self start for a trilinear Function
Self starter for a tri-linear function with parameters a (intercept), b (first slope), xs1 (first break-point), c (second slope), xs2 (second break-point) and d (third slope)
trlin(x, a, b, xs1, c, xs2, d) SStrlin(x, a, b, xs1, c, xs2, d)
x |
input vector |
a |
the intercept |
b |
the first-phase slope |
xs1 |
first break-point of transition between first-phase linear and second-phase linear |
c |
the second-phase slope |
xs2 |
second break-point of transition between second-phase linear and third-phase linear |
d |
the third-phase slope |
This is a special case with just three parts (and two break points) but a more general approach is to consider a segmented function with several breakpoints and linear segments. Splines would be even more general. Also this model assumes that there are two break-points that needs to be estimated. The guess for the initial values splits the dataset in half, so it this will work when one break-point is in the first half and the second is in the second half.
a numeric vector of the same length as x containing parameter estimates for equation specified
trlin: vector of the same length as x using the tri-linear function
package segmented.
require(ggplot2) set.seed(1234) x <- 1:30 y <- trlin(x, 0.5, 2, 10, 0.1, 20, 1.75) + rnorm(30, 0, 0.5) dat <- data.frame(x = x, y = y) fit <- nls(y ~ SStrlin(x, a, b, xs1, c, xs2, d), data = dat) ## plot ggplot(data = dat, aes(x = x, y = y)) + geom_point() + geom_line(aes(y = fitted(fit))) ## Minimal example ## This is probably about the smallest dataset you ## should use with this function dat2 <- data.frame(x = 1:8, y = c(1.1, 1.9, 3.1, 2.5, 1.4, 0.9, 2.2, 2.9)) fit2 <- nls(y ~ SStrlin(x, a, b, xs1, c, xs2, d), data = dat2) ## expangin for plotting ndat <- data.frame(x = seq(1, 8, by = 0.1)) ndat$prd <- predict(fit2, newdata = ndat) ggplot() + geom_point(data = dat2, aes(x = x, y = y)) + geom_line(data = ndat, aes(x = x, y = prd))
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