0, 3.5, 0))
plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,5), xlim = c(-1/4, 5),
xlab = "", ylab = "", lwd = 2,
main = quote("Parameters in the SSasympOrig model"~~ f[phi](x)))
mtext(quote(list(phi[1] == "Asym", phi[2] == "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)
axis(2, at = 5*c(1/2,1), labels= expression(frac(phi[1],2), phi[1]), pos=0, las=1)
arrows(c(.3,.7), 5/2,
c(0, 1 ), 5/2, length = 0.08, angle = 25)
text( 0.5, 5/2, quote(t[0.5]))
text( 1 +.4, 5/2,
quote({f(t[0.5]) == frac(phi[1],2)}~{} %=>% {}~~{t[0.5] == frac(log(2), e^{phi[2]})}),
adj = c(0, 0.5))
par(op)