biometrics (version 1.0.3)

asymreg.fx: Function to compute the result of the asymptotic regression model, as an allometric functional form.

Description

Function of the asymptotic regression model, based upon its parameters and a variable, as follows $$y_i= \alpha + \left(\beta-\alpha\right) \left\{\mathrm{e}^{ \left[-\left(\mathrm{e}^{-\gamma}\right) x_i \right] }\right\}, $$ 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).

Usage

asymreg.fx(x, a = alpha, b = beta, phi = 0)

Value

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

Arguments

x

is the predictor variable.

a

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

b

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

phi

is an optional constant term that force the prediction of y when x=0. Thus, the new model becomes \( y_i = \alpha + \left(\phi-\alpha\right) \left\{\mathrm{e}^{ \left[-\left(\mathrm{e}^{-\beta}\right) x_i \right] }\right\} \), thus the model will have only two parameters. By default \(\phi\) is set to 0.

Author

Christian Salas-Eljatib.

References

• Pinheiro JC, DM Bates. 2000. Mixed-effects Models in S and Splus. New York, USA. Springer-Verlag. 528 p.

• 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

#---------------------
# 2-parameters variant
# Predictor variable values to be used
time<-seq(0,50,by=0.1)
# Using the function, phi must be provided
y<-asymreg.fx(x=time,a=20,b=2.5,phi =5)
plot(time,y,type="l",ylim=c(0,20))