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).

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