drc (version 1.3-0)

braincousens: The Brain-Cousens hormesis models

Description

'braincousens' provides a very general way of specifying Brain-Cousens' modified log- logistic model for describing hormesis, 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)

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.

Value

• The value returned is a list containing the non-linear function, the self starter function, the parameter names and additional model specific objects.

concept

hormesis hormetic effect initial stimulation

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.

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

A special case of the function 'braincousens' is BC.4.

Examples

## Brain-Cousens model with the constraint b>1
model1 <- multdrc(ryegrass, 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(ryegrass, 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)