drc (version 0.8-2)

gompertz: The Gompertz (Weibull) function

Description

'gompertz' provides a very general way of specifying Gompertz/Weibull dose response functions, under various constraints on the parameters.

Usage

gompertz(lowerc = c(-Inf, -Inf, -Inf, -Inf),
         upperc = c(Inf, Inf, Inf, Inf), 
         fixed = c(NA, NA, NA, NA), 
         names = c("b", "c", "d", "e"), useDer = FALSE)

Arguments

lowerc

numeric vector. The lower bound on parameters. Default is minus infinity.

upperc

numeric vector. The upper bound on parameters. Default is plus infinity.

fixed

numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.

names

a vector of character strings giving the names of the parameters (should not contain ":"). The default is reasonable (see under 'Usage'). The order of the parameters is: b, c, d, e (see under 'Details').

useDer

logical. If TRUE derivatives are supplied, otherwise they are not supplied. Not yet implemented!

Value

• The value returned by the 'gompertz' is a list with the following components
• fct
  The dose response function.
• ssfct
  The self starter function.
• deriv1
  The first derivative.
• deriv2
  The second derivative.
• lowerc
  The lower bounds on the parameters.
• upperc
  The upper bounds on the parameters.
• edfct
  The ED function.
• sifct
  The SI function.

Details

The default arguments yield a four-parameter Gompertz model $$f(x) = c + (d-c) \exp(-\exp(b(\log(x)-e))).$$ The function is asymmetric about the inflection point, that is the parameter $\exp(e)$. Due to the parameterisation used, fitting a Gompertz model may be more robust than fitting a logistic model.

References

Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley & Sons (pp. 330--331).

See Also

Special cases of the function 'gompertz' are g3 and g4.

Examples

## A four-parameter Gompertz model with b fixed at 1
model1 <- multdrc(FA, fct=gompertz(fixed=c(1, NA, NA, NA)))
summary(model1)

## A four-parameter Gompertz model with the constraint b>3
model2 <- multdrc(FA, fct=gompertz(lowerc=c(3, -Inf, -Inf, -Inf)), control=mdControl(constr=TRUE))
summary(model2)

rm(model1, model2)