The Cedergreen-Ritz-Streibig model
'CRS.4a', 'CRS.4b' and 'CRS.4c' provide the Cedergreen-Ritz-Streibig modified log-logistic model for describing hormesis with the lower limit equal to 0.
'UCRS.4a', 'UCRS.4b' and 'UCRS.4c' provide the Cedergreen-Ritz-Streibig modified log-logistic model for describing u-shaped hormesis with the lower limit equal to 0.
CRS.4a(names = c("b", "d", "e", "f"), ...)
UCRS.4a(names = c("b", "d", "e", "f"), ...)names |
a vector of character strings giving the names of the parameters. The default is reasonable (see above). |
... |
additional arguments to be passed from the convenience functions. |
The model is given by the expression
f(x) = 0 + \frac{d-0+f \exp(-1/x)}{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.
The u-shaped model is given by the expression
f(x) = 0 + d - \frac{d-0+f \exp(-1/x^{α})}{1+\exp(b(\log(x)-\log(e)))}
The a,b,c models are obtained by setting alpha equal to 1, 0.5 and 0.25, respectively.
See cedergreen.
This function is for use with the function drm.
Christian Ritz
See the reference under cedergreen.
## Fitting modified logistic models lettuce.crsm1 <- drm(lettuce[,c(2,1)], fct=CRS.4a()) summary(lettuce.crsm1) ED(lettuce.crsm1, c(50)) ## Need to explicitly specify that the upper limit ## is the reference in order to get ED10 and ED90 right ED(lettuce.crsm1, c(10, 50, 90), reference = "upper") lettuce.crsm2 <- drm(lettuce[,c(2,1)], fct=CRS.4b()) summary(lettuce.crsm2) ED(lettuce.crsm2, c(50)) lettuce.crsm3 <- drm(lettuce[,c(2,1)], fct=CRS.4c()) summary(lettuce.crsm3) ED(lettuce.crsm3, c(50))
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