[R] Finding the knots in a smoothing spline using nknots

[David Winsemius]

On Feb 27, 2013, at 6:39 AM, Mike Nielsen wrote:

> Hi r-helpers.
> 
> Please forgive my ignorance, but I would like to plot a smoothing spline
> (smooth.spline) from package "stats", and show the knots in the plot, and I
> can't seem to figure out where smooth.spline has located the knots (when I
> use nknots).  Unfortunately, I don't know a lot about splines, but I know
> that they provide me an easy way to estimate the location of local maxima
> and minima on varying time-scales (number of knots) in my original data.
> 
> I see there is a fit$knot, but it's not clear to me what those values are:
> for some reason I had expected that they would be contained in my original
> y values, but they're not.

It appears they are in the range of [0-1] and the ss$fit$min and ss$fit$range provide the scaling data (.... for the x-values rather than the y-values):

> unique(ss$fit$knot)
 [1] 0.00000000 0.04095904 0.08291708 0.12487512 0.16583417 0.20779221 0.24975025 0.29070929
 [9] 0.33266733 0.37462537 0.41658342 0.45754246 0.49950050 0.54145854 0.58241758 0.62437562
[17] 0.66633367 0.70829171 0.74925075 0.79120879 0.83316683 0.87412587 0.91608392 0.95804196
[25] 1.00000000

I would think that in your case with x0 being 0 you could just use ss$fit$range*unique(ss$fit$knot) as your knot positions. In the more geneneral case you would need to add ss$fit$min. I tried confirming this hunch by looking "statiscal Models in S", inMASSe4, and at the R code but the R code calls a FORTRAN routine, so you would need to pull the source to confirm.

-- 
David.

>  I tried generating nknots equally spaced points
> in my x, but when I plotted the points that corresponded to my original y
> values at those equally-spaced x values, I found that the spline did not
> pass through them, which, perhaps naively, I thought it might.
> 
> Also, the manual says that yin comprises "the y values used at the unique y
> values" -- should this read "at the unique x values"?
> 
> Could someone kindly point to a resource where I can get a slightly fuller
> explanation?  I looked at the code for smooth.spline, but can't readily
> follow it.
> 
> Here's a toy example:
> 
>> x<-seq(from=0,to=4*pi,length=1002)
>> y<-sin(x)
>> ss<-smooth.spline(x,y=y,all.knots=F,nknots=25)
>> ss
> Call:
> smooth.spline(x = x, y = y, all.knots = F, nknots = 25)
> 
> Smoothing Parameter  spar= -0.4573636  lambda= 1.006117e-09 (14 iterations)
> Equivalent Degrees of Freedom (Df): 26.99935
> Penalized Criterion: 3.027077e-06
> GCV: 3.190666e-09
>> str(ss)
> List of 15
> $ x       : num [1:1002] 0 0.0126 0.0251 0.0377 0.0502 ...
> $ y       : num [1:1002] 2.88e-05 1.26e-02 2.51e-02 3.77e-02 5.02e-02 ...
> $ w       : num [1:1002] 1 1 1 1 1 1 1 1 1 1 ...
> $ yin     : num [1:1002] 0 0.0126 0.0251 0.0377 0.0502 ...
> $ data    :List of 3
>  ..$ x: num [1:1002] 0 0.0126 0.0251 0.0377 0.0502 ...
>  ..$ y: num [1:1002] 0 0.0126 0.0251 0.0377 0.0502 ...
>  ..$ w: num [1:1002] 1 1 1 1 1 1 1 1 1 1 ...
> $ lev     : num [1:1002] 0.2238 0.177 0.1399 0.1111 0.0891 ...
> $ cv.crit : num 3.19e-09
> $ pen.crit: num 3.03e-06
> $ crit    : num 3.19e-09
> $ df      : num 27
> $ spar    : num -0.457
> $ lambda  : num 1.01e-09
> $ iparms  : Named int [1:3] 1 0 14
>  ..- attr(*, "names")= chr [1:3] "icrit" "ispar" "iter"
> $ fit     :List of 5
>  ..$ knot : num [1:31] 0 0 0 0 0.041 ...
>  ..$ nk   : num 27
>  ..$ min  : num 0
>  ..$ range: num 12.6
>  ..$ coef : num [1:27] 2.88e-05 1.72e-01 5.19e-01 9.04e-01 1.05 ...
>  ..- attr(*, "class")= chr "smooth.spline.fit"
> $ call    : language smooth.spline(x = x, y = y, all.knots = F, nknots =
> 25)
> - attr(*, "class")= chr "smooth.spline"
>> 
> 
> Many thanks!
> 
> 
> Regards,
> 
> Mike Nielsen
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
> 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.

David Winsemius
Alameda, CA, USA