mlogistic {drc} | R Documentation |
'mlogistic' provides a very general way of specifying Cedergreen-Ritz-Streibig's modified logistic dose response functions, under various constraints on the parameters.
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)
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! |
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.
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. |
This function is for use with the function multdrc
.
Christian Ritz
Cedergreen, N. and Ritz, C. and Streibig, J. C. (2005) Improved empirical models describing hormesis, To appear in ET&C.
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
## 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)