Dear Xing Zhao, To elaborate slightly on Michael's comments, a natural cubic spline with 2 df has one *interior* knot and two boundary knots (as is apparent in the output you provided). The linearity constraint applies beyond the boundary knots.
I hope this helps, John ------------------------------------------------ John Fox, Professor McMaster University Hamilton, Ontario, Canada http://socserv.mcmaster.ca/jfox/ On Tue, 15 Apr 2014 08:18:40 -0400 Michael Friendly <frien...@yorku.ca> wrote: > No, the curves on each side of the know are cubics, joined > so they are continuous. Se the discussion in \S 17.2 in > Fox's Applied Regression Analysis. > > On 4/15/2014 4:14 AM, Xing Zhao wrote: > > Dear all > > > > I understand the definition of Natural Cubic Splines are those with > > linear constraints on the end points. However, it is hard to think > > about how this can be implement when df=2. df=2 implies there is just > > one knot, which, according the the definition, the curves on its left > > and its right should be both be lines. This means the whole line > > should be a line. But when making some fits. the result still looks > > like 2nd order polynomial. > > > > How to think about this problem? > > > > Thanks > > Xing > > > > ns(1:15,df =2) > > 1 2 > > [1,] 0.0000000 0.00000000 > > [2,] 0.1084782 -0.07183290 > > [3,] 0.2135085 -0.13845171 > > [4,] 0.3116429 -0.19464237 > > [5,] 0.3994334 -0.23519080 > > [6,] 0.4734322 -0.25488292 > > [7,] 0.5301914 -0.24850464 > > [8,] 0.5662628 -0.21084190 > > [9,] 0.5793481 -0.13841863 > > [10,] 0.5717456 -0.03471090 > > [11,] 0.5469035 0.09506722 > > [12,] 0.5082697 0.24570166 > > [13,] 0.4592920 0.41197833 > > [14,] 0.4034184 0.58868315 > > [15,] 0.3440969 0.77060206 > > attr(,"degree") > > [1] 3 > > attr(,"knots") > > 50% > > 8 > > attr(,"Boundary.knots") > > [1] 1 15 > > attr(,"intercept") > > [1] FALSE > > attr(,"class") > > [1] "ns" "basis" "matrix" > > > > > -- > Michael Friendly Email: friendly AT yorku DOT ca > Professor, Psychology Dept. & Chair, Quantitative Methods > York University Voice: 416 736-2100 x66249 Fax: 416 736-5814 > 4700 Keele Street Web: http://www.datavis.ca > Toronto, ONT M3J 1P3 CANADA > > ______________________________________________ > R-help@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. ______________________________________________ R-help@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.
