R: Four-parameter Logistic Model

SSfpl {nls} | R Documentation

## Four-parameter Logistic Model

### Description

This `selfStart` model evaluates the four-parameter logistic function and its gradient. It has an `initial` attribute that will evaluate 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)

Jose Pinheiro and Douglas Bates

### See Also

`nls`, `selfStart`

### Examples

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

[Package Contents]