R: The Cedergreen-Ritz-Streibig model

cedergreen {drc} | R Documentation

## The Cedergreen-Ritz-Streibig model

### Description

'cedergreen' provides a very general way of specifying then Cedergreen-Ritz-Streibig modified log-logistic model for describing hormesis, under various constraints on the parameters.

`CRS.6` is the extension of `link{cedergreen}` with freely varying alpha parameter.

For u-shaped hormesis data 'ucedergreen' provides a very general way of specifying the Cedergreen-Ritz-Streibig modified log-logistic model, under various constraints on the parameters.

### Usage

      cedergreen(fixed = c(NA, NA, NA, NA, NA),
      names = c("b", "c", "d", "e", "f"),
      method = c("1", "2", "3", "4"), ssfct = NULL,
      alpha, fctName, fctText)

      CRS.6(fixed = c(NA, NA, NA, NA, NA, NA),
      names = c("b","c","d","e","f","g"),
      method = c("1", "2", "3", "4"), ssfct = NULL)

      ucedergreen(fixed = c(NA, NA, NA, NA, NA),
      names = c("b", "c", "d", "e", "f"),
      method = c("1", "2", "3", "4"), ssfct = NULL,
      alpha)

### Arguments

`fixed` | numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.
`names` | a vector of character strings giving the names of the parameters (should not contain ":"). The order of the parameters is: b, c, d, e, f (see under 'Details').
`method` | character string indicating the self starter function to use.
`ssfct` | a self starter function to be used.
`alpha` | numeric value between 0 and 1, reflecting the steepness of the hormesis peak. This argument needs to be specified.
`fctName` | optional character string used internally by convenience functions.
`fctText` | optional character string used internally by convenience functions.

### 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 (alpha is fixed or freely varying). Not all features (eg EC/ED calculation) are available for the model with freely varying alpha.

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) = cd - \frac{d-c+f \exp(-1/x^{α})}{1+\exp(b(\log(x)-\log(e)))}

### Value

The value returned is a list containing the non-linear function, the self starter function and the parameter names.

### Note

The functions are for use with the functions `drm`.

### Author(s)

Christian Ritz

### References

Cedergreen, N. and Ritz, C. and Streibig, J. C. (2005) Improved empirical models describing hormesis, Environmental Toxicology and Chemistry 24, 3166–3172.

### See Also

For fixed alpha, several special cases are handled by the following convenience functions `CRS.4a`, `CRS.4b`, `CRS.4c`, `CRS.5a`, `CRS.5b`, `CRS.5c`, `UCRS.4a`, `UCRS.4b`, `UCRS.4c`, `UCRS.5a`, `UCRS.5b`, `UCRS.5c` where a, b and c correspond to the pre-specified alpha values 1, 0.5 and 0.25, respectively.

### Examples

    ## Estimating CRS model with alpha unknown
    lettuce.crsm1 <- drm(weight~conc, data = lettuce, fct = CRS.6())
    summary(lettuce.crsm1)
    plot(lettuce.crsm1)  # oops: not increasing until hormesis peak

[Package drc version 3.0-1 Index]