Table 3:
Simulation results: Biases and coverage rates of µρw (average within-person relation) estimates when µρw = 0, N = 100, and one predictor is included.
| T | Individual differences in within-person relations exist | No individual differences in within-person relations | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Bias | Coverage rates (%) | Bias | Coverage rates (%) | ||||||||
| All 5 methods | MG1 | MG2 | MG3 | MPS | MEB | All 4 methods | MG1 | MG2 | MG3 | MPS | |
| Between-person differences in within-person standard deviations of X and Y exist | |||||||||||
| 5 | 0.00 | 94.5 | 94.5 | 94.9 | 95.4 | 34.2 | 0.00 | 91.1 | 91.1 | 87.7 | 91.8 |
| 10 | 0.00 | 94.1 | 94.1 | 93.9 | 94.4 | 44.6 | 0.00 | 93.9 | 93.9 | 92.2 | 94.0 |
| 20 | 0.00 | 94.0 | 94.0 | 93.7 | 94.1 | 63.4 | 0.00 | 93.2 | 93.2 | 92.4 | 94.6 |
| 30 | 0.00 | 93.7 | 93.7 | 93.9 | 93.8 | 75.8 | 0.00 | 94.6 | 94.6 | 94.3 | 95.9 |
| 56 | 0.00 | 95.3 | 95.3 | 95.6 | 94.7 | 85.7 | 0.00 | 93.4 | 93.4 | 93.3 | 94.9 |
| 100 | 0.00 | 95.3 | 95.3 | 95.4 | 94.6 | 91.8 | 0.00 | 93.3 | 93.3 | 93.3 | 96.2 |
|
Between-person differences in within-person standard deviations exist for Y but not for X | |||||||||||
| 5 | 0.00 | 93.2 | 93.2 | 93.9 | 93.2 | 31.0 | 0.00 | 95.5 | 95.5 | 93.7 | 92.0 |
| 10 | 0.00 | 95.1 | 95.1 | 95.2 | 95.9 | 48.0 | 0.00 | 95.8 | 95.8 | 94.8 | 94.6 |
| 20 | 0.00 | 94.4 | 94.4 | 94.4 | 94.3 | 67.9 | 0.00 | 94.9 | 94.9 | 94.6 | 94.1 |
| 30 | 0.00 | 94.9 | 94.9 | 95.0 | 94.3 | 74.8 | 0.00 | 94.9 | 94.9 | 94.6 | 95.9 |
| 56 | 0.00 | 95.5 | 95.5 | 95.5 | 94.6 | 87.1 | 0.00 | 94.3 | 94.3 | 94.3 | 93.2 |
| 100 | 0.00 | 95.2 | 95.2 | 95.2 | 95.3 | 92.0 | 0.00 | 95.7 | 95.7 | 95.6 | 95.5 |
|
Between-person differences in within-person standard deviations of X and Y do not exist | |||||||||||
| 5 | 0.00 | 94.0 | 94.0 | 94.1 | 95.3 | 32.9 | 0.00 | 95.7 | 95.7 | 92.8 | 92.5 |
| 10 | 0.00 | 94.5 | 94.5 | 94.5 | 94.4 | 53.6 | 0.00 | 95.6 | 95.6 | 94.5 | 94.7 |
| 20 | 0.00 | 94.3 | 94.3 | 94.2 | 93.7 | 70.7 | 0.00 | 95.9 | 95.9 | 95.4 | 96.0 |
| 30 | 0.00 | 95.5 | 95.5 | 95.6 | 95.4 | 83.0 | 0.00 | 95.1 | 95.1 | 94.5 | 94.6 |
| 56 | 0.00 | 93.7 | 93.7 | 93.7 | 94.1 | 86.1 | 0.00 | 95.4 | 95.4 | 95.2 | 94.9 |
| 100 | 0.00 | 94.3 | 94.3 | 94.3 | 94.2 | 90.8 | 0.00 | 95.6 | 95.6 | 95.6 | 96.1 |
Note: MG1: the person-mean centering (P-C) model in Eq (2) followed by global standardization in Eq (5); MG2: the P-C model in Eq (2) followed by global standardization in Eq (6); MG3: the P-C model in Eq (4) followed by global standardization in Eq (7); MPS : the P-S standardization approach in Eq (9); MEB: the P-C model in Eq (2) with EB standardization.