CRS.5a {drc}R Documentation

The Cedergreen-Ritz-Streibig model

Description

'CRS.5a', 'CRS.5b' and 'CRS.5c' provide the Cedergreen-Ritz-Streibig modified log-logistic model for describing (inverse u-shaped) hormesis.

'UCRS.5a', 'UCRS.5b' and 'UCRS.5c' provide the Cedergreen-Ritz-Streibig modified log-logistic model for describing u-shaped hormesis.

Usage

  CRS.5a(names = c("b", "c", "d", "e", "f"))

  UCRS.5a(names = c("b", "c", "d", "e", "f"))

Arguments

names a vector of character strings giving the names of the parameters. The default is reasonable (see above).

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.

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^{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.

Value

See cedergreen.

Note

This function is for use with the function drm.

Author(s)

Christian Ritz

References

See the reference under cedergreen.

See Also

Similar functions are CRS.4a and UCRS.4a, but with the lower limit fixed at 0 (one parameter less).

Examples


## Modified logistic model
lettuce.m1 <- drm(lettuce[,c(2,1)], fct=CRS.5a())
summary(lettuce.m1)
ED(lettuce.m1, c(50))

lettuce.m2 <- drm(lettuce[,c(2,1)], fct=CRS.5b())
summary(lettuce.m2)
ED(lettuce.m2, c(50))

lettuce.m3 <- drm(lettuce[,c(2,1)], fct=CRS.5c())
summary(lettuce.m3)
ED(lettuce.m3, c(50))


[Package drc version 1.6-1 Index]