nlraa (version 1.2)

SSlogis5: self start for five-parameter logistic function

Description

Self starter for a five-parameter logistic function.

Usage

logis5(x, asym1, asym2, xmid, iscal, theta)
SSlogis5(x, asym1, asym2, xmid, iscal, theta)

Value

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

logis5: vector of the same length as x (time) using the 5-parameter logistic

Arguments

x

input vector (x)

asym1

asymptotic value for low values of x

asym2

asymptotic value for high values of x

xmid

value of x at which y = (asym1 + asym2)/2 (only when theta = 1)

iscal

steepness of transition from asym1 to asym2 (inverse of the scale)

theta

asymmetry parameter, if it is equal to 1, this is the four parameter logistic

Details

The equation for this function is:

$$f(x) = asym2 + (asym1 - asym2)/(1 + exp(iscal * (log(x) - log(xmid))))^theta$$

This is known as the Richards' function or the log-logistic and it is described in Archontoulis and Miguez (2015) - (doi:10.2134/agronj2012.0506).

Examples

# \donttest{
require(ggplot2)
set.seed(1234)
x <- seq(0, 2000, 100)
y <- logis5(x, 35, 10, 800, 5, 2) + rnorm(length(x), 0, 0.5)
dat <- data.frame(x = x, y = y)
fit <- nls(y ~ SSlogis5(x, asym1, asym2, xmid, iscal, theta), data = dat)
## plot
ggplot(data = dat, aes(x = x, y = y)) + 
  geom_point() + 
  geom_line(aes(y = fitted(fit)))
# }
x <- seq(0, 2000)
y <- logis5(x, 30, 10, 800, 5, 2)
plot(x, y)