llogistic: The log-logistic function

In DoseResponse/drc: Analysis of Dose-Response Data

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.

DoseResponse/drc documentation built on May 7, 2021, 4:55 p.m.