self start for quadratic-plateau function
Self starter for quadratic plateau function with (three) parameters a (intercept), b (slope), c (quadratic)
quadp3(x, a, b, c) SSquadp3(x, a, b, c)
x |
input vector |
a |
the intercept |
b |
the slope |
c |
quadratic term |
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 -b/c
and the asymptote is (a + (-b^2)/(4 * c))
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
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)))
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