drc (version 2.5-12)

LL.4: 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).

Value

• See llogistic.

concept

Hill 4-parameter four-parameter

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 ($e$).

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

rm(model1)