'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.

1 2 3 |

`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. |

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.

See `cedergreen`

.

This function is for use with the function `drm`

.

Christian Ritz

See the reference under `cedergreen`

.

Similar functions are `CRS.5a`

and `UCRS.5a`

,
but with an extra parameter for the lower limit.

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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