llogistic.Rd'llogistic' provides a very general way of specifying log-logistic models, under various constraints on the parameters.
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)
| 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. |
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.
The value returned is a list containing the nonlinear function, the self starter function and the parameter names.
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).
The functions are for use with the function drm.