TABLE 1.
Posterior means and standard deviations (SDs) of β0 (true value = 15) and β1 (true value = −0.5), along with posterior mean deviance (Dbar) for five analysis models and six data-generating scenarios. Simulation study results averaged over 100 simulated datasets. Monte Carlo standard error (mcse) reported for each estimate in parentheses.
| Analysis Model |
mean(β0)(mcse) | SD(β0)(mcse) | mean(β1)(mcse) | SD(β1)(mcse) | Dbar(mcse) |
|---|---|---|---|---|---|
| (a) Best model: CAR (ρ = 0.00) | |||||
| LGM | 15.00 (0.01) | 0.0828 (0.0003) | −0.498 (0.005) | 0.0518 (0.0003) | 5205 (9) |
| HLM | 14.99 (0.01) | 0.1026 (0.0003) | −0.495 (0.005) | 0.0519 (0.0003) | 4169 (7) |
| CAR | 14.98 (0.01) | 0.1131 (0.0003) | −0.492 (0.005) | 0.0531 (0.0003) | 4177 (7) |
| PMM | 15.00 (0.01) | 0.0910 (0.0003) | −0.496 (0.007) | 0.0627 (0.0003) | 5205 (9) |
| CAR+PMM | 14.98 (0.01) | 0.1125 (0.0003) | −0.495 (0.006) | 0.0614 (0.0003) | 4177 (7) |
| (b) Best model: CAR (ρ = 0.25) | |||||
| LGM | 15.01 (0.01) | 0.0863 (0.0005) | −0.508 (0.006) | 0.0522 (0.0003) | 5126 (9) |
| HLM | 15.01 (0.01) | 0.1017 (0.0003) | −0.509 (0.005) | 0.0523 (0.0003) | 4162 (7) |
| CAR | 15.00 (0.01) | 0.1125 (0.0004) | −0.505 (0.005) | 0.0537 (0.0003) | 4171 (7) |
| PMM | 15.01 (0.01) | 0.0940 (0.0005) | −0.501 (0.007) | 0.0627 (0.0003) | 5126 (9) |
| CAR+PMM | 15.00 (0.01) | 0.1118 (0.0003) | −0.508 (0.006) | 0.0620 (0.0003) | 4170 (7) |
| (c) Best model: CAR (ρ = 0.50) | |||||
| LGM | 15.00 (0.02) | 0.0928 (0.0007) | −0.494 (0.005) | 0.0516 (0.0003) | 5021 (9) |
| HLM | 15.01 (0.01) | 0.1011 (0.0004) | −0.495 (0.005) | 0.0515 (0.0003) | 4169 (6) |
| CAR | 15.01 (0.01) | 0.1132 (0.0004) | −0.494 (0.005) | 0.0534 (0.0003) | 4179 (6) |
| PMM | 15.01 (0.02) | 0.0999 (0.0006) | −0.489 (0.006) | 0.0617 (0.0003) | 5020 (9) |
| CAR+PMM | 15.02 (0.01) | 0.1114 (0.0004) | −0.496 (0.005) | 0.0615 (0.0003) | 4178 (6) |
| (d) Best model: CAR+PMM (ρ = 0.00) | |||||
| LGM | 14.82 (0.01) | 1.378 (0.0009) | −0.208 (0.006) | 0.0687 (0.0005) | 5236 (10) |
| HLM | 14.87 (0.01) | 1.382 (0.0007) | −0.244 (0.005) | 0.0730 (0.0005) | 4201 (7) |
| CAR | 14.59 (0.01) | 1.387 (0.0008) | −0.268 (0.006) | 0.0797 (0.0005) | 4211 (7) |
| PMM | 15.11 (0.01) | 1.412 (0.0009) | −0.488 (0.006) | 0.0931 (0.0006) | 5197 (10) |
| CAR+PMM | 15.09 (0.01) | 1.405 (0.0007) | −0.494 (0.006) | 0.0917 (0.0005) | 4178 (7) |
| (e) Best model: CAR+PMM (ρ = 0.25) | |||||
| LGM | 14.78 (0.01) | 1.379 (0.0010) | −0.209 (0.006) | 0.0701 (0.0006) | 5146 (9) |
| HLM | 14.83 (0.01) | 1.381 (0.0009) | −0.240 (0.006) | 0.0734 (0.0005) | 4196 (8) |
| CAR | 14.55 (0.01) | 1.390 (0.0009) | −0.273 (0.007) | 0.0827 (0.0006) | 4205 (7) |
| PMM | 15.06 (0.01) | 1.411 (0.0010) | −0.484 (0.007) | 0.0933 (0.0006) | 5116 (9) |
| CAR+PMM | 15.05 (0.01) | 1.404 (0.0008) | −0.492 (0.007) | 0.0921 (0.0006) | 4173 (7) |
| (f) Best model: CAR+PMM (ρ = 0.50) | |||||
| LGM | 14.84 (0.02) | 1.383 (0.0011) | −0.226 (0.006) | 0.0715 (0.0005) | 5054 (9) |
| HLM | 14.87 (0.02) | 1.384 (0.0009) | −0.251 (0.005) | 0.0741 (0.0005) | 4204 (6) |
| CAR | 14.63 (0.02) | 1.397 (0.0010) | −0.307 (0.006) | 0.0876 (0.0005) | 4211 (6) |
| PMM | 15.11 (0.02) | 1.413 (0.0011) | −0.499 (0.007) | 0.0939 (0.0006) | 5031 (9) |
| CAR+PMM | 15.09 (0.02) | 1.406 (0.0007) | −0.507 (0.006) | 0.0932 (0.0005) | 4174 (6) |