dear all,
I apologize for my delay in replying you. Here my contribution, maybe
just for completeness:
Similar to "earth", "segmented" also fits piecewise linear relationships
with the number of breakpoints being selected by the AIC or BIC
(recommended).
#code (example and code from Martin Maechler previous email)
library(segmented)
o<-selgmented(y, ~x, Kmax=20, type="bic", msg=TRUE)
plot(o, add=TRUE)
lines(o, col=2) #the approx CI for the breakpoints
confint(o) #the estimated breakpoints (with CI's)
slope(o) #the estimated slopes (with CI's)
However segmented appears to be less efficient than earth (although with
reasonable running times), it does NOT work with multivariate responses
neither products between piecewise linear terms.
kind regards,
Vito
Il 16/07/2024 11:22, Martin Maechler ha scritto:
Anupam Tyagi
on Tue, 9 Jul 2024 16:16:43 +0530 writes:
> How can I do automatic knot selection while fitting piecewise linear
> splines to two variables x and y? Which package to use to do it simply? I
> also want to visualize the splines (and the scatter plot) with a graph.
> Anupam
NB: linear splines, i.e. piecewise linear continuous functions.
Given the knots, use approx() or approxfun() however, the
automatic knots selection does not happen in the base R packages.
I'm sure there are several R packages doing this.
The best such package in my opinion is "earth" which does a
re-implementation (and extensive *generalization*) of the
famous MARS algorithm of Friedman.
==> https://en.wikipedia.org/wiki/Multivariate_adaptive_regression_splines
Note that their strengths and power is that they do their work
for multivariate x (MARS := Multivariate Adaptive Regression
Splines), but indeed do work for the simple 1D case.
In the following example, we always get 11 final knots,
but I'm sure one can tweak the many tuning paramters of earth()
to get more:
## Can we do knot-selection for simple (x,y) splines? === Yes, via earth()
{using MARS}!
x <- (0:800)/8
f <- function(x) 7 * sin(pi/8*x) * abs((x-50)/20)^1.25 - (x-40)*(12-x)/64
curve(f(x), 0, 100, n = 1000, col=2, lwd=2)
set.seed(11)
y <- f(x) + 10*rnorm(x)
m.sspl <- smooth.spline(x,y) # base line "standard smoother"
require(earth)
fm1 <- earth(x, y) # default settings
summary(fm1, style = "pmax") #-- got 10 knots (x = 44 "used twice") below
## Call: earth(x=x, y=y)
## y =
## 175.9612
## - 10.6744 * pmax(0, x - 4.625)
## + 9.928496 * pmax(0, x - 10.875)
## - 5.940857 * pmax(0, x - 20.25)
## + 3.438948 * pmax(0, x - 27.125)
## - 3.828159 * pmax(0, 44 - x)
## + 4.207046 * pmax(0, x - 44)
## + 2.573822 * pmax(0, x - 76.5)
## - 10.99073 * pmax(0, x - 87.125)
## + 10.97592 * pmax(0, x - 90.875)
## + 9.331949 * pmax(0, x - 94)
## - 8.48575 * pmax(0, x - 96.5)
## Selected 12 of 12 terms, and 1 of 1 predictors
## Termination condition: Reached nk 21
## Importance: x
## Number of terms at each degree of interaction: 1 11 (additive model)
## GCV 108.6592 RSS 82109.44 GRSq 0.861423 RSq 0.86894
fm2 <- earth(x, y, fast.k = 0) # (more extensive forward pass)
summary(fm2)
all.equal(fm1, fm2)# they are identical (apart from 'call'):
fm3 <- earth(x, y, fast.k = 0, pmethod = "none", trace = 3) # extensive forward
pass; *no* pruning
## still no change: fm3 "==" fm1
all.equal(predict(fm1, xx), predict(fm3, xx))
## BTW: The chosen knots and coefficients are
mat <- with(fm1, cbind(dirs, cuts=c(cuts), coef = c(coefficients)))
## Plots : fine grid for visualization: instead of xx <- seq(x[1],
x[length(x)], length.out = 1024)
rnx <- extendrange(x) ## to extrapolate a bit
xx <- do.call(seq.int, c(rnx, list(length.out = 1200)))
cbind(f = f(xx),
sspl = predict(m.sspl, xx)$y,
mars = predict(fm1, xx)) -> fits
plot(x,y, xlim=rnx, cex = 1/4, col = adjustcolor(1, 1/2))
cols <- c(adjustcolor(2, 1/3),
adjustcolor(4, 2/3),
adjustcolor("orange4", 2/3))
lwds <- c(3, 2, 2)
matlines(xx, fits, col = cols, lwd = lwds, lty=1)
legend("topleft", c("true f(x)", "smooth.spline()", "earth()"),
col=cols, lwd=lwds, bty = "n")
title(paste("earth() linear spline vs. smooth.spline(); n =", length(x)))
mtext(substitute(f(x) == FDEF, list(FDEF = body(f))))
______________________________________________
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
--
=================================================
Vito M.R. Muggeo, PhD
Professor of Statistics
Dip.to Sc Econom, Az e Statistiche
Università di Palermo
viale delle Scienze, edificio 13
90128 Palermo - ITALY
tel: 091 23895240; fax: 091 485726
http://www.unipa.it/persone/docenti/m/vito.muggeo
Associate Editor: Statistical Modelling
past chair, Statistical Modelling Society
coordinator, PhD Program in Econ, Businss, Statist
______________________________________________
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
