R: The log-logistic function

llogistic {drc} | R Documentation

## The log-logistic function

### Description

'llogistic' provides a very general way of specifying log-logistic models, under various constraints on the parameters.

### Usage

      llogistic(fixed = c(NA, NA, NA, NA, NA),
      names = c("b", "c", "d", "e", "f"),
      method = c("1", "2", "3", "4"), ssfct = NULL,
      fctName, fctText)

      llogistic2(fixed = c(NA, NA, NA, NA, NA),
      names = c("b", "c", "d", "e", "f"),
      ss = c("1", "2", "3"), ssfct = NULL,
      fctName, fctText)

### 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 (should not contain ":"). The default is reasonable (see under 'Usage'). The order of the parameters is: b, c, d, e, f (see under 'Details').
`method` | character string indicating the self starter function to use.
`ss` | character string indicating the self starter function to use.
`ssfct` | a self starter function to be used.
`fctName` | optional character string used internally by convenience functions.
`fctText` | optional character string used internally by convenience functions.

### Details

The default arguments yields the five-parameter log-logistic function given by the expression

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

If the parameter f differs from 1 then the function is asymmetric; otherwise it is symmetric (on log scale). This function is fitted using `llogistic`.

The log-logistic function with log(e) rather than e as a parameter, that is using the parameterisation

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

is fitted using `llogistic2`.

Sometimes the log-logistic models are also called Hill models.

### Value

The value returned is a list containing the nonlinear function, the self starter function and the parameter names.

### Note

The functions are for use with the function `drm`.

### Author(s)

Christian Ritz

### References

Finney, D. J. (1979) Bioassay and the Practise of Statistical Inference, Int. Statist. Rev., 47, 1–12.

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

### See Also

For convenience several special cases are available: `LL.2`, `LL.3`, `LL.4` and `LL.5`. Examples are provided in the help pages for these functions.

[Package drc version 3.0-1 Index]