SSratio: self start for a rational curve

In nlraa: Nonlinear Regression for Agricultural Applications

self start for a rational curve

Description

Self starter for a rational curve

Usage

ratio(x, a, b, c, d)

SSratio(x, a, b, c, d)

Arguments

x	input vector
a	parameter related to the maximum value of the response (numerator)
b	power exponent for numerator
c	parameter related to the maximum value of the response (denominator)
d	power exponent for denominator

Details

The equation is:

a * x ^ c / (1 + b * x ^ d)

This function is described in Archontoulis and Miguez (2015) - (doi:10.2134/agronj2012.0506). One example application is in Bril et al. (1994) https://edepot.wur.nl/333930 - pages 19 and 21. The parameters are difficult to interpret, but the function is very flexible. I have not tested this, but it might be beneficial to re-scale x and y to the (0,1) range if this function is hard to fit. https://en.wikipedia.org/wiki/Rational_function.

Value

a numeric vector of the same length as x containing parameter estimates for equation specified

ratio: vector of the same length as x using a rational function

Examples

require(ggplot2)
require(minpack.lm)
set.seed(1234)
x <- 1:100
y <- ratio(x, 1, 0.5, 1, 1.5) + rnorm(length(x), 0, 0.025)
dat <- data.frame(x = x, y = y)
fit <- nlsLM(y ~ SSratio(x, a, b, c, d), data = dat)
## plot
ggplot(data = dat, aes(x = x, y = y)) + 
  geom_point() + 
  geom_line(aes(y = fitted(fit)))

nlraa documentation built on Aug. 21, 2025, 5:59 p.m.