U-shaped Cedergreen-Ritz-Streibig model

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

Usage

ucedergreen(
  fixed = c(NA, NA, NA, NA, NA),
  names = c("b", "c", "d", "e", "f"),
  method = c("loglinear", "anke", "method3", "normolle"),
  ssfct = NULL,
  alpha,
  fctName,
  fctText
)

Arguments

fixed: A numeric vector of length 5 specifying any parameters to be held fixed during the estimation. The order is c(b, c, d, e, f). Use NA for parameters that should be estimated. The default is to estimate all parameters.
names: A character vector of length 5 providing names for the parameters. The default is c("b", "c", "d", "e", "f").
method: A character string specifying the method for the self-starter function to use for finding initial parameter values. Options are "loglinear", "anke", "method3", and "normolle". This is only used if ssfct is NULL.
ssfct: A custom self-starter function. If NULL (the default), a self-starter is automatically generated by calling cedergreen.ssf with the specified method, fixed, and alpha arguments.
alpha: A mandatory numeric value specifying the fixed shape parameter $\alpha$. The function will stop if this is not provided.
fctName: An optional character string to name the function object.
fctText: An optional character string providing a descriptive text for the model.

Value

A list of class "UCRS", containing the model function (fct), the self-starter function (ssfct), parameter names (names), and other components required for use with modeling functions like drm.

Details

The u-shaped model is given by the expression $$f(x) = c + d - \frac{d-c+f \exp(-1/x^{\alpha})}{1+\exp(b(\log(x)-\log(e)))}$$

References

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

Author

Christian Ritz, Hannes Reinwald