braincousens {drc}R Documentation

The Brain-Cousens modification of the logistic function

Description

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

Usage

  braincousens(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 Brain-Cousens model is given by the expression

f(x) = c + frac{d-c+fx}{1+exp(b(log(x)-log(e)))}

which is a five-parameter model.

It is a modification of the four-parameter logistic curve to take hormesis into account.

Value

The value returned by the 'braincousens' 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 ED function.
sifct The SI function.
maxfct The function for calculating the mean maximum of the dose response curve.

Note

This function is for use with the function multdrc.

Author(s)

Christian Ritz

References

Brain, P. and Cousens, R. (1989) An equation to describe dose responses where there is stimulation of growth at low doses, Weed Research, 29, 93–96.

See Also

Special cases of the function 'braincousens' are bcl3 and bcl4.

Examples


## Brain-Cousens model with the constraint b>1
model1 <- multdrc(FA, fct=braincousens(fixed=c(NA, NA, NA, NA, NA), 
lowerc=c(1, -Inf, -Inf, -Inf, -Inf)), control=mdControl(constr=TRUE))

summary(model1)

## Brain-Cousens model with the constraint f>0
model2 <- multdrc(FA, fct=braincousens(fixed=c(NA, NA, NA, NA, NA), 
lowerc=c(-Inf, -Inf, -Inf, -Inf, 0)), control=mdControl(constr=TRUE))

summary(model2)
rm(model1, model2)


[Package drc version 0.9-0 Index]