llogistic: The log-logistic function

Description

'llogistic' provides a very general way of specifying log-logistic models, under various constraints on the parameters.

Usage

llogistic(lowerc = c(-Inf, -Inf, -Inf, -Inf, -Inf), upperc = c(Inf, Inf, Inf, Inf, Inf),
  fixed = c(NA, NA, NA, NA, NA), 
  names = c("b", "c", "d", "e", "f"),
  ss = c("1", "2"))

Arguments

lowerc

numeric vector. The lower bound on parameters. Default is minus infinity.

upperc

numeric vector. The upper bound on parameters. Default is plus infinity.

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').

character string indicating the self starter function to use.

Value

The value returned is a list containing the non-linear function, the self starter function and the parameter names.

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 $f$ is different from 1 then the function is asymmetric.

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).