statforbiology (version 0.9.9)

SSpowerCurve: Power curve equation

Description

These functions provide the Power curve equation, that is also known as the Freundlich equation and it is very used in agricultural chemistry, e.g. to model the sorption of xenobiotics in soil. It is also used to model the number of plant species as a function of sampling area (Muller-Dumbois method). These functions provide the equation ('powerCurve.fun()') as well as the self-starters for the nls function ( 'NLS.powerCurve()' ) and for the drm function in the 'drc' package ('DRC.powerCurve()')

Usage

powerCurve.fun(predictor, a, b)
NLS.powerCurve(predictor, a, b)
DRC.powerCurve(fixed = c(NA, NA), names = c("a", "b"))

Value

powerCurve.fun() and NLS.powerCurve() return a numeric value, while DRC.powerCurve() returns 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

a

model parameter

b

model parameter

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

These functions provide the Power curve equation, that is parameterised as: $$ f(x) = a \, x^b $$ which is totally equivalent to an exponential curve on the logarithm of X: $$ f(x) = a \, \exp \left[ b \, \log(x) \right] $$ We see that both parameters relate to the ‘slope’ of the curve and b dictates its shape. If 0 < b < 1, the response Y increases as X increases and the curve is convex up. If b < 0 the curve is concave up and Y decreases as X increases. Otherwise, if b > 1, the curve is concave up and Y increases as X increases.

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

dataset <-getAgroData("speciesArea")

#nls fit
model <- nls(numSpecies ~ NLS.powerCurve(Area, a, b),
             data = dataset)
summary(model)
# drm fit
model <- drm(numSpecies ~ Area, fct = DRC.powerCurve(),
             data = dataset)
summary(model)