# CRS.4a: 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

 1 2 3  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.

Christian Ritz

### References

See the reference under cedergreen.

Similar functions are CRS.5a and UCRS.5a, but with an extra parameter for the lower limit.

### Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ## 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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