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.