The logistic model

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

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).

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.

Value

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

Examples

## Fitting the four-parameter logistic model
ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = L.4())
summary(ryegrass.m1)
#> 
#> Model fitted: Logistic (ED50 as parameter) (4 parms)
#> 
#> Parameter estimates:
#> 
#>               Estimate Std. Error t-value   p-value    
#> b:(Intercept)  1.10548    0.22737  4.8621 9.444e-05 ***
#> c:(Intercept)  0.64966    0.18978  3.4231  0.002694 ** 
#> d:(Intercept)  8.07122    0.35994 22.4239 1.268e-15 ***
#> e:(Intercept)  3.06924    0.19638 15.6290 1.126e-12 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error:
#> 
#>  0.5527393 (20 degrees of freedom)

## 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