statforbiology (version 0.9.9)

SSE: Modified Gompertz equations

Description

These functions provide the modified Gompertz equations with 4 (E4.fun), 3 (E3.fun) and 2 (E2.fun) parameters with self-starter for the nls function (NLS.E4, NLS.E3 and NLS.E2) and for the drm function in the 'drc' package (DRC.E4, DRC.E3 and DRC.E2).

Usage

E4.fun(predictor, b, c, d, e)
E3.fun(predictor, b, d, e)
E2.fun(predictor, b, e)
NLS.E4(predictor, b, c, d, e)
NLS.E3(predictor, b, d, e)
NLS.E2(predictor, b, e)
DRC.E4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"))
DRC.E3(fixed = c(NA, NA, NA), names = c("b", "d", "e"))
DRC.E2(fixed = c(NA, NA), names = c("b", "e"))

Value

E4.fun, E3.fun, E2.fun, NLS.E4, NLS.E3 and NLS.E2 return a numeric value, while DRC.E4, DRC.E3 and DRC.E2 return a list containing the nonlinear function, the self starter function and the parameter names.

Arguments

predictor

a numeric vector of values at which to evaluate the model

b

model parameter (slope at inflection point)

c

model parameter (lower asymptote)

d

model parameter (higher asymptote)

e

model parameter (abscissa at inflection point)

fixed

numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.

names

names. A vector of character strings giving the names of the parameters. The default is reasonable.

Author

Andrea Onofri

Details

The modified Gompertz equation is parameterised as: $$ f(x) = c + (d - c) \, (1 - \exp \left[-exp( b (x - e))) \right] $$ It is a sygmoidally shaped curve and it is asymmetric about its inflection point, but the type of asymmetry is different from the Gompertz equation. For the 3- and 2-parameter model c is equal to 0, while for the 2-parameter model d is equal to 1.

Examples

data(beetGrowth)
mod3 <- nls(weightInf ~ NLS.E3(DAE, b, c, d), data = beetGrowth)
summary(mod3)
plot(mod3)