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
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