| SSasymp {stats} | R Documentation |
This selfStart model evaluates the asymptotic regression
function and its gradient. It has an initial attribute that
will evaluate initial estimates of the parameters Asym, R0,
and lrc for a given set of data.
Note that SSweibull() generalizes this asymptotic model
with an extra parameter.
SSasymp(input, Asym, R0, lrc)
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 |
R0 |
a numeric parameter representing the response when
|
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+(R0-Asym)*exp(-exp(lrc)*input). If all of
the arguments Asym, R0, 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$Seed == "329", ]
SSasymp( Lob.329$age, 100, -8.5, -3.2 ) # response only
local({
Asym <- 100 ; resp0 <- -8.5 ; lrc <- -3.2
SSasymp( Lob.329$age, Asym, resp0, lrc) # response _and_ gradient
})
getInitial(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
## Initial values are in fact the converged values
fm1 <- nls(height ~ SSasymp( age, Asym, resp0, lrc), data = Lob.329)
summary(fm1)
## Visualize the SSasymp() model parametrization :
xx <- seq(-.3, 5, len = 101)
## Asym + (R0-Asym) * exp(-exp(lrc)* x) :
yy <- 5 - 4 * exp(-xx / exp(3/4))
stopifnot( all.equal(yy, SSasymp(xx, Asym = 5, R0 = 1, lrc = -3/4)) )
require(graphics)
op <- par(mar = c(0, .2, 4.1, 0))
plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,5.2), xlim = c(-.3, 5),
xlab = "", ylab = "", lwd = 2,
main = quote("Parameters in the SSasymp model " ~
{f[phi](x) == phi[1] + (phi[2]-phi[1])*~e^{-e^{phi[3]}*~x}}))
mtext(quote(list(phi[1] == "Asym", phi[2] == "R0", phi[3] == "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)
arrows(c(0.35, 0.65), 1,
c(0 , 1 ), 1, length = 0.08, angle = 25); text(0.5, 1, quote(1))
y0 <- 1 + 4*exp(-3/4) ; t.5 <- log(2) / exp(-3/4) ; AR2 <- 3 # (Asym + R0)/2
segments(c(1, 1), c( 1, y0),
c(1, 0), c(y0, 1), lty = 2, lwd = 0.75)
text(1.1, 1/2+y0/2, quote((phi[1]-phi[2])*e^phi[3]), adj = c(0,.5))
axis(2, at = c(1,AR2,5), labels= expression(phi[2], frac(phi[1]+phi[2],2), phi[1]),
pos=0, las=1)
arrows(c(.6,t.5-.6), AR2,
c(0, t.5 ), AR2, length = 0.08, angle = 25)
text( t.5/2, AR2, quote(t[0.5]))
text( t.5 +.4, AR2,
quote({f(t[0.5]) == frac(phi[1]+phi[2],2)}~{} %=>% {}~~
{t[0.5] == frac(log(2), e^{phi[3]})}), adj = c(0, 0.5))
par(op)