R: The Cedergreen-Ritz-Streibig model

CRS.4a {drc} | R Documentation

## The Cedergreen-Ritz-Streibig model

### 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

      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

    ## 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))

[Package drc version 3.0-1 Index]