mlogistic {drc}R Documentation

The modified logistic function

Description

'mlogistic' provides a very general way of specifying Cedergreen-Ritz-Streibig's modified logistic dose response functions, under various constraints on the parameters.

Usage

  mlogistic(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"), alpha, 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').
alpha numeric. The degree of hormesis. Needs to be specified!
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 model is given by the expression

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

which is a five-parameter model (

α

is fixed).

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

Value

The value returned by the 'mlogistic' 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

Cedergreen, N. and Ritz, C. and Streibig, J. C. (2005) Improved empirical models describing hormesis, To appear in ET&C.

See Also

Special cases of the function 'braincousens' are ml3a, ml3b, ml3c, ml4a, ml4b and ml4c where a,b and c denotes the pre-specified alpha values 1, 0.5 and 0.25, respectively

Examples


## Modified logistic model with the constraint f>0
model1 <- multdrc(hormesis[,c(2,1)], fct=mlogistic(fixed=c(NA, NA, NA, NA, NA), 
lowerc=c(-Inf, -Inf, -Inf, -Inf, 0), alpha=1), control=mdControl(constr=TRUE))
summary(model1)
ED(model1, c(10, 50, 90))

rm(model1)


[Package drc version 0.9-0 Index]