unitran {resde}

Unified transformation

Description

Calculates a variable transformation that produces various growth curve models, depending on the values of two shape parameters, alpha and beta. Models can also be specified by name. Uses bc(), bc_inv(), bc_prime().

Usage

unitran(x, name=NULL, par=NULL, alpha=NULL, beta=NULL, reverse="auto")

unitran_inv(y, name=NULL, par=NULL, alpha=NULL, beta=NULL, reverse="auto")

unitran_prime(x, name=NULL, par=NULL, alpha=NULL, beta=NULL, reverse="auto")

Arguments

x, y

Variable to be transformed, x must be between 0 and 1.

name

Optional model name, case-insensitive, in quotes. One of Richards, monomolecular, Mitscherlich, Bertalanffy, Gompertz, logistic, Levacovic, Weibull, Korf, exponential, Schumacher, Hosfeld.

par

Model parameter, if needed and model name supplied.

alpha, beta

Shape parameters, if the model is not specified by name.

reverse

Reverse x and t axes? One of "yes", "no", "auto". With "auto", axes are reversed as necessary for an upper asymptote. (i.e., if alpha <= 0 and beta > 0).

Value

unitran(): Transformed x, i.e., y = \varphi(x).

unitran_inv(): Inverse of unitran(), x = \varphi^{-1}(y).

unitran_prime(): Derivative of unitran(), y' = \varphi'(x).

Functions

• unitran(): Unified transformation.

• unitran_inv(): Inverse of unitran().

• unitran_prime(): Derivative of unitran() with respect to x.

Examples

curve(unitran(x, "Gompertz"))  # same as unitran(x, alpha=0, beta=0)
curve(unitran_inv(y, "logistic"), xname="y", from=-4, to=4)
curve(unitran_prime(x, "logistic"))