The Cedergreen-Ritz-Streibig model

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Description

'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.

Usage

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  CRS.4a(names = c("b", "d", "e", "f"), ...)

  UCRS.4a(names = c("b", "d", "e", "f"), ...)

Arguments

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.

Details

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.

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.5a and UCRS.5a, but with an extra parameter for the lower limit.

Examples

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## 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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