Re: st: Why does mkspline only have "restricted" cubic splines and what does it mean in practice?

[Roger Newson <r.newson@imperial.ac.uk>]

If you want to fit unrestricted cubic splines, with parameters that you 
can understand, then you might like to use the -flexcurv- module of the 
-bspline- package. The -bspline- package is usually downloaded from SSC. 
However, because of Kit Baum's absence from Boston, the very latest 
version can currently be downloaded only from my website. In Stata, type

net from "http://www.imperial.ac.uk/nhli/r.newson/stata10/";

and select and install -bspline-, and also get the manual -bspline.pdf-, 
distributed with the package as an ancillary file.

The -frencurv- module is usually the one to use, although another 2 
modules also exist. If you type


        . sysuse auto, clear
        . describe
        . flexcurv, xvar(weight) refpts(1760(770)4840) gen(cs) power(3)
        . describe cs*
        . regress mpg cs*, robust noconst


then you will fit an unrestricted cubic spline model for -mpg- as a 
function of -weight-, with parameters named -cs1-, -cs2-, -cs3-, -cs4- 
and -cs5-, whose values (with confidence limits) are values of the 
spline at weights of 1750, 2530, 3300, 4070 and 4840 US (or Imperial) 
pounds, respectively. And, if you type

        . flexcurv, xvar(weight) refpts(1760(770)4840) omit(1760) 
gen(ics) power(3)
        . describe ics*
        . regress mpg ics*, robust

yhen you will fit the same unrestricted cubic spline model, with 
parameters -ics2-, -ics3-, -ics4-, -ics5-, and -_cons-. The parameter 
-_cons- is then the value of the spline at the base value of 1760 
pounds, and the parameters -ics2-, -ics3-, -ics4- and -ics5- ate 
differences between the values of the spline at 2530, 3300, 4070 and 
4840 pounds (respectively) and the value of the spline at 1760 pounds.

You can choose more reference points if you like. The knots will be 
generated automatically, and (in default) will be regularly spaced.

I hope this helps.

Best wishes

Roger


Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 08/03/2011 12:33, Jen Zhen wrote:
> Dear all,
>
> I've used Stata's -mkspline- to create the 2 kinds of spline it
> offers, a linear one:
> - mkspline Age_1 50 Age_2 52 Age_3 54 Age_4 56 Age_5 58 Age_6 59 Age_7
> 60 Age_8 61 Age_9 62 Age_10 63 Age_11 64 Age_12 65 Age_13 66 Age_14 =
> Age -
> and a restricted cubic one:
> - mkspline rcs = Age, cubic knots(50 52 54 56 58 59 60 61 62 63 64 65 66) -
> The knot points are given by my context.
>
> What the linear spline maker does is very clear and transparent when I
> browse it: For instance, for someone aged 55.04, it will make
> Age_1=50, Age_2=2, Age_3=2, Age_4=1.04, Age_5=0, etc.
> But I have trouble understanding what the "cubic" one does, where I
> get the following:
> Age	rcs1	rcs2	rcs3	rcs4	rcs5	…
> 55.04383	55.04383	0.5012364	0.1101598	0.0044428	0	…
> Obviously rcs1 is just Age linearly for all elements thrown together,
> but I have no idea how rcs2 and higher are computed, and indeed why
> -mkspline- allows only for "restricted" and not "unrestricted" cubic
> splines.
>
> Searching for answers and literature led me to some great introduction
> slides on this by Maarten
> (http://www.maartenbuis.nl/presentations/bonn09.pdf). However I am
> still puzzled by the commands for cubic spline on page 17, which seems
> to make only the cubic term different for each knot interval, wheras
> in terms of linear and quadratic terms there is just one each for the
> full range. Is that because they would otherwise be collinear?
>
> Thanks a lot for any wisdom you might be able to share on this.
> JZ
>
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