Table 2.
Simulation results for the two-level logistic model:the average of parameter estimates (RMSE).
| Software | SAS GLIMMIX | R lme4 | HLM | SuperMix | Stata xtmelogit | |||||
|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
|
|
|
||||||
| Estimation | PQL | Laplace | AGQ-10 | Laplace | AGQ-10 | PQL | Laplace6 | AGQ-10 | Laplace | AGQ-10 |
| True Values | Regression Coefficients | |||||||||
| β0= −1.2 | −1.146 (0.301) |
−1.227 (0.318) |
−1.228 (0.318) |
−1.223 (0.319) |
−1.219 (0.315) |
−1.146 (0.296) |
−1.223 (0.315) |
−1.228 (0.317) |
−1.190 (0.394) |
−1.217 (0.307) |
| β1= 1.0 | 0.930 (0.147) |
1.002 (0.141) |
1.003 (0.141) |
0.999 (0.140) |
0.996 (0.139) |
0.930 (0.129) |
0.999 (0.140) |
1.003 (0.141) |
0.973 (0.131) |
0.977 (0.130) |
| β2= 1.0 | 0.940 (0.102) |
0.990 (0.088) |
0.991 (0.088) |
0.999 (0.088) |
0.988 (0.088) |
0.940 (0.082) |
0.989 (0.087) |
0.991 (0.087) |
0.969 (0.230) |
0.992 (0.089) |
| β3= −0.5 | −0.403 (0.449) |
−0.431 (0.474) |
−0.431 (0.473) |
−0.430 (0.473) |
−0.429 (0.467) |
−0.403 (0.438) |
−0.428 (0.465) |
−0.431 (0.468) |
−0.391 (0.442) |
−0.390 (0.440) |
|
| ||||||||||
| Variance-Covariance Matrix of Random Effects | ||||||||||
| θ00= 3.0 | 2.698 (0.694) |
2.990 (0.721) |
3.018 (0.729) |
2.986 (0.722) |
2.959 (0.713) |
2.698 (0.625) |
2.969 (0.715) |
3.018 (0.728) |
3.032 (0.820) |
3.061 (0.760) |
| θ01= −0.69 | −0.573 (0.267) |
−0.666 (0.280) |
−0.677 (0.282) |
−0.664 (0.280) |
−0.680 (0.259) |
−0.573 (0.240) |
−0.660 (0.275) |
−0.677 (0.282) |
−0.696 (0.285) |
−0.707 (0.279) |
| θ02= 0.23 | 0.205 (0.134) |
0.228 (0.150) |
0.226 (0.151) |
0.228 (0.150) |
0.223 (0.149) |
0.205 (0.131) |
0.230 (0.149) |
0.227 (0.151) |
0.233 (0.151) |
0.232 (0.151) |
| θ11= 1.00 | 0.861 (0.250) |
0.979 (0.245) |
0.991 (0.247) |
0.978 (0.243) |
0.962 (0.235) |
0.861 (0.208) |
0.973 (0.243) |
0.991 (0.247) |
0.986 (0.270) |
1.005 (0.240) |
|
θ12= 0.00045 |
0.00423 (0.07955) |
0.00681 (0.09136) |
0.00949 (0.09265) |
0.00671 (0.09119) |
0.00460 (0.09248) |
0.00423 (0.07946) |
0.00755 (0.09133) |
0.00947 (0.09221) |
0.00575 (0.09028) |
0.00842 (0.09197) |
| θ22=0.2 | 0.177 (0.064) |
0.193 (0.067) |
0.199 (0.068) |
0.193 (0.068) |
0.188 (0.067) |
0.177 (0.060) |
0.185 (0.067) |
0.199 (0.068) |
0.195 (0.070) |
0.202 (0.069) |