SSasympOff {stats} R Documentation

## Self-Starting Nls Asymptotic Regression Model with an Offset

### Description

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`.

### Usage

```SSasympOff(input, Asym, lrc, c0)
```

### 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`). `lrc` a numeric parameter representing the natural logarithm of the rate constant. `c0` a numeric parameter representing the `input` for which the response is zero.

### Value

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`.

### Author(s)

José Pinheiro and Douglas Bates

`nls`, `selfStart`; `example(SSasympOff)` gives graph showing the `SSasympOff` parametrization.

### Examples

```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 == "Asym", phi == "lrc", phi == "c0")))
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)
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))
segments(3/4, -.2, 3/4, 1.6, lty = 2)
text    (3/4,    c(-.3, 1.7), quote(phi))
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*e^phi), adj = c(0, .5))
par(op)
```

[Package stats version 4.1.1 Index]