R: The four-parameter log-logistic function

LL.4 {drc} | R Documentation

## The four-parameter log-logistic function

### Description

'LL.4' and 'LL2.4' provide the four-parameter log-logistic function, self starter function, names of the parameters and, optionally, first and second derivatives for a faster estimation.

### Usage

      LL.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)

      l4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)

      LL2.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)

### Arguments

`fixed` | numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.
`names` | a vector of character strings giving the names of the parameters. The default is reasonable.
`...` | Additional arguments (see `llogistic`).

### Details

The four-parameter log-logistic function is given by the expression

f(x) = c + \frac{d-c}{1+\exp(b(\log(x)-\log(e)))}

or in another parameterisation (converting the term \log(e) into a parameter)

f(x) = c + \frac{d-c}{1+\exp(b(\log(x)-\tilde{e}))}

The function is symmetric about the inflection point (e).

### Value

See `llogistic`.

### Note

This function is for use with the function `drm`.

### Author(s)

Christian Ritz and Jens C. Streibig

### References

Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley \& Sons (p. 330).

### See Also

Setting c=0 yields `LL.3`. See also `LL.5`.

### Examples

    spinach.m1 <- drm(SLOPE~DOSE, CURVE, data = spinach, fct = LL.4())
    spinach.m1

[Package drc version 3.0-1 Index]