TABLE 5.
Mean Estimate and Relative Bias of the Latent Interaction Effect (Statistical Power = 0.7)
| |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Sample Size | Distribution | γ3 | CPI
|
GAPI
|
UPI
|
LMS
|
|||||
E (γ̂3) | RB(γ̂3) | E (γ̂3) | RB(γ̂3) | E (γ̂3) | RB(γ̂3) | E (γ̂3) | RB(γ̂3) | ||||
100 | Normal | 3.233 | 3.337 | 3.2% * | 3.909 | 20.9% | 3.874 | 19.8% | 3.220 | −0.4% * | |
Uniform | 3.233 | 3.074 | −4.9% * | 4.106 | 27.0% | 4.006 | 23.9% | 2.987 | −7.6% * | ||
K1 | 3.233 | 3.837 | 18.7% | 3.845 | 18.9% | 3.713 | 14.9% | 3.981 | 23.2% | ||
K2 | 3.233 | 4.130 | 27.7% | 3.816 | 18.1% | 3.907 | 20.9% | 4.237 | 31.1% | ||
|
3.233 | 5.759 | 78.1% | 3.974 | 22.9% | 3.556 | 10.0% | 6.147 | 90.1% | ||
| |||||||||||
200 | Normal | 2.309 | 2.392 | 3.6% * | 2.637 | 14.2% | 2.533 | 9.7% * | 2.426 | 5.1% * | |
Uniform | 2.309 | 2.121 | −8.1% * | 2.651 | 14.8% | 2.714 | 17.6% | 2.070 | −10.3% | ||
K1 | 2.309 | 2.793 | 20.9% | 2.492 | 7.9% * | 2.420 | 4.8% * | 2.833 | 22.7% | ||
K2 | 2.309 | 2.830 | 22.6% | 2.440 | 5.7% * | 2.469 | 6.9% * | 3.069 | 32.9% | ||
|
2.309 | 4.352 | 88.5% | 2.532 | 9.7% * | 2.586 | 12.0% | 4.918 | 113.0% | ||
| |||||||||||
500 | Normal | 1.469 | 1.511 | 2.8% * | 1.554 | 5.8% * | 1.554 | 5.7% * | 1.510 | 2.7% * | |
Uniform | 1.469 | 1.315 | −10.5% | 1.548 | 5.3% * | 1.545 | 5.1% * | 1.298 | −11.6% | ||
K1 | 1.469 | 1.790 | 21.8% | 1.509 | 2.7% * | 1.498 | 2.0% * | 1.921 | 30.7% | ||
K2 | 1.469 | 1.849 | 25.9% | 1.549 | 5.4% * | 1.529 | 4.1% * | 2.063 | 40.4% | ||
|
1.469 | 3.244 | 120.8% | 1.566 | 6.6% * | 1.556 | 5.9% * | 3.969 | 170.1% | ||
| |||||||||||
1000 | Normal | 1.041 | 1.035 | −0.6% * | 1.048 | 0.7% * | 1.044 | 0.3% * | 1.051 | 0.9% * | |
Uniform | 1.041 | 0.929 | −10.8% | 1.071 | 2.8% * | 1.067 | 2.5% * | 0.920 | −11.6% | ||
K1 | 1.041 | 1.267 | 21.7% | 1.052 | 1.0% * | 1.048 | 0.7% * | 1.363 | 30.9% | ||
K2 | 1.041 | 1.283 | 23.2% | 1.057 | 1.6% * | 1.054 | 1.2% * | 1.465 | 40.7% | ||
|
1.041 | 2.577 | 147.5% | 1.116 | 7.2% * | 1.113 | 6.9% * | 3.311 | 218.0% | ||
| |||||||||||
5000 | Normal | 0.466 | 0.487 | 4.4% * | 0.490 | 5.0% * | 0.489 | 4.8% * | 0.489 | 4.7% * | |
Uniform | 0.466 | 0.426 | −8.7% * | 0.480 | 2.9% * | 0.480 | 3.0% * | 0.423 | −9.4% * | ||
K1 | 0.466 | 0.567 | 21.5% | 0.465 | −0.2% * | 0.465 | −0.3% * | 0.634 | 35.8% | ||
K2 | 0.466 | 0.552 | 18.3% | 0.463 | −0.8% * | 0.463 | −0.6% * | 0.668 | 43.3% | ||
|
0.466 | 1.770 | 279.6% | 0.483 | 3.5% * | 0.483 | 3.5% * | 2.410 | 416.6% |
Mean Estimate and Relative Bias of the Latent Interaction Effect (Statistical Power = 0.9)
| |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Sample Size | Distribution | γ3 | CPI
|
GAPI
|
UPI
|
LMS
|
|||||
E (γ̂3) | RB(γ̂3) | E (γ̂3) | RB(γ̂3) | E (γ̂3) | RB(γ̂3) | E (γ̂3) | RB(γ̂3) | ||||
100 | Normal | 4.133 | 4.277 | 3.5% * | 5.220 | 26.3% | 4.824 | 16.7% | 4.175 | 1.0% * | |
Uniform | 4.133 | 3.730 | −9.8% * | 5.005 | 21.1% | 4.924 | 19.1% | 3.794 | −8.2% * | ||
K1 | 4.133 | 5.084 | 23.0% | 4.923 | 19.1% | 4.784 | 15.7% | 5.141 | 24.4% | ||
K2 | 4.133 | 5.241 | 26.8% | 4.831 | 16.9% | 4.720 | 14.2% | 5.540 | 34.0% | ||
|
4.133 | 6.549 | 58.5% | 5.018 | 21.4% | 4.588 | 11.0% | 7.164 | 73.3% | ||
| |||||||||||
200 | Normal | 2.981 | 3.063 | 2.7% * | 3.393 | 13.8% | 3.362 | 12.8% | 2.991 | 0.3% * | |
Uniform | 2.981 | 2.772 | −7.0% * | 3.502 | 17.5% | 3.561 | 19.4% | 2.762 | −7.4% * | ||
K1 | 2.981 | 3.740 | 25.5% | 3.297 | 10.6% | 3.257 | 9.2% * | 3.831 | 28.5% | ||
K2 | 2.981 | 3.837 | 28.7% | 3.364 | 12.8% | 3.291 | 10.4% | 4.087 | 37.1% | ||
|
2.981 | 5.260 | 76.4% | 3.403 | 14.2% | 3.402 | 14.1% | 5.821 | 95.3% | ||
| |||||||||||
500 | Normal | 1.909 | 1.995 | 4.5% * | 2.058 | 7.8% * | 2.051 | 7.4% * | 1.934 | 1.3% * | |
Uniform | 1.909 | 1.652 | −13.5% | 1.914 | 0.2% * | 1.908 | −0.1% * | 1.670 | −12.5% | ||
K1 | 1.909 | 2.362 | 23.7% | 1.990 | 4.2% * | 1.964 | 2.9% * | 2.536 | 32.8% | ||
K2 | 1.909 | 2.395 | 25.5% | 1.990 | 4.2% * | 1.985 | 4.0% * | 2.643 | 38.4% | ||
|
1.909 | 3.684 | 93.0% | 2.044 | 7.1% * | 2.027 | 6.2% * | 4.529 | 137.3% | ||
| |||||||||||
1000 | Normal | 1.356 | 1.362 | 0.4% * | 1.384 | 2.1% * | 1.383 | 2.0% * | 1.371 | 1.2% * | |
Uniform | 1.356 | 1.232 | −9.1% * | 1.414 | 4.3% * | 1.409 | 3.9% * | 1.247 | −8.0% * | ||
K1 | 1.356 | 1.693 | 24.9% | 1.405 | 3.7% * | 1.402 | 3.4% * | 1.836 | 35.5% | ||
K2 | 1.356 | 1.681 | 24.0% | 1.405 | 3.6% * | 1.391 | 2.6% * | 2.198 | 62.2% | ||
|
1.356 | 2.883 | 112.7% | 1.385 | 2.2% * | 1.388 | 2.4% * | 3.709 | 173.6% | ||
| |||||||||||
5000 | Normal | 0.608 | 0.613 | 0.7% * | 0.616 | 1.2% * | 0.616 | 1.2% * | 0.625 | 2.7% * | |
Uniform | 0.608 | 0.546 | −10.2% | 0.622 | 2.3% * | 0.623 | 2.4% * | 0.552 | −9.2% * | ||
K1 | 0.608 | 0.739 | 21.4% | 0.610 | 0.3% * | 0.609 | 0.1% * | 0.820 | 34.7% | ||
K2 | 0.608 | 0.730 | 19.9% | 0.614 | 0.9% * | 0.613 | 0.8% * | 0.876 | 44.1% | ||
|
0.608 | 1.909 | 213.8% | 0.612 | 0.5% * | 0.613 | 0.7% * | 2.597 | 326.9% |
Note. RB means relative bias.
means relative bias ≤ |10%| criterion met.
Note. RB means relative bias.
means relative bias ≤ |10%| criterion met.