R: Self-Starting 'nls' Asymptotic Model with an Offset

SSasympOff {stats}

R Documentation

Self-Starting `nls` Asymptotic 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

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[1] == "Asym", phi[2] == "lrc", phi[3] == "c0")))
  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(-0.8, c(2.1, 2.9),
         -0.8, c(0  , 5  ), length = 0.1, angle = 25)
  text  (-0.8, 2.5, quote(phi[1]))
  segments(3/4, -.2, 3/4, 1.6, lty = 2)
  text    (3/4,    c(-.3, 1.7), quote(phi[3]))
  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[1]*e^phi[2]), adj = c(0, .5))
  par(op)

[Package stats version 4.4.0 Index]

Self-Starting nls Asymptotic Model with an Offset