SSasympOrig {stats} R Documentation

## Self-Starting Nls Asymptotic Regression Model through the Origin

### Description

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.

### Usage

```SSasympOrig(input, Asym, lrc)
```

### Arguments

 `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.

### Value

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`.

### Author(s)

José Pinheiro and Douglas Bates

`nls`, `selfStart`

### Examples

```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 == "Asym", phi == "lrc")))
usr <- par("usr")
arrows(usr, 0, usr, 0, length = 0.1, angle = 25)
arrows(0, usr, 0, usr, length = 0.1, angle = 25)
text(usr - 0.2, 0.1, "x", adj = c(1, 0))
text(   -0.1,   usr, "y", adj = c(1, 1))
abline(h = 5, lty = 3)
axis(2, at = 5*c(1/2,1), labels= expression(frac(phi,2), phi), 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,2)}~{} %=>% {}~~{t[0.5] == frac(log(2), e^{phi})}),