Log-normal dose-response model

lnormal provides a general framework for specifying the mean function of the decreasing or increasing log-normal dose-response model.

Usage

lnormal(
  fixed = c(NA, NA, NA, NA),
  names = c("b", "c", "d", "e"),
  method = c("1", "2", "3", "4"),
  ssfct = NULL,
  fctName,
  fctText,
  loge = FALSE
)

Arguments

fixed: numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameters that are not fixed.
names: vector of character strings giving the names of the parameters (should not contain ":"). The order of the parameters is: b, c, d, e.
method: character string indicating the self starter function to use.
ssfct: a self starter function to be used.
fctName: optional character string used internally by convenience functions.
fctText: optional character string used internally by convenience functions.
loge: logical indicating whether or not ED50 or log(ED50) should be a parameter in the model. By default ED50 is a model parameter.

Value

A list containing the non-linear function, the self starter function and the parameter names.

Details

For the case where log(ED50) is a parameter in the model, the mean function is: $$f(x) = c + (d-c)(\Phi(b(\log(x)-e)))$$ and in case ED50 is a parameter: $$f(x) = c + (d-c)(\Phi(b(\log(x)-\log(e))))$$

For $c=0$ and $d=1$, the model reduces to the classic probit model.

References

Finney, D. J. (1971) Probit analysis, London: Cambridge University Press.

Bruce, R. D. and Versteeg, D. J. (1992) A statistical procedure for modeling continuous toxicity data, Environ. Toxicol. Chem., 11, 1485–1494.

Author

Christian Ritz