nlraa (version 1.9.7)

SSquadp3: self start for quadratic-plateau function

Description

Self starter for quadratic plateau function with (three) parameters a (intercept), b (slope), c (quadratic)

Usage

quadp3(x, a, b, c)
SSquadp3(x, a, b, c)

Value

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

quadp: vector of the same length as x using the quadratic-plateau function

Arguments

x

input vector

a

the intercept

b

the slope

c

quadratic term

Details

The equation is, for a response (y) and a predictor (x):
\(y ~ (x <= xs) * (a + b * x + c * x^2) + (x > xs) * (a + (-b^2)/(4 * c))\)

where the break-point (xs) is -0.5*b/c
and the asymptote is (a + (-b^2)/(4 * c))

In this model the parameter ‘xs’ is not directly estimated. If this is required, the model ‘SSquadp3xs’ should be used instead.

Examples

# \donttest{
require(ggplot2)
set.seed(123)
x <- 1:30
y <- quadp3(x, 5, 1.7, -0.04) + rnorm(30, 0, 0.6)
dat <- data.frame(x = x, y = y)
fit <- nls(y ~ SSquadp3(x, a, b, c), data = dat)
## plot
ggplot(data = dat, aes(x = x, y = y)) + 
  geom_point() + 
  geom_line(aes(y = fitted(fit)))
# }