# LL.4: The four-parameter log-logistic function In drc: Analysis of Dose-Response Curves

## 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

 1 2 3 4 5  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.
 1 2 spinach.m1 <- drm(SLOPE~DOSE, CURVE, data = spinach, fct = LL.4()) spinach.m1