R: Self-Starting Nls Four-Parameter Logistic Model

SSfpl {stats} | R Documentation

## Self-Starting Nls Four-Parameter Logistic Model

### Description

This `selfStart` model evaluates the four-parameter logistic function and its gradient. It has an `initial` attribute computing initial estimates of the parameters `A`, `B`, `xmid`, and `scal` for a given set of data.

### Usage

    SSfpl(input, A, B, xmid, scal)

### Arguments

`input` | a numeric vector of values at which to evaluate the model.
`A` | a numeric parameter representing the horizontal asymptote on the left side (very small values of `input`).
`B` | a numeric parameter representing the horizontal asymptote on the right side (very large values of `input`).
`xmid` | a numeric parameter representing the `input` value at the inflection point of the curve. The value of `SSfpl` will be midway between `A` and `B` at `xmid`.
`scal` | a numeric scale parameter on the `input` axis.

### Value

a numeric vector of the same length as `input`. It is the value of the expression `A+(B-A)/(1+exp((xmid-input)/scal))`. If all of the arguments `A`, `B`, `xmid`, and `scal` 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

    Chick.1 <- ChickWeight[ChickWeight$Chick == 1, ]
    SSfpl(Chick.1$Time, 13, 368, 14, 6)  # response only
    local({
      A <- 13; B <- 368; xmid <- 14; scal <- 6
      SSfpl(Chick.1$Time, A, B, xmid, scal) # response _and_ gradient
    })
    print(getInitial(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1),
          digits = 5)
    ## Initial values are in fact the converged values
    fm1 <- nls(weight ~ SSfpl(Time, A, B, xmid, scal), data = Chick.1)
    summary(fm1)

    ## Visualizing the  SSfpl()  parametrization
      xx <- seq(-0.5, 5, len = 101)
      yy <- 1 + 4 / (1 + exp((2-xx))) # == SSfpl(xx, *) :
      stopifnot( all.equal(yy, SSfpl(xx, A = 1, B = 5, xmid = 2, scal = 1)) )
      require(graphics)
      op <- par(mar = c(0, 0, 3.5, 0))
      plot(xx, yy, type = "l", axes = FALSE, ylim = c(0,6), xlim = c(-1, 5),
           xlab = "", ylab = "", lwd = 2,
           main = "Parameters in the SSfpl model")
      mtext(quote(list(phi[1] == "A", phi[2] == "B", phi[3] == "xmid", phi[4] == "scal")))
      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 = c(1, 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]))
      arrows(-0.3, c(1/4, 3/4),
             -0.3, c(0,   1  ), length = 0.07, angle = 25)
      text  (-0.3, 0.5, quote(phi[2]))
      text(2, -.1, quote(phi[3]))
      segments(c(2,3,3), c(0,3,4), # SSfpl(x = xmid = 2) = 3
               c(2,3,2), c(3,4,3),    lty = 2, lwd = 0.75)
      arrows(c(2.3, 2.7), 3,
             c(2.0, 3  ), 3, length = 0.08, angle = 25)
      text(      2.5,     3, quote(phi[4])); text(3.1, 3.5, "1")
      par(op)

[Package stats version 3.5.1 Index]