SSnegExp: Negative exponential functions

In OnofriAndreaPG/aomisc: Statistical methods for the agricultural sciences

Negative exponential functions

Description

These functions provide the negative exponential model (negExp.fun) with the related self-starters for the nls function (NLS.negExp) drm function in the 'drc' package (DRC.negExp) and the exponential cumulative distribution function (negExpDist.fun), with self-starters for both 'nls' (NLS.negExpDist) and 'drc' (DRC.negExpDist).

Usage

  negExp.fun(predictor, a, c)
  negExpDist.fun(predictor, c)
  NLS.negExp(predictor, a, c)
  DRC.negExp(fixed = c(NA, NA), names = c("a", "c"))
  NLS.negExpDist(predictor, c)
  DRC.negExpDist(fixed = NA, names = c("c"))

Arguments

predictor	a numeric vector of values at which to evaluate the model.
a	a numeric parameter representing the higher asymptote
c	a numeric parameter that is proportional to the relative rate of increase of the fitted function
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. The default is reasonable.

Details

The negative exponential model is given by the following function:

f(x) = \textrm{a} \{1 - \exp [- \exp( c x )] \}

while the exponential CDF is obtained by setting a = 1:

f(x) = 1 - \exp [- \exp( c x )]

The ‘drc’ package contains also the function AR.2(), where c is replaced by e = 1/c. The ‘nlme’ package also contains an alternative parameterisation named 'SSasympOrig()', where c is replaced by ϕ3 = log(c).

Value

negExp.fun and negExpDist.fun return a numeric value, while the self-starters return a list containing the nonlinear function, the self starter function and the parameter names.

Author(s)

Andrea Onofri

References

Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc. Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/

Examples

X <- c(1, 3, 5, 7, 9, 11, 13, 20)
Y <- c(4.5, 12.0, 16.1, 16.4, 18.9, 19.5, 19.3, 19.6)
model <- drm(Y ~ X, fct = DRC.negExp())
summary(model)

OnofriAndreaPG/aomisc documentation built on Feb. 26, 2024, 8:21 p.m.