R: Mean function for the Gompertz dose-response or growth curve

gompertz {drc} | R Documentation

## Mean function for the Gompertz dose-response or growth curve

### 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

      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.

[Package drc version 3.0-1 Index]