This function provides a very general way of specifying the mean function of the decreasing or incresing Gompertz dose-response or growth curve models.
gompertz(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"),
method = c("1", "2", "3", "4"), ssfct = NULL,
fctName, fctText)The value returned is a list containing the non-linear function, the self starter function and the parameter names.
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.
Seber, G. A. F. and Wild, C. J. (1989) Nonlinear Regression, New York: Wiley and Sons (p. 331).
The Weibull model weibull2 is closely related to the Gompertz model.