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-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of liufang at
uchicago.edu
Sent: Thursday, February 02, 2006 8:48 AM
To: r-help at stat.math.ethz.ch
Subject: [R] the meaning of the B-spline coefficients
Dear all,
I'm trying to figure out the exact meaning of the B-spline
coefficients generated by the R command bs(). After reading a
lot of things, I still have no clue...
Here's my data.
> test
time f0
1 1 94.76328
2 2 102.47954
3 3 105.01234
4 4 107.21387
5 5 108.63279
6 6 109.54507
7 7 113.87931
8 8 118.21356
9 9 121.08652
10 10 121.78338
11 11 118.84742
12 12 112.15230
13 13 99.64756
14 14 85.87430
15 15 80.15959
16 16 78.16951
17 17 76.85120
18 18 76.64255
19 19 75.23007
20 20 74.18679
21 21 97.82914
22 22 97.99156
23 23 98.24108
24 24 99.96225
25 25 100.91948
26 26 101.75905
27 27 114.88339
28 28 125.78792
29 29 130.62168
30 30 132.42147
31 31 120.75498
32 32 116.46438
33 33 95.83809
34 34 83.55815
35 35 83.49363
36 36 83.42912
37 37 83.43273
38 38 83.49382
39 39 83.55078
40 40 83.55078
41 41 89.22781
42 42 93.01460
43 43 94.13982
44 44 95.12909
45 45 97.24925
46 46 100.00507
47 47 108.08150
48 48 115.54357
49 49 126.74814
50 50 127.63650
51 51 123.09723
52 52 115.97800
53 53 107.58863
54 54 99.78626
55 55 90.47310
56 56 81.92469
57 57 79.50943
58 58 75.78710
59 59 73.05736
60 60 72.26699
61 61 93.12932
62 62 91.30452
63 63 91.02817
64 64 91.16687
65 65 93.74704
66 66 96.39891
67 67 99.64934
68 68 104.37769
69 69 110.45508
70 70 111.70428
71 71 93.69037
72 72 85.67118
73 73 85.06033
74 74 84.44947
75 75 83.83862
76 76 82.93448
77 77 80.80928
78 78 78.70249
79 79 78.70249
80 80 78.70249
81 81 140.00112
82 82 139.98659
83 83 142.49656
84 84 145.00654
85 85 147.25728
86 86 149.06518
87 87 151.23441
88 88 156.06892
89 89 160.21311
90 90 162.04904
91 91 124.28610
92 92 86.27715
93 93 69.96150
94 94 70.23389
95 95 74.23542
96 96 78.23695
97 97 82.23848
98 98 86.24001
99 99 92.06214
100 100 114.89530
Here's my R output.> bsp = lm(f0~bs(time,df=13),data=test)
> summary(bsp)
Call:
lm(formula = f0 ~ bs(time, df = 13), data = test)
Residuals:
Min 1Q Median 3Q Max
-31.6519 -7.1230 0.1433 6.1755 25.2094
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 97.307 10.343 9.408 7.26e-15 ***
bs(time, df = 13)1 5.029 20.150 0.250 0.803490
bs(time, df = 13)2 50.806 14.396 3.529 0.000672 ***
bs(time, df = 13)3 -66.700 15.579 -4.281 4.81e-05 ***
bs(time, df = 13)4 73.981 13.516 5.474 4.29e-07 ***
bs(time, df = 13)5 -59.803 14.225 -4.204 6.40e-05 ***
bs(time, df = 13)6 46.817 13.740 3.407 0.001000 ***
bs(time, df = 13)7 -23.807 13.982 -1.703 0.092235 .
bs(time, df = 13)8 8.090 13.889 0.582 0.561776
bs(time, df = 13)9 -22.132 14.100 -1.570 0.120170
bs(time, df = 13)10 16.759 14.566 1.151 0.253083
bs(time, df = 13)11 98.630 16.566 5.954 5.55e-08 ***
bs(time, df = 13)12 -102.236 16.784 -6.091 3.06e-08 ***
bs(time, df = 13)13 31.919 14.629 2.182 0.031839 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1
Residual standard error: 12.46 on 86 degrees of freedom
Multiple R-Squared: 0.7316, Adjusted R-squared: 0.691
F-statistic: 18.03 on 13 and 86 DF, p-value: < 2.2e-16
Do the above coefficients imply the feature of the independent
variable "f0"? For example, does "intercept" approximate the
initial value of "f0" at "time" 1? I specified df=13, so
there
are 10 knots in this case. Do bs(time, df = 13)4 through
bs(time, df = 13)13 indicate the slope or intercept of the
original curve (of "f0") within the 10 knot spans? What's the
meaning of bs(time, df = 13)1 - 3 then?
I'm reading "B(asic)-Spline Basics" by Carl de Boor, but
really don't understand those formula of splines. I'd really
appreciate it if someone could help me with this.
Many thanks!
Fang Liu
liufang at uchicago.edu
Ph.D. student
Department of linguistics
University of Chicago