drc (version 2.5-12)

logistic: The logistic model

Description

The general asymmetric five-parameter logistic model for describing dose-response relationships.

Usage

logistic(fixed = c(NA, NA, NA, NA, NA), names = c("b", "c", "d", "e", "f"),
  method = c("1", "2", "3", "4"), ssfct = NULL, 
  fctName, fctText) 

  L.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)
  L.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)
  L.5(fixed = c(NA, NA, NA, NA, NA), names = c("b", "c", "d", "e", "f"), ...)

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 order of the parameters is: b, c, d, e, f (see under 'Details').

method

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.

...

Additional arguments (see llogistic).

Value

• The value returned is a list containing the nonlinear function, the self starter function and the parameter names.

Details

The default arguments yields the five-parameter logistic mean function given by the expression $$f(x) = c + \frac{d-c}{(1+\exp(b(x - e)))^f}$$ The model is different from the log-logistic models llogistic and llogistic2 where the term $$log(x)$$ is used instead of $$x$$. The model is sometimes referred to as the Boltzmann model.

Examples

## Fitting the four-parameter logistic model
ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = L.4())
summary(ryegrass.m1)

## Fitting an asymmetric logistic model
##  requires installing the package 'NISTnls'
# Ratkowsky3.m1 <- drm(y~x, data = Ratkowsky3, 
# fct = L.5(fixed = c(NA, 0, NA, NA, NA)))
# plot(Ratkowsky3.m1)
# summary(Ratkowsky3.m1)  
## okay agreement with NIST values
##  for the two parameters that are the same