Table 4.
The empirical sizes and powers of the LRT, Wald test, and score test for testing the null hypotheses H10, H20, and H30 at the significance level 0.05
| Model | n1(Vx,Plb) | n2(Vx,Plb) | LRT | Wald | Score |
|---|---|---|---|---|---|
| Testing H10:β1=β2=β12=0 | |||||
| M10 | 250 (24,46) | 250 (34,60) | 6.4 | 4.8 | 6.2 |
| 400 (39,73) | 400 (54,97) | 4.7 | 3.6 | 4.4 | |
| M11 | 250 (25,46) | 250 (35,60) | 56.4 | 53.2 | 54.9 |
| 400 (41,74) | 400 (51,97) | 74.1 | 73.2 | 73.8 | |
| M12 | 250 (30,46) | 250 (42,60) | 76.4 | 72.9 | 75.9 |
| 400 (49,74) | 400 (67,97) | 91.7 | 91.2 | 91.5 | |
| Testing H20:β12=0 | |||||
| M20 | 250 (25,46) | 250 (36,60) | 4.9 | 4.2 | 4.6 |
| 400 (41,74) | 400 (57,96) | 3.9 | 3.8 | 3.8 | |
| M21 | 250 (23,46) | 250 (32,60) | 34.0 | 39.3 | 38.2 |
| 400 (37,74) | 400 (52,97) | 51.0 | 55.2 | 54.2 | |
| M22 | 250 (30,46) | 250 (41,60) | 40.0 | 43.3 | 42.0 |
| 400 (48,74) | 400 (67,97) | 53.7 | 57.6 | 56.8 | |
| Testing H30:β2=β12=0 | |||||
| M30 | 250 (20,46) | 250 (29,60) | 5.6 | 4.8 | 5.5 |
| 400 (33,74) | 400 (47.97) | 3.9 | 3.6 | 3.9 | |
| M31 | 250 (29,46) | 250 (41,60) | 62.8 | 60.2 | 61.8 |
| 400 (48,74) | 400 (65,96) | 83.0 | 82.1 | 82.6 | |
| M32 | 250 (30,46) | 250 (41,60) | 74.6 | 73.3 | 74.2 |
| 400 (48,74) | 400 (66,97) | 91.3 | 90.9 | 91.2 | |