From: i.m.s.white <i.m.s.white_at_ed.ac.uk>

Date: Fri 30 Jun 2006 - 19:48:23 EST

Date: Fri 30 Jun 2006 - 19:48:23 EST

Steven,

I cannot vouch for the behaviour of the function smooth.spline(), but the theoretical answer to your question is yes. If g = Sy is the transformation from data vector y to spline vector g, the equivalent degrees of freedom are usually defined as EDF = trace(S), where S is the n x n smoothing matrix:

EDF = sum_i(1/(1+theta*lambda_i)),

where lambda_1 to lambda_n are the eigenvalues of S. Two of these are zero, so

EDF = 2 + sum(1/(1+theta*lambda_i))

the sum now over i=3 to n. Here theta is the smoothing parameter. Setting theta = 0 (no smoothing) gives EDF=n and produces the interpolating spline. Setting theta = infty gives EDF=2 and a straight line fit. See either

Green and Silverman, Nonparametric regression and generalized linear models,
(p37), or

Hastie and Tibshirani, Generalized additive models, p52.

On Sat, Jun 24, 2006 at 11:35:16AM -0400, Steven Shechter wrote:

*> Hi,
*

> If I set df=2 in my smooth.spline function, is that equivalent to running

*> a linear regression through my data? It appears that df=# of data points
**> gives the interpolating spline and that df = 2 gives the linear
**> regression, but I just want to confirm this.
**>
**> Thank you,
**> Steven
**>
**> ______________________________________________
**> R-help@stat.math.ethz.ch mailing list
**> https://stat.ethz.ch/mailman/listinfo/r-help
**> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
*

-- ************************************************ * I.White * * University of Edinburgh * * Ashworth Laboratories, West Mains Road * * Edinburgh EH9 3JT * * Fax: 0131 650 6564 Tel: 0131 650 5490 * * E-mail: i.m.s.white@ed.ac.uk * ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Fri Jun 30 20:59:10 2006

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.1.8, at Fri 30 Jun 2006 - 22:14:04 EST.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*