'braincousens' provides a very general way of specifying Brain-Cousens' modified log- logistic model for describing hormesis, under various constraints on the parameters.
braincousens(fixed = c(NA, NA, NA, NA, NA),
names = c("b", "c", "d", "e", "f"),
method = c("1", "2", "3", "4"), ssfct = NULL,
fctName, fctText)The value returned is a list containing the non-linear function, the self starter function, the parameter names and additional model specific objects.
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.
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').
character string indicating the self starter function to use.
a self starter function to be used.
optional character string used internally by convenience functions.
optional character string used internally by convenience functions.
Christian Ritz
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 proposed by Brain and Cousens (1989).
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.