Table 3.
The MMMS and RSD (in parenthesis) of the simulated examples for linear and logistic regression model III using different number of PCs with n = 500 when p = 1000 and p = 10000.
| PCs | Variance | SIS-PCA-MLR | SIS-PCA-MMLE | SIS-PCA-MLR | SIS-PCA-MMLE |
|---|---|---|---|---|---|
| Setting 1, linear model with p = 1000 | |||||
| s = 6, β★ = (3,−3, 3,−3, …)T | s = 12, β★ = (3, 4, 3, 4, …)T | ||||
| 0 | 0 | 29(20) | 29(20) | 802.5(121) | 802.5(121) |
| 1 | 7.5% | 157.5(173) | 135.5(153) | 808(229) | 813.5(222) |
| 2 | 14.0% | 90.5(150) | 50.5(120) | 669.5(291) | 685(284) |
| 3 | 20.0% | 56.5(161) | 26(95) | 369(372) | 378.5(367) |
| 5 | 30.8% | 6(0) | 6(0) | 16(6) | 15(7) |
| 10 | 34.0% | 6(0) | 6(0) | 15(6) | 14.5(4) |
| 30 | 44.7% | 6(0) | 6(0) | 14.5(6) | 14(6) |
| 50 | 53.3% | 6(0) | 6(0) | 14(4) | 14(6) |
| 100 | 69.3% | 6(0) | 6(0) | 14(4) | 15(5) |
| Setting 2, logistic regression with p = 1000 | |||||
| s = 6, β★ = (3,−3, 3,−3, …)T | s = 8, β★ = (1.3, 1, 1.3, 1, …)T | ||||
| 0 | 0 | 43.5(34) | 44(35) | 333.5(124) | 333.5(124) |
| 1 | 6.9% | 24(35) | 24(32) | 378.5(190) | 613(336) |
| 2 | 13.6% | 18.5(19) | 18(18) | 364(164) | 387(151) |
| 3 | 19.7% | 11.5(13) | 9.5(10) | 291(247) | 272.5(237) |
| 5 | 30.8% | 6(0) | 6(0) | 8(0) | 8(0) |
| 10 | 34.0% | 6(0) | 6(0) | 8(0) | 8(1) |
| 30 | 44.7% | 6(0) | 6(0) | 8(0) | 8(0) |
| 50 | 53.3% | 6(0) | 6(0) | 8(0) | 8(0) |
| 100 | 69.2% | 7(4) | 8(4) | 8(0) | 8(1) |
| Setting 3, linear model with p = 10000 | |||||
| s = 6, β★ = (0.2,−0.2, 0.2, …)T | s = 12, β★ = (3, 4, 3, 4, …)T | ||||
| 0 | 0 | 98(117) | 98(117) | 142.5(291) | 142.5(291) |
| 1 | 2.1% | 111(126) | 106(135) | 62(134) | 65(142) |
| 2 | 4.2% | 87.5(149) | 92(161) | 19(72) | 21(58) |
| 3 | 6.2% | 60(120) | 54.5(123) | 15(9) | 15.5(11) |
| 5 | 9.8% | 58(127) | 52(141) | 12(2) | 12(3) |
| 10 | 11.4% | 54(106) | 53.5(110) | 12.5(2) | 13(3) |
| 30 | 17.5% | 73.5(152) | 96.5(180) | 12(3) | 13(5) |
| 50 | 23.3% | 90(235) | 101(204) | 13(2) | 13(3) |
| 100 | 36.3% | 261(383) | 282.5(395) | 14(13) | 15(17) |
| Setting 4, logistic regression with p = 10000 | |||||
| s = 6, β★ = (0.5,−0.5, 0.5,−0.5, …)T | s = 8, β★ = (1.3, 1, 1.3, 1, …)T | ||||
| 0 | 0 | 48(118) | 48(118) | 13(26) | 13(26) |
| 1 | 1.3% | 42.5(110) | 43(106) | 13(22) | 13(26) |
| 3 | 3.6% | 40.5(95) | 44(88) | 12.5(13) | 13(14) |
| 5 | 5.6% | 38.5(73) | 40(78) | 11(11) | 11(12) |
| 10 | 7.3% | 44(74) | 46(84) | 11(9) | 12(11) |
| 30 | 13.7% | 61(120) | 60(131) | 12(17) | 13(21) |
| 50 | 19.7% | 94.5(181) | 95.5(178) | 15.5(25) | 16(28) |
| 100 | 33.3% | 186.5(351) | 202(334) | 34.5(66) | 35(73) |