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. Author manuscript; available in PMC: 2011 Dec 29.
Published in final edited form as: J R Stat Soc Ser A Stat Soc. 2009 Apr;172(2):405–425. doi: 10.1111/j.1467-985X.2009.00580.x

Table 2.

A. Percentages of selecting different joinpoint models M0–M3 using BIC for 0-joinpoint or 1-joinpoint models *

n = 5000 n = 1000 n = 500
(c, μ) M0 M1 M2 M3 M0 M1 M2 M3 M0 M1 M2 M3
Case 1: K = 0, APC=−2
(0.7,10) 99.8 0.2 . . 99.6 0.4 . . 99.6 0.4 . .
(0,60) 99.4 0.6 . . 99.4 0.5 0.1 . 99.7 0.3 . .
(0.4,5) 99.7 0.3 . . 99.8 0.2 . . 99.5 0.5 . .
(0,20) 99.8 0.2 . . 99.8 0.2 . . 99.5 0.5 . .
(0.1,2) 99.3 0.6 0.1 . 99.0 1.0 . . 98.6 1.3 0.1 .
(0,4) 99.5 0.5 . . 100.0 . . . 100.0 . . .
Case 2: K = 1, JP=10, APC=(−5, 0)
(0.7,10) . 99.4 0.6 . 3.3 96.6 0.1 . 37.9 62.0 0.1 .
(0,60) . 99.6 0.4 . 6.0 93.9 0.1 . 46.4 53.6 . .
(0.4,5) . 99.1 0.9 . . 99.8 0.2 . 0.1 99.3 0.6 .
(0,20) . 99.5 0.5 . . 99.4 0.6 . 1.2 98.3 0.4 0.1
(0.1,2) . 99.2 0.8 . . 98.6 1.3 0.1 . 98.4 1.5 0.1
(0,4) . 99.0 1.0 . . 99.4 0.6 . . 100.0 . .
Case 3: K = 1, JP=10, APC=(−5, −2)
(0.7,10) . 99.9 0.1 . 61.1 38.8 0.1 . 87.4 12.5 0.1 .
(0,60) 0.2 99.3 0.5 . 68.8 31.0 0.2 . 90.8 9.1 0.1 .
(0.4,5) . 99.1 0.9 . 4.4 95.0 0.6 . 33.2 66.4 0.4 .
(0,20) . 99.5 0.5 . 11.1 88.5 0.4 . 55.6 44.2 0.2 .
(0.1,2) . 99.2 0.8 . . 99.0 0.9 0.1 1.2 97.5 1.3 .
(0,4) . 99.0 1.0 . . 100.0 . . 1.4 98.6 . .
Case 4: K = 1, JP=15, APC=(−5, 0)
(0.7,10) . 99.1 0.9 . 16.2 83.4 0.4 . 59.4 40.4 0.2 .
(0,60) . 99.6 0.4 . 32.3 67.1 0.6 . 74.1 25.9 . .
(0.4,5) . 99.4 0.5 0.1 . 99.7 0.3 . 1.7 97.8 0.5 .
(0,20) . 99.4 0.6 . 0.5 99.0 0.5 . 14.6 85.4 . .
(0.1,2) . 99.0 1.0 . . 98.9 1.0 0.1 . 98.9 1.1 .
(0,4) . 99.3 0.7 . . 99.5 0.5 . . 98.8 1.2 .
Case 5: K = 1, JP=15, APC=(−5, −2)
(0.7,10) 1.6 98.2 0.2 . 77.5 22.5 . . 93.6 6.3 0.1 .
(0,60) 5.8 93.8 0.4 . 84.9 14.9 0.2 . 95.4 4.6 . .
(0.4,5) . 99.8 0.2 . 10.9 88.5 0.6 . 53.1 46.8 0.1 .
(0,20) . 99.5 0.5 . 36.4 63.3 0.3 . 75.0 25.0 . .
(0.1,2) . 99.0 1.0 . . 98.7 1.3 . 2.3 96.8 0.9 .
(0,4) . 99.3 0.6 0.1 . 99.5 0.5 . 6.0 92.8 1.2 .
Case 6: K = 1, JP=23, APC=(−5, 0)
(0.7,10) 87.9 11.8 0.3 . 99.3 0.7 . . 99.8 0.2 . .
(0,60) 95.1 4.9 . . 99.3 0.7 . . 99.8 0.2 . .
(0.4,5) 27.8 71.8 0.3 0.1 93.3 6.7 . . 96.7 3.3 . .
(0,20) 68.5 31.5 . . 97.8 2.1 0.1 . 99.1 0.9 . .
(0.1,2) . 99.5 0.5 . 42.8 56.2 0.9 0.1 73.3 26.4 0.3 .
(0,4) 0.9 99.0 0.1 . 76.1 23.9 . . 87.7 11.1 1.2 .
Case 7: K = 1, JP=23, APC=(−5, −2)
(0.7,10) 98.0 2.0 . . 99.7 0.3 . . 99.5 0.5 . .
(0,60) 98.6 1.4 . . 99.8 0.2 . . 99.7 0.3 . .
(0.4,5) 80.5 19.4 0.1 . 99.1 0.9 . . 99.3 0.7 . .
(0,20) 94.5 5.4 0.1 . 99.3 0.7 . . 99.5 0.5 . .
(0.1,2) 14.5 85.0 0.5 . 84.1 15.9 . . 91.6 8.4 . .
(0,4) 45.7 54.0 0.3 . 91.1 8.9 . . 98.8 1.2 . .
Case 8: K = 2, JP=(10,15), APC=(0, −5, 0)
(0.7,10) 0.8 0.2 98.7 0.3 87.4 5.1 7.5 . 97.2 2.0 0.7 0.1
(0,60) 2.0 2.4 95.5 0.1 89.9 5.0 5.1 . 97.6 1.7 0.6 0.1
(0.4,5) . . 99.2 0.8 27.9 2.7 69.2 0.2 76.5 3.9 19.3 0.3
(0,20) . . 99.6 0.4 40.5 7.8 51.5 0.2 81.7 7.1 11.0 0.2
(0.1,2) . . 99.2 0.8 0.2 0.1 98.5 1.2 16.0 2.4 80.3 1.3
(0,4) . . 99.1 0.9 . . 100.0 . 44.4 . 55.6 .
Case 9: K = 2, JP=(10,15), APC=(0, −5, −2)
(0.7,10) . 47.2 52.8 . 50.5 47.7 1.8 . 86.8 12.7 0.5 .
(0,60) . 61.3 38.7 . 53.8 44.4 1.8 . 86.6 13.0 0.4 .
(0.4,5) . 1.5 97.8 0.7 2.2 74.2 23.6 . 36.9 56.0 7.1 .
(0,20) . 7.5 92.1 0.4 6.4 79.7 13.8 0.1 44.0 52.5 3.5 .
(0.1,2) . . 98.8 1.2 . 28.8 70.0 1.2 3.7 61.7 34.2 0.4
(0,4) . . 99.6 0.4 . 37.9 58.6 3.4 . 42.9 57.1 .
Case 10: K = 2, JP=(10,23), APC=(0, −5, 0)
(0.7,10) . 81.7 18.2 0.1 2.0 96.3 1.7 . 36.2 63.1 0.7 .
(0,60) . 90.6 9.2 0.2 5.4 93.0 1.6 . 43.7 55.8 0.5 .
(0.4,5) . 11.8 87.6 0.6 . 89.1 10.9 . 0.5 94.5 5.0 .
(0,20) . 50.4 49.2 0.4 . 95.5 4.4 0.1 1.8 96.2 1.9 0.1
(0.1,2) . . 99.1 0.9 . 29.3 70.0 0.7 . 64.3 35.5 0.2
(0,4) . 0.2 99.6 0.2 . 62.1 37.9 . . 75.0 25.0 .
Case 11: K = 2, JP=(10,23), APC=(0, −5, −2)
(0.7,10) . 95.0 4.9 0.1 2.6 96.4 1.0 . 34.6 64.7 0.7 .
(0,60) . 98.0 1.9 0.1 3.9 95.5 0.6 . 37.9 61.8 0.3 .
(0.4,5) . 72.6 27.4 . . 97.9 2.1 . 0.2 98.4 1.4 .
(0,20) . 88.8 11.2 . . 98.2 1.7 0.1 1.0 98.4 0.6 .
(0.1,2) . 7.9 91.7 0.4 . 80.6 19.3 0.1 . 90.6 9.4 .
(0,4) . 28.3 71.4 0.4 . 88.3 11.7 . . 92.3 7.7 .
Case 12: K = 2, JP=(15,23), APC=(0, −5, 0)
(0.7,10) . 80.4 19.6 . 10.2 87.9 1.9 . 49.1 50.3 0.6 .
(0,60) . 89.5 10.5 . 18.1 80.9 1.0 . 63.3 36.4 0.3 .
(0.4,5) . 12.7 87.1 0.2 . 88.3 11.6 0.1 0.6 95.0 4.4 .
(0,20) . 55.8 44.2 . . 95.9 4.1 . 6.9 91.5 1.6 .
(0.1,2) . . 99.3 0.7 . 41.5 58.0 0.5 . 71.5 28.4 0.1
(0,4) . . 99.6 0.4 . 68.9 31.1 . . 100.0 . .
Case 13: K = 2, JP=(15,23), APC=(0, −5, −2)
(0.7,10) . 96.0 3.9 0.1 5.0 94.2 0.8 . 41.5 58.1 0.4 .
(0,60) . 96.7 3.2 0.1 13.5 85.9 0.6 . 61.2 38.4 0.4 .
(0.4,5) . 77.0 23.0 . . 97.7 2.3 . 0.2 98.5 1.2 0.1
(0,20) . 90.9 9.1 . . 99.0 0.9 0.1 3.6 95.6 0.8 .
(0.1,2) . 12.9 86.3 0.8 . 82.0 17.8 0.2 . 90.7 9.2 0.1
(0,4) . 34.0 66.0 . . 88.1 11.9 . . 100.0 . .
*

K is the true number of jointpoints, Mk denotes a k-joinpoint model, k = 0, .., 3, JP is the location of the joinpoints