logistic {drc}R Documentation

The logistic function

Description

'logistic' provides a very general way of specifying logistic dose response functions, under various constraints on the parameters.

Usage

  logistic(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"), scaleDose = TRUE, useDer = FALSE)

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').
scaleDose logical. If TRUE dose values are scaled around 1 during estimation; this is required for datasets where all dose values are small.
useDer logical. If TRUE derivatives are supplied, otherwise they are not supplied. Not yet implemented!

Details

The default arguments yields the five-parameter 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.

Value

The value returned is a list with the following components

fct The dose response function.
ssfct The self starter function.
deriv1 The first derivative.
deriv2 The second derivative.
lowerc The lower bounds on the parameters.
upperc The upper bounds on the parameters.
edfct The function used to calculate ED values.
sifct The function used to calculate SI values.

Note

The functions are for use with the function multdrc.

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 of the function 'logistic' are available: l2, l3, l4 and l5.

Examples


## A four-parameter logistic model with b fixed at 1
model1 <- multdrc(FA, fct=logistic(fixed=c(1, NA, NA, NA, 1)))
summary(model1)
## Can also be specified using the function 'l4(fixed=c(1,NA,NA,NA))'

## A four-parameter logistic model with the constraint b>3
model2 <- multdrc(FA, fct=logistic(fixed=c(NA, NA, NA, NA, 1), 
lowerc=c(3, -Inf, -Inf, -Inf, -Inf)), control=mdControl(constr=TRUE))
summary(model2)

rm(model1, model2)


[Package drc version 0.9-0 Index]