Table 1 Coefficients of the first five Legendre polynomials for adjusted time points (t*) used in the poplar growth study.
From: A joint model for nonparametric functional mapping of longitudinal trajectory and time-to-event
t | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
t* | -1 | -4/5 | -3/5 | -2/5 | -1/5 | 0 | 1/5 | 2/5 | 3/5 | 4/5 | 1 |
P0(t*) | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
P1(t*) | -1 | -4/5 | -3/5 | -2/5 | -1/5 | 0 | 1/5 | 2/5 | 3/5 | 4/5 | 1 |
P2(t*) | 1 | 23/50 | 1/25 | -13/50 | -11/25 | -1/2 | -11/25 | -13/50 | 1/25 | 23/50 | 1 |
P3(t*) | -1 | -2/25 | 9/25 | 11/25 | 7/25 | 0 | -7/25 | -11/25 | -9/25 | 2/25 | 1 |
P4(t*) | 1 | -24/103 | -51/125 | -93/823 | 29/125 | 3/8 | 29/125 | -93/823 | -51/125 | -24/103 | 1 |
P5(t*) | -1 | 167/418 | 107/701 | -59/218 | -274/891 | 0 | 274/891 | 59/218 | -107/701 | -167/418 | 1 |
P6(t*) | 1 | -172/439 | 132/767 | 163/557 | -56/695 | -5/16 | -56/695 | 163/557 | 132/767 | -172/439 | 1 |
P7(t*) | -1 | 110/459 | -10/31 | 13/891 | 231/787 | 0 | -231/787 | -13/891 | 10/31 | -110/459 | 1 |