drc (version 1.0-3)

mlogistic: The modified logistic function

Description

For 'mlogistic' provides a very general way of specifying Cedergreen-Ritz-Streibig's modified logistic dose response functions, under various constraints on the parameters. For u-shaped hormesis data: 'umlogistic' 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)
  
  umlogistic(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!

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.

Details

The model is given by the expression $$f(x) = c + \frac{d-c+f exp(-1/(x^{\alpha}))}{1+exp(b(log(x)-log(e)))}$$ which is a five-parameter model (alpha is fixed). It is a modification of the four-parameter logistic curve to take hormesis into account. The u-shaped model is given by the expression $$f(x) = c + d - \frac{d-c+f \exp(-1/x^{\alpha})}{1+\exp(b(\log(x)-\log(e)))}$$

References

Cedergreen, N. and Ritz, C. and Streibig, J. C. (2005) Improved empirical models describing hormesis, Environmental Toxicology and Chemistry {24, 3166--3172. } [object Object] This function is for use with the function multdrc. Special cases of the function 'mlogistic' 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 ## 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) models nonlinear hormesis hormetic effect initial stimulation