biometrics (version 1.0.3)

ogawa.fx: Function that computes the result of the Ogawa allometric model.

Description

Function of the Ogawa allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression $$\frac{1}{y_i}= \frac{1}{\alpha} + \frac{1}{\beta {x_i}^{\gamma}}, $$ 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

ogawa.fx(x, alpha, beta, gamma, phi = 0)

Value

Returns the inverse of the response variable based upon the predictor variable and the coefficients shown above.

Arguments

x

is the predictor variable.

alpha

is the coefficient-parameter \(\alpha\).

beta

is the coefficient-parameter \(\beta\).

gamma

is the coefficient-parameter \(\gamma\).

phi

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

Author

Christian Salas-Eljatib.

References

• Kohyama T, T Hara, T Tadaki. 1990. Patterns of trunk diameter, tree height and crown depth in crowded abies stands. Annals of Botany 65(5):567–574.

• Salas-Eljatib C. 2026. 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. 53 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
d<-ogawa.fx(x=time,alpha=22,beta=0.013,gamma=1.13)
plot(time,d,type="l")