SSasymp {stats} R Documentation

## Self-Starting nls Asymptotic Model

### Description

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.

### Usage

SSasymp(input, Asym, R0, lrc)


### Arguments

 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 input). R0 a numeric parameter representing the response when input is zero. lrc a numeric parameter representing the natural logarithm of the rate constant.

### Value

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.

### Author(s)

nls, selfStart

### Examples


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, length.out = 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)


[Package stats version 4.4.0 Index]