R: Self-Starting Nls Asymptotic Regression Model through the...

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

### See Also

`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[1] == "Asym", phi[2] == "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)
      axis(2, at = 5*c(1/2,1), labels= expression(frac(phi[1],2), phi[1]), 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[1],2)}~{} %=>% {}~~{t[0.5] == frac(log(2), e^{phi[2]})}),
           adj = c(0, 0.5))
      par(op)

[Package stats version 4.0.5 Index]