TABLE 2.
Model parameter estimate percent bias (MSE) for the simulation study.
| Condition | Y Intercept | Y Resid. Var. | β 1 | β 2 |
| n = 25 | ||||
| 1 | 34.91 (0.0508) | −0.10 (0.2979) | −40.29 (0.1745) | −38.50 (0.0474) |
| 2 | 21.38 (0.0452) | −0.18 (0.1811) | −25.66 (0.0774) | −23.82 (0.0245) |
| 3 | 11.90 (0.0403) | −0.34 (0.1239) | −0.05 (0.0115) | 1.82 (0.0105) |
| 4 | 54.99 (0.0520) | −0.70 (0.5269) | 56.87 (0.3383) | 58.30 (0.0961) |
| 5 | 350.76 (0.1468) | −0.68 (14.0520) | 157.51 (2.4857) | 157.86 (0.6300) |
| 6 | 22.42 (0.0461) | −0.12 (0.1914) | −26.50 (0.0919) | −23.94 (0.0328) |
| 7 | 16.66 (0.0434) | −0.18 (0.1513) | −17.16 (0.0499) | −14.60 (0.0235) |
| 8 | 12.38 (0.0408) | −0.30 (0.1266) | −0.02 (0.0199) | 2.48 (0.0184) |
| 9 | 30.36 (0.0453) | −0.62 (0.2582) | 36.66 (0.1601) | 38.82 (0.0580) |
| 10 | 159.46 (0.0866) | −1.08 (3.3256) | 104.37 (1.1327) | 105.58 (0.3039) |
| 11 | 15.37 (0.0426) | −0.20 (0.1451) | 0.03 (0.0469) | 4.08 (0.0447) |
| n = 100 | ||||
| 1 | 4.44 (0.0106) | 0.00 (0.0211) | −13.59 (0.0265) | −12.58 (0.0111) |
| 2 | 3.16 (0.0104) | 0.02 (0.0194) | −9.06 (0.0160) | −8.06 (0.0086) |
| 3 | 2.17 (0.0103) | 0.04 (0.0183) | −0.26 (0.0076) | 0.70 (0.0068) |
| 4 | 6.37 (0.0107) | 0.08 (0.0245) | 17.76 (0.0395) | 18.64 (0.0155) |
| 5 | 23.57 (0.0123) | 0.14 (0.0908) | 40.44 (0.1742) | 41.22 (0.0502) |
| 6 | 2.98 (0.0105) | 0.00 (0.0192) | −7.55 (0.0151) | −6.46 (0.0094) |
| 7 | 2.60 (0.0104) | 0.00 (0.0187) | −5.12 (0.0119) | −4.04 (0.0087) |
| 8 | 2.30 (0.0104) | 0.02 (0.0184) | −0.30 (0.0091) | 0.76 (0.0082) |
| 9 | 3.52 (0.0105) | 0.04 (0.0199) | 9.40 (0.0180) | 10.42 (0.0108) |
| 10 | 7.52 (0.0108) | 0.06 (0.0272) | 19.79 (0.0490) | 20.76 (0.0191) |
| 11 | 2.49 (0.0104) | −0.02 (0.0186) | −0.36 (0.0112) | 0.84 (0.0100) |
| n = 1000 | ||||
| 1 | 0.27 (0.0010) | −0.36 (0.0020) | −1.33 (0.0012) | −1.56 (0.0010) |
| 2 | 0.26 (0.0010) | −0.36 (0.0020) | −0.83 (0.0010) | −1.08 (0.0009) |
| 3 | 0.25 (0.0010) | −0.36 (0.0020) | 0.16 (0.0010) | −0.08 (0.0009) |
| 4 | 0.30 (0.0010) | −0.36 (0.0020) | 2.14 (0.0014) | 1.90 (0.0010) |
| 5 | 0.44 (0.0010) | −0.36 (0.0021) | 4.12 (0.0027) | 3.88 (0.0013) |
| 6 | 0.26 (0.0010) | −0.36 (0.0020) | −0.59 (0.0010) | −0.84 (0.0010) |
| 7 | 0.25 (0.0010) | −0.36 (0.0020) | −0.34 (0.0010) | −0.58 (0.0009) |
| 8 | 0.25 (0.0010) | −0.36 (0.0020) | 0.16 (0.0010) | −0.08 (0.0009) |
| 9 | 0.26 (0.0010) | −0.36 (0.0020) | 1.16 (0.0011) | 0.92 (0.0010) |
| 10 | 0.30 (0.0010) | −0.36 (0.0020) | 2.16 (0.0014) | 1.92 (0.0010) |
| 11 | 0.25 (0.0010) | −0.36 (0.0020) | 0.16 (0.0010) | −0.08 (0.0010) |
Prior conditions (column 1) are described in Table 1. MSE, mean square error, which captures a measure of variability accompanied by bias for the simulation estimates. It can be used as a measure that reflects efficiency and accuracy in the simulation results. Bolded values represent percent bias exceeding 10%. Percent bias = [(estimate − population value)/population value] ∗ 100. β1 = Y on X1. β2 = Y on X2.