|  |  | True covariance structure | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
 |  |  | IND | AR1 | UNS | |||||||||
 |  |  | LMM working covariance |  | LMM working covariance |  | LMM working covariance |  | ||||||
( m, n ) | β 1 | β 2 | IND | AR1 | UNS | SMA(UMA) | IND | AR1 | UNS | SMA(UMA) | IND | AR1 | UNS | SMA(UMA) |
(5,5) | 0 | 0 | 0.031 | 0.038 | 0.231 | 0.042 | 0.049 | 0.037 | 0.189 | 0.040 | 0.049 | 0.048 | 0.217 | 0.043 |
 | 0.25 | 0.020 | 0.132 | 0.142 | 0.336 | 0.142 | 0.085 | 0.071 | 0.211 | 0.078 | 0.103 | 0.102 | 0.269 | 0.095 |
 | 0.35 | 0.040 | 0.211 | 0.207 | 0.409 | 0.213 | 0.138 | 0.126 | 0.273 | 0.123 | 0.146 | 0.145 | 0.313 | 0.124 |
(5,10) | 0 | 0 | 0.052 | 0.056 | 0.082 | 0.054 | 0.058 | 0.045 | 0.082 | 0.055 | 0.053 | 0.052 | 0.088 | 0.051 |
 | 0.25 | 0.020 | 0.253 | 0.260 | 0.291 | 0.257 | 0.144 | 0.146 | 0.177 | 0.143 | 0.149 | 0.151 | 0.188 | 0.144 |
 | 0.35 | 0.040 | 0.451 | 0.448 | 0.473 | 0.450 | 0.239 | 0.223 | 0.249 | 0.234 | 0.259 | 0.259 | 0.298 | 0.255 |
(5,30) | 0 | 0 | 0.044 | 0.046 | 0.052 | 0.044 | 0.047 | 0.051 | 0.058 | 0.046 | 0.053 | 0.055 | 0.061 | 0.053 |
 | 0.25 | 0.020 | 0.673 | 0.673 | 0.682 | 0.672 | 0.332 | 0.336 | 0.346 | 0.331 | 0.386 | 0.382 | 0.394 | 0.386 |
 | 0.35 | 0.040 | 0.923 | 0.922 | 0.939 | 0.922 | 0.578 | 0.581 | 0.590 | 0.578 | 0.621 | 0.619 | 0.622 | 0.620 |
(5,50) | 0 | 0 | 0.049 | 0.049 | 0.049 | 0.046 | 0.050 | 0.054 | 0.051 | 0.050 | 0.047 | 0.046 | 0.045 | 0.047 |
 | 0.25 | 0.020 | 0.886 | 0.884 | 0.890 | 0.886 | 0.509 | 0.580 | 0.577 | 0.509 | 0.569 | 0.570 | 0.534 | 0.566 |
 | 0.35 | 0.040 | 0.986 | 0.986 | 0.990 | 0.986 | 0.800 | 0.804 | 0.806 | 0.800 | 0.847 | 0.847 | 0.839 | 0.852 |
(10,5) | 0 | 0 | 0.039 | 0.043 | --* | 0.034 | 0.034 | 0.030 | --* | 0.038 | 0.037 | 0.038 | --* | 0.035 |
 | 0.25 | 0.010 | 0.175 | 0.178 | --* | 0.174 | 0.079 | 0.079 | --* | 0.089 | 0.107 | 0.106 | --* | 0.097 |
 | 0.35 | 0.020 | 0.295 | 0.296 | --* | 0.286 | 0.143 | 0.144 | --* | 0.153 | 0.141 | 0.143 | --* | 0.125 |
(10,10) | 0 | 0 | 0.050 | 0.052 | 0.244 | 0.050 | 0.065 | 0.047 | 0.237 | 0.063 | 0.047 | 0.048 | 0.259 | 0.045 |
 | 0.25 | 0.010 | 0.330 | 0.330 | 0.541 | 0.328 | 0.173 | 0.175 | 0.348 | 0.172 | 0.185 | 0.185 | 0.393 | 0.182 |
 | 0.35 | 0.020 | 0.574 | 0.570 | 0.709 | 0.573 | 0.307 | 0.300 | 0.470 | 0.302 | 0.302 | 0.300 | 0.451 | 0.298 |
(10,30) | 0 | 0 | 0.043 | 0.049 | 0.058 | 0.043 | 0.050 | 0.048 | 0.058 | 0.050 | 0.049 | 0.050 | 0.057 | 0.049 |
 | 0.25 | 0.010 | 0.822 | 0.822 | 0.840 | 0.822 | 0.454 | 0.453 | 0.462 | 0.454 | 0.465 | 0.467 | 0.480 | 0.467 |
 | 0.35 | 0.020 | 0.979 | 0.971 | 0.986 | 0.979 | 0.726 | 0.762 | 0.769 | 0.726 | 0.733 | 0.731 | 0.743 | 0.733 |
(10,50) | 0 | 0 | 0.045 | 0.045 | 0.050 | 0.045 | 0.050 | 0.042 | 0.050 | 0.050 | 0.049 | 0.049 | 0.050 | 0.050 |
 | 0.25 | 0.010 | 0.952 | 0.951 | 0.954 | 0.952 | 0.671 | 0.695 | 0.671 | 0.671 | 0.671 | 0.671 | 0.670 | 0.675 |
 | 0.35 | 0.020 | 1.000 | 1.000 | 1.000 | 1.000 | 0.906 | 0.934 | 0.935 | 0.906 | 0.909 | 0.909 | 0.916 | 0.911 |
(20,5) | 0 | 0 | 0.053 | 0.057 | --* | 0.043 | 0.052 | 0.040 | --* | 0.049 | 0.048 | 0.049 | --* | 0.038 |
 | 0.25 | 0.005 | 0.214 | 0.221 | --* | 0.204 | 0.120 | 0.107 | --* | 0.103 | 0.100 | 0.101 | --* | 0.091 |
 | 0.35 | 0.010 | 0.399 | 0.403 | --* | 0.369 | 0.203 | 0.193 | --* | 0.185 | 0.206 | 0.206 | --* | 0.189 |
(20,10) | 0 | 0 | 0.050 | 0.050 | --* | 0.048 | 0.046 | 0.046 | --* | 0.045 | 0.050 | 0.053 | --* | 0.057 |
 | 0.25 | 0.005 | 0.455 | 0.455 | --* | 0.451 | 0.238 | 0.237 | --* | 0.238 | 0.237 | 0.239 | --* | 0.236 |
 | 0.35 | 0.010 | 0.716 | 0.714 | --* | 0.705 | 0.387 | 0.392 | --* | 0.383 | 0.360 | 0.359 | --* | 0.368 |
(20,30) | 0 | 0 | 0.055 | 0.056 | 0.103 | 0.055 | 0.056 | 0.066 | 0.097 | 0.060 | 0.049 | 0.049 | 0.110 | 0.048 |
 | 0.25 | 0.005 | 0.899 | 0.899 | 0.942 | 0.899 | 0.595 | 0.611 | 0.646 | 0.597 | 0.580 | 0.580 | 0.619 | 0.583 |
 | 0.35 | 0.010 | 0.993 | 0.993 | 1.000 | 0.993 | 0.873 | 0.890 | 0.917 | 0.873 | 0.830 | 0.832 | 0.881 | 0.844 |
(20,50) | 0 | 0 | 0.046 | 0.047 | 0.079 | 0.045 | 0.042 | 0.042 | 0.079 | 0.047 | 0.049 | 0.049 | 0.082 | 0.050 |
 | 0.25 | 0.005 | 0.992 | 0.990 | 1.000 | 0.990 | 0.831 | 0.855 | 0.881 | 0.831 | 0.781 | 0.780 | 0.834 | 0.796 |
 | 0.35 | 0.010 | 1.000 | 1.000 | 1.000 | 1.000 | 0.960 | 0.979 | 1.000 | 0.977 | 0.999 | 0.998 | 1.000 | 1.000 |