ratkow.fx: Function that computes the result of the Ratkowsky allometric...

In biometrics: A Package for Biometrics and Modelling

Function that computes the result of the Ratkowsky allometric model.

Description

Function of the Ratkowsky allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

y_i= \alpha \mathrm{e}^{\left(\frac{-\beta}{x_i +\gamma}\right)},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients). Further details on this function can be found in Salas-Eljatib (2025).

Usage

ratkow.fx(x, alpha, beta, gamma, upsilon = 0)

Arguments

x	is the predictor variable.
alpha	is the coefficient-parameter \alpha.
beta	is the coefficient-parameter \beta.
gamma	is the coefficient-parameter \gamma.
upsilon	is an optional constant term that force the prediction of y when x=0. Thus, the new model becomes y_i = \Upsilon+ f(x_i,\mathbf{\theta}), where \mathbf{\theta} is the vector of coefficients of the above described function represented by f(\cdot). The default value for \Upsilon is 0.

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Zhang L. 1997. Cross-validation of non-linear growth functions for modelling tree height-diameter relationships. Annals of Botany 79(3):251–257.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
d<-seq(5,60,by=0.01)
# Using the function
h<-ratkow.fx(x=d,alpha=28,beta=34,gamma=.85)
plot(d,h,type="l")
 

biometrics documentation built on March 20, 2026, 5:09 p.m.