Mean function for the Gompertz dose-response or growth curve

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Description

This function provides a very general way of specifying the mean function of the decreasing or incresing Gompertz dose-response or growth curve models.

Usage

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

Arguments

fixed

numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter 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 (see under 'Details' for the precise meaning of each parameter).

method

character string indicating the self starter function to use.

ssfct

a self starter function to be used.

fctName

character string used internally by convenience functions (optional).

fctText

character string used internally by convenience functions (optional).

Details

The Gompertz model is given by the mean function

f(x) = c + (d-c)(\exp(-\exp(b(x-e))))

and it is a dose-response/growth curve on the entire real axis, that is it is not limited to non-negative values even though this is the range for most dose-response and growth data. One consequence is that the curve needs not reach the lower asymptote at dose 0.

If

b<0

the mean function is increasing and it is decreasing for

b>0

. The decreasing Gompertz model is not a well-defined dose-response model and other dose-response models such as the Weibull models should be used instead.

Various re-parameterisations of the model are used in practice.

Value

The value returned is a list containing the non-linear function, the self starter function and the parameter names.

Note

The function is for use with the function drm, but typically the convenience functions G.2, G.3, G.3u, and G.4 should be used.

Author(s)

Christian Ritz

References

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

See Also

The Weibull model weibull2 is closely related to the Gompertz model.

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