R: Self-Starting Nls Asymptotic Regression Model with an Offset

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

### See Also

`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[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 4.0.5 Index]