|  | True covariance structure | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
 |  | IND | AR1 | UNS | ||||||||||||
 |  | LMM working covariance |  |  | LMM working covariance |  |  | LMM working covariance |  |  | ||||||
( m, n ) | β 3 | IND | AR1 | UNS | SMA | UMA | IND | AR1 | UNS | SMA | UMA | IND | AR1 | UNS | SMA | UMA |
(5,5) | 0 | 0.057 | 0.065 | 0.222 | 0.043 | 0.043 | 0.192 | 0.079 | 0.270 | 0.047 | 0.055 | 0.044 | 0.074 | 0.251 | 0.042 | 0.068 |
 | 0.040 | 0.074 | 0.087 | 0.260 | 0.065 | 0.052 | 0.240 | 0.126 | 0.276 | 0.076 | 0.061 | 0.095 | 0.160 | 0.358 | 0.099 | 0.086 |
 | 0.080 | 0.209 | 0.232 | 0.399 | 0.167 | 0.095 | 0.424 | 0.242 | 0.391 | 0.141 | 0.071 | 0.278 | 0.361 | 0.589 | 0.247 | 0.114 |
(5,10) | 0 | 0.050 | 0.062 | 0.099 | 0.049 | 0.059 | 0.185 | 0.064 | 0.100 | 0.047 | 0.050 | 0.040 | 0.060 | 0.100 | 0.044 | 0.042 |
 | 0.040 | 0.128 | 0.135 | 0.196 | 0.111 | 0.090 | 0.381 | 0.136 | 0.202 | 0.099 | 0.076 | 0.155 | 0.202 | 0.316 | 0.161 | 0.117 |
 | 0.080 | 0.351 | 0.362 | 0.412 | 0.329 | 0.166 | 0.776 | 0.405 | 0.478 | 0.317 | 0.166 | 0.545 | 0.621 | 0.766 | 0.569 | 0.442 |
(5,30) | 0 | 0.049 | 0.054 | 0.062 | 0.050 | 0.056 | 0.188 | 0.055 | 0.057 | 0.055 | 0.048 | 0.045 | 0.064 | 0.056 | 0.056 | 0.062 |
 | 0.040 | 0.295 | 0.305 | 0.316 | 0.285 | 0.171 | 0.501 | 0.297 | 0.302 | 0.263 | 0.156 | 0.465 | 0.532 | 0.637 | 0.488 | 0.401 |
 | 0.080 | 0.807 | 0.810 | 0.823 | 0.779 | 0.522 | 0.973 | 0.828 | 0.840 | 0.786 | 0.580 | 0.968 | 0.980 | 0.995 | 0.971 | 0.976 |
(5,50) | 0 | 0.038 | 0.039 | 0.045 | 0.041 | 0.039 | 0.176 | 0.059 | 0.058 | 0.054 | 0.056 | 0.039 | 0.062 | 0.049 | 0.048 | 0.040 |
 | 0.040 | 0.421 | 0.425 | 0.429 | 0.414 | 0.235 | 0.685 | 0.445 | 0.446 | 0.393 | 0.239 | 0.685 | 0.745 | 0.780 | 0.717 | 0.674 |
 | 0.080 | 0.952 | 0.952 | 0.954 | 0.948 | 0.824 | 1.000 | 0.954 | 0.957 | 0.946 | 0.838 | 0.998 | 0.998 | 1.000 | 0.998 | 0.998 |
(10,5) | 0 | 0.059 | 0.065 | --* | 0.052 | --†| 0.300 | 0.072 | --* | 0.039 | --†| 0.050 | 0.059 | --* | 0.042 | --†|
 | 0.020 | 0.129 | 0.138 | --* | 0.100 | --†| 0.412 | 0.123 | --* | 0.071 | --†| 0.172 | 0.189 | --* | 0.159 | --†|
 | 0.040 | 0.362 | 0.371 | --* | 0.280 | --†| 0.540 | 0.248 | --* | 0.146 | --†| 0.545 | 0.545 | --* | 0.418 | --†|
(10,10) | 0 | 0.050 | 0.053 | 0.275 | 0.055 | 0.045 | 0.309 | 0.045 | 0.241 | 0.040 | 0.039 | 0.044 | 0.044 | 0.281 | 0.049 | 0.044 |
 | 0.020 | 0.177 | 0.177 | 0.400 | 0.184 | 0.078 | 0.453 | 0.162 | 0.375 | 0.129 | 0.066 | 0.284 | 0.289 | 0.493 | 0.275 | 0.113 |
 | 0.040 | 0.323 | 0.326 | 0.641 | 0.576 | 0.178 | 0.707 | 0.391 | 0.616 | 0.299 | 0.097 | 0.828 | 0.825 | 0.840 | 0.772 | 0.254 |
(10,30) | 0 | 0.050 | 0.051 | 0.097 | 0.047 | 0.048 | 0.278 | 0.051 | 0.088 | 0.060 | 0.057 | 0.059 | 0.059 | 0.095 | 0.053 | 0.049 |
 | 0.020 | 0.502 | 0.502 | 0.587 | 0.494 | 0.191 | 0.596 | 0.297 | 0.344 | 0.259 | 0.112 | 0.660 | 0.660 | 0.774 | 0.673 | 0.320 |
 | 0.040 | 0.977 | 0.972 | 1.000 | 0.977 | 0.725 | 0.980 | 0.802 | 0.866 | 0.747 | 0.370 | 1.000 | 1.000 | 1.000 | 0.997 | 0.943 |
(10,50) | 0 | 0.052 | 0.052 | 0.075 | 0.049 | 0.047 | 0.283 | 0.058 | 0.072 | 0.049 | 0.065 | 0.050 | 0.052 | 0.078 | 0.048 | 0.049 |
 | 0.020 | 0.698 | 0.696 | 0.708 | 0.686 | 0.351 | 0.762 | 0.460 | 0.471 | 0.399 | 0.180 | 0.876 | 0.877 | 0.909 | 0.887 | 0.600 |
 | 0.040 | 0.998 | 0.998 | 1.000 | 0.998 | 0.949 | 1.000 | 0.966 | 0.970 | 0.938 | 0.686 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
(20,5) | 0 | 0.049 | 0.055 | --* | 0.044 | --†| 0.340 | 0.052 | --* | 0.048 | --†| 0.050 | 0.054 | --* | 0.054 | --†|
 | 0.010 | 0.208 | 0.217 | --* | 0.157 | --†| 0.436 | 0.119 | --* | 0.083 | --†| 0.210 | 0.218 | --* | 0.211 | --†|
 | 0.020 | 0.614 | 0.619 | --* | 0.489 | --†| 0.647 | 0.288 | --* | 0.200 | --†| 0.641 | 0.639 | --* | 0.655 | --†|
(20,10) | 0 | 0.050 | 0.057 | --* | 0.051 | --†| 0.329 | 0.053 | --* | 0.043 | --†| 0.049 | 0.053 | --* | 0.054 | --†|
 | 0.010 | 0.361 | 0.361 | --* | 0.316 | --†| 0.788 | 0.154 | --* | 0.122 | --†| 0.446 | 0.448 | --* | 0.445 | --†|
 | 0.020 | 0.911 | 0.908 | --* | 0.863 | --†| 0.803 | 0.460 | --* | 0.382 | --†| 0.972 | 0.971 | --* | 0.955 | --†|
(20,30) | 0 | 0.057 | 0.055 | 0.178 | 0.063 | 0.065 | 0.350 | 0.048 | 0.169 | 0.044 | 0.041 | 0.052 | 0.052 | 0.181 | 0.048 | 0.050 |
 | 0.010 | 0.808 | 0.808 | 0.928 | 0.795 | 0.258 | 0.736 | 0.384 | 0.444 | 0.340 | 0.101 | 0.914 | 0.914 | 1.000 | 0.927 | 0.399 |
 | 0.020 | 1.000 | 1.000 | 1.000 | 1.000 | 0.871 | 1.000 | 0.914 | 1.000 | 0.855 | 0.293 | 1.000 | 1.000 | 1.000 | 1.000 | 0.987 |
(20,50) | 0 | 0.049 | 0.046 | 0.095 | 0.046 | 0.049 | 0.346 | 0.042 | 0.089 | 0.042 | 0.051 | 0.049 | 0.050 | 0.104 | 0.049 | 0.052 |
 | 0.010 | 0.935 | 0.932 | 0.986 | 0.926 | 0.442 | 0.833 | 0.525 | 0.550 | 0.482 | 0.154 | 0.990 | 0.992 | 1.000 | 0.992 | 0.715 |
 | 0.020 | 1.000 | 1.000 | 1.000 | 1.000 | 0.997 | 1.000 | 0.986 | 1.000 | 0.969 | 0.597 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |