LL.4 {drc}

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