drc (version 1.2-0)

CRS.5a: The Cedergreen-Ritz-Streibig model

Description

'CRS.5a', 'CRS.5b' and 'CRS.5c' provide the Cedergreen-Ritz-Streibig modified log-logistic model for describing (inverse u-shaped) hormesis. 'UCRS.5a', 'UCRS.5b' and 'UCRS.5c' provide the Cedergreen-Ritz-Streibig modified log-logistic model for describing u-shaped hormesis.

Usage

CRS.5a(names = c("b", "c", "d", "e", "f"))

  UCRS.5a(names = c("b", "c", "d", "e", "f"))

Arguments

names

a vector of character strings giving the names of the parameters. The default is reasonable (see above).

Value

• See cedergreen.

Details

The model is given by the expression $$f(x) = c + \frac{d-c+f \exp(-1/x^{\alpha})}{1+\exp(b(\log(x)-\log(e)))}$$ 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 $$f(x) = c + d - \frac{d-c+f \exp(-1/x^{\alpha})}{1+\exp(b(\log(x)-\log(e)))}$$ The a,b,c models are obtained by setting alpha equal to 1, 0.5 and 0.25, respectively.

References

See the reference under cedergreen.

See Also

Similar functions are CRS.4a and UCRS.4a, but with the lower limit fixed at 0 (one parameter less).

Examples

## Modified logistic model
model1 <- multdrc(hormesis[,c(2,1)], fct=CRS.5a())
summary(model1)
ED(model1, c(50))

model2 <- multdrc(hormesis[,c(2,1)], fct=CRS.5b())
summary(model2)
ED(model2, c(50))

model3 <- multdrc(hormesis[,c(2,1)], fct=CRS.5c())
summary(model3)
ED(model3, c(50))

rm(model1, model2, model3)