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wenjie2wang / splines2

Regression Spline Functions and Classes
https://wwenjie.org/splines2
GNU General Public License v3.0
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Can boundary knots be specified with multiplicities? #1

Closed mihaiconstantin closed 4 years ago

mihaiconstantin commented 4 years ago

This may not be the best place to ask this question. I apologize for that.

I would appreciate it if you can help me understand a use case scenario regarding the boundary_knots.

Is it possible to define an extended partition (i.e., by specifying some knots with multiplicities)? I a nutshell, I am interested to see if splines2 can account for the following scenario (https://rpubs.com/deleeuw/268327):

Splines Extended Parition

Looking at the code of clean_knots() in class SplineBase, I believe this is not possible since only unique elements are retained after executing arma::unique(boundary_knots).

https://github.com/wenjie2wang/splines2/blob/1de1d904bc6c48fdaa6a7e8806e3e3d8ea6206c2/inst/include/splines2Armadillo/SplineBase.h#L81-L89

Is there a workaround for this, or am I missing something?

P.S. Thanks for this great package! :)

wenjie2wang commented 4 years ago

I am glad that you ask a question here. It would be of help to other users having similar questions.

By the definition of knot sequence, each boundary knot is repeated m times, where m represents the order of spline basis. Given specified boundary knots and order, the generation of such a knot sequence is done internally in splines2 so that users can simply specify the range to anchor the splines via boundary_knots without generating the knot sequence on their own. In contrast, splines::splineDesign() requires users to specify the knot sequence. The difference is clear in the following example.

library(splines)
library(splines2)

x <- seq.int(0, 1, 0.01)
degree <- 3
ord <- degree + 1
knots <- seq.int(0.1, 0.9, 0.1)
b_knots <- range(x)
all_knots <- sort(c(knots, rep(b_knots, ord)))

out1 <- splineDesign(x, knots = all_knots, ord = ord)
out2 <- bSpline(x, knots = knots, degree = degree,
                intercept = TRUE, Boundary.knots = b_knots)
all.equal(out1, out2, check.attributes = FALSE)
mihaiconstantin commented 4 years ago

Hi @wenjie2wang,

Thank you very much for the prompt and detailed response! This not only answers my question but also helps me clarify a couple of things. I hope it will also be helpful to others as well.

Do you want me to close the 'issue'?

wenjie2wang commented 4 years ago

My pleasure. Glad to hear that it helps. I can close this issue.