Table 4:
Parameter estimates from fitted penalized Benter-Plackett-Luce (BPL) models applied to case A data, ordered by estimated values of θk from using λ = λAIC. The final row , gives the number of non-zero parameters in the estimated model. For comparison, the remaining columns give the ranked list of problems according to the listed alternative algorithm or model; comparator entries in bold indicate ranks that were either (i) discrepant with λAIC by not more than 1 position or (ii) ranks that were larger than the total number of non-zero estimated weights according to λAIC and which λAIC estimated to be zero. The parenthetical numbers in the AMean, GMean, and Median rank columns correspond to the summary rank of that problem, and the parenthetical numbers in the MC columns correspond to the estimated transition probability for the stationary distribution (×100).
| Problem / Parameter | BPL |
LDRBO | AMean Rank | GMean Rank | Median Rank | MC1 | MC2 | MC3 | CEMCρ | CEMCτ | EMM | MM | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| λ = 0 | λAIC | λBIC | ||||||||||||
| θ0 | 3.95 | 2.57 | 2.78 | |||||||||||
| PNEUMONIA | 9.54 | 6.86 | 7.32 | 1 | 1(3.3) | 1(1.6) | 1(1.0) | 1(5.6) | 1(19.8) | 1(15.2) | 1 | 1 | 1 | 1 |
| DIABETES MELLITUS | 7.94 | 5.31 | 5.74 | 2 | 2(5.5) | 2(4.4) | 3(5.0) | 5(3.9) | 3(10.5) | 3(8.8) | 3 | 3 | 4 | 3 |
| ANEMIA | 7.93 | 5.30 | 5.74 | 3 | 3(6.5) | 3(4.6) | 2(4.0) | 2(4.5) | 2(14.1) | 2(9.1) | 2 | 2 | 2 | 2 |
| DEPRESSION WITH ANXIETY | 7.15 | 4.55 | 4.98 | 5 | 4(8.2) | 4(6.9) | 4(7.0) | 9(3.7) | 4(7.8) | 4(6.3) | 7 | 4 | 5 | 5 |
| OSTEOARTHRITIS | 6.64 | 4.07 | 4.49 | 6 | 5(10.1) | 6(9.1) | 5(8.0) | 12(3.6) | 5(5.8) | 6(4.9) | 8 | 6 | 6 | 8 |
| SPLENOMEGALY | 6.42 | 3.79 | 4.21 | 4 | 6(l0.8) | 5(8.0) | 7(12.5) | 3(4.1) | 7(3.9) | 5(5.5) | 4 | 5 | 3 | 4 |
| POST MENOPAUSAL ON HRT | 6.25 | 3.68 | 4.09 | 7(11.4) | 9(9.8) | 6(9.5) | 15(3.5) | 6(4.7) | 9(4.4) | 13 | 9 | 8 | 9 | |
| RENAL FAILURE | 5.90 | 3.29 | 3.70 | 7 | 8(12.3) | 8(9.6) | 8(16.8) | 7(3.8) | 8(2.0) | 8(4.5) | 5 | 7 | 9 | 7 |
| SYSTOLIC MURMUR | 5.84 | 3.22 | 3.64 | 9(12.4) | 7(9.3) | 10(17.0) | 4(3.9) | 9(2.0) | 7(4.5) | 6 | 8 | 7 | 6 | |
| HISTORY OF SMOKING | 4.76 | 2.26 | 2.65 | 10(15.1) | 11(13.9) | 9(17.0) | 16(3.4) | 21(1.5) | 11(2.7) | 25 | 10 | 10 | 10 | |
| CHEST PAIN | 4.17 | 0.00 | 2.00 | 11(15.7) | 10(13.1) | 12(18.0) | 8(3.8) | 14(1.6) | 10(2.7) | 15 | 12 | 12 | 11 | |
| LOWER EXTREMITY EDEMA | 4.10 | 0.00 | 2.00 | 12(15.8) | 12(14.4) | 11(17.8) | 14(3.5) | 20(1.5) | 12(2.5) | 9 | 11 | 11 | 12 | |
| IRON DEFICIENCY | 3.37 | 0.00 | 0.00 | 13(16.6) | 15(15.7) | 13(18.0) | 22(3.3) | 15(1.6) | 14(2.1) | 11 | 14 | 13 | 14 | |
| HYPOXEMIA | 3.04 | 0.00 | 0.00 | 14(16.7) | 13(14.9) | 17(18.2) | 6(3.8) | 17(1.6) | 13(2.2) | 24 | 13 | 20 | 13 | |
| HYPOPHOSPHATEMIA | 2.87 | 0.00 | 0.00 | 16(17.0) | 19(16.4) | 15(18.0) | 23(3.3) | 11(1.6) | 17(1.9) | 10 | 16 | 16 | 16 | |
| THROMBOCYTOPENIA | 2.83 | 0.00 | 0.00 | 15(17.0) | 18(16.4) | 14(18.0) | 21(3.3) | 24(1.5) | 16(2.0) | 16 | 15 | 15 | 15 | |
| SHORT OF BREATH | 2.68 | 0.00 | 0.00 | 17(17.2) | 14(15.5) | 18(18.5) | 10(3.6) | 19(1.6) | 15(2.0) | 27 | 17 | 19 | 18 | |
| HYPOXIA | 2.36 | 0.00 | 0.00 | 8 | 18(17.2) | 16(15.8) | 21(18.5) | 19(3.4) | 12(1.6) | 19(1.9) | 28 | 18 | 23 | 17 |
| PANCYTOPENIA | 2.30 | 0.00 | 0.00 | 19(17.3) | 17(15.9) | 23(18.5) | 11(3.6) | 13(1.6) | 18(1.9) | 19 | 20 | 24 | 19 | |
| HYPOALBUMINEMIA | 2.14 | 0.00 | 0.00 | 20(17.4) | 20(16.9) | 16(18.2) | 25(3.2) | 28(1.5) | 20(1.8) | 20 | 19 | 14 | 20 | |
| FEVER | 1.15 | 0.00 | 0.00 | 21(17.7) | 21(16.9) | 19(18.5) | 13(3.5) | 22(1.5) | 21(1.7) | 14 | 22 | 21 | 21 | |
| CONGESTIVE HEART FAILURE | 1.10 | 0.00 | 0.00 | 23(17.8) | 22(17.0) | 27(18.5) | 18(3.4) | 10(1.6) | 23(1.7) | 22 | 27 | 27 | 24 | |
| PULMONARY EDEMA | 1.07 | 0.00 | 0.00 | 25(17.8) | 23(17.0) | 25(18.5) | 17(3.4) | 18(1.6) | 24(1.6) | 17 | 25 | 28 | 26 | |
| PULMONARY EMBOLISM | 0.95 | 0.00 | 0.00 | 22(17.7) | 24(17.3) | 24(18.5) | 20(3.3) | 16(1.6) | 22(1.7) | 23 | 21 | 25 | 22 | |
| TACHYCARDIA | 0.90 | 0.00 | 0.00 | 24(17.8) | 26(17.5) | 28(18.5) | 27(3.0) | 23(1.5) | 25(1.6) | 12 | 28 | 22 | 23 | |
| DEPRESSION | 0.86 | 0.00 | 0.00 | 26(17.9) | 25(17.5) | 20(18.5) | 24(3.2) | 26(1.5) | 26(1.6) | 21 | 23 | 17 | 27 | |
| HIGH HAPTOGLOBIN | 0.86 | 0.00 | 0.00 | 27(17.9) | 28(17.7) | 22(18.5) | 28(2.7) | 25(1.5) | 28(1.6) | 18 | 24 | 26 | 25 | |
| ANXIETY | 0.00 | 0.00 | 0.00 | 28(17.9) | 27(17.6) | 26(18.5) | 26(3.0) | 27(1.5) | 27(1.6) | 26 | 26 | 18 | 28 | |
| δ1 | 0.99 | 1.00 | 1.00 | |||||||||||
| δ2 | 0.61 | 0.62 | 0.61 | |||||||||||
| λ | 0 | 3.38 | 1.19 | |||||||||||
| 30 | 12 | 14 | ||||||||||||