BC.5 {drc} | R Documentation |
'BC.4' and 'BC.5' provide the Brain-Cousens modified log-logistic models for describing u-shaped hormesis.
BC.5(fixed = c(NA, NA, NA, NA, NA), names = c("b", "c", "d", "e", "f")) BC.4(fixed = c(NA, NA, NA, NA), names = c("b", "d", "e", "f"))
fixed |
numeric vector specifying which parameters are fixed and at which values they are fixed. NAs designate parameters that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is reasonable. |
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 log-logistic curve to take u-shaped hormesis into account.
Fixing the lower limit at 0 yields the four-parameter model
f(x) = 0 + frac{d-0+fx}{1+exp(b(log(x)-log(e)))}
See braincousens
.
This function is for use with the function drm
.
Christian Ritz
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.
van Ewijk, P. H. and Hoekstra, J. A. (1993) Calculation of the EC50 and its Confidence Interval When Subtoxic Stimulus Is Present, Ecotoxicology and Environmental Safety, 25, 25–32.
More details are found for the general model function braincousens
.
## Fitting the data in van Ewijk and Hoekstra (1993) lettuce.bcm1 <- drm(weight ~ conc, data = lettuce, fct=BC.5()) modelFit(lettuce.bcm1) plot(lettuce.bcm1) lettuce.bcm2 <- drm(weight ~conc, data = lettuce, fct=BC.4()) summary(lettuce.bcm2) ED(lettuce.bcm2, c(50)) # compare the parameter estimate and # its estimated standard error # to the values in the paper by # van Ewijk and Hoekstra (1993) ## Brain-Cousens model with the constraint b>3 ryegrass.bcm1 <- drm(rootl ~conc, data = ryegrass, fct = BC.5(), lower = c(3, -Inf, -Inf, -Inf, -Inf), control = drmc(constr=TRUE)) summary(ryegrass.bcm1) ## Brain-Cousens model with the constraint f>0 ## (no effect as the estimate of f is positive anyway) ryegrass.bcm2 <- drm(rootl ~conc, data = ryegrass, fct = BC.5(), lower = c(-Inf, -Inf, -Inf, -Inf, 0), control = drmc(constr=TRUE)) summary(ryegrass.bcm2)