Background
Methods
Unstructured multivariate approach (UMA)
Linear mixed model (LMM)
The summary measure approach (SMA)
Simulation study
Results
Simulation results
Within-subject (time) and within-by-between-subjects (interaction) effects
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 | 0.052 | 0.071 | 0.230 | 0.059 | 0.052 | 0.188 | 0.079 | 0.230 | 0.050 | 0.043 | 0.045 | 0.075 | 0.252 | 0.059 | 0.041 |
0.25 | 0.020 | 0.097 | 0.118 | 0.258 | 0.086 | 0.064 | 0.264 | 0.129 | 0.288 | 0.081 | 0.064 | 0.120 | 0.169 | 0.352 | 0.112 | 0.065 | |
0.35 | 0.040 | 0.197 | 0.216 | 0.373 | 0.181 | 0.080 | 0.418 | 0.251 | 0.418 | 0.168 | 0.070 | 0.287 | 0.378 | 0.590 | 0.289 | 0.140 | |
(5,10) | 0 | 0 | 0.052 | 0.070 | 0.100 | 0.053 | 0.046 | 0.165 | 0.072 | 0.109 | 0.047 | 0.055 | 0.035 | 0.060 | 0.101 | 0.040 | 0.042 |
0.25 | 0.020 | 0.114 | 0.133 | 0.165 | 0.107 | 0.057 | 0.317 | 0.146 | 0.194 | 0.115 | 0.083 | 0.159 | 0.212 | 0.315 | 0.171 | 0.124 | |
0.35 | 0.040 | 0.352 | 0.370 | 0.429 | 0.338 | 0.188 | 0.577 | 0.393 | 0.443 | 0.315 | 0.183 | 0.565 | 0.634 | 0.765 | 0.565 | 0.428 | |
(5,30) | 0 | 0 | 0.044 | 0.065 | 0.069 | 0.043 | 0.051 | 0.177 | 0.056 | 0.064 | 0.053 | 0.051 | 0.051 | 0.065 | 0.065 | 0.058 | 0.053 |
0.25 | 0.020 | 0.305 | 0.320 | 0.331 | 0.296 | 0.163 | 0.530 | 0.316 | 0.335 | 0.287 | 0.171 | 0.458 | 0.513 | 0.629 | 0.466 | 0.393 | |
0.35 | 0.040 | 0.785 | 0.792 | 0.809 | 0.772 | 0.532 | 0.910 | 0.809 | 0.810 | 0.775 | 0.576 | 0.963 | 0.975 | 0.995 | 0.958 | 0.965 | |
(5,50) | 0 | 0 | 0.049 | 0.054 | 0.058 | 0.048 | 0.050 | 0.173 | 0.059 | 0.050 | 0.057 | 0.047 | 0.048 | 0.069 | 0.045 | 0.041 | 0.045 |
0.25 | 0.020 | 0.437 | 0.443 | 0.450 | 0.431 | 0.243 | 0.681 | 0.480 | 0.485 | 0.424 | 0.262 | 0.686 | 0.737 | 0.783 | 0.715 | 0.658 | |
0.35 | 0.040 | 0.940 | 0.939 | 0.941 | 0.941 | 0.810 | 0.988 | 0.960 | 0.972 | 0.950 | 0.831 | 0.998 | 0.999 | 1.000 | 0.999 | 1.000 | |
(10,5) | 0 | 0 | 0.049 | 0.071 | --* | 0.048 | --† | 0.277 | 0.070 | --* | 0.058 | --† | 0.047 | 0.060 | --* | 0.048 | --† |
0.25 | 0.010 | 0.158 | 0.179 | --* | 0.148 | --† | 0.366 | 0.105 | --* | 0.070 | --† | 0.176 | 0.194 | --* | 0.156 | --† | |
0.35 | 0.020 | 0.360 | 0.371 | --* | 0.286 | --† | 0.519 | 0.256 | --* | 0.157 | --† | 0.492 | 0.488 | --* | 0.409 | --† | |
(10,10) | 0 | 0 | 0.065 | 0.078 | 0.265 | 0.059 | 0.043 | 0.290 | 0.063 | 0.277 | 0.055 | 0.057 | 0.040 | 0.043 | 0.279 | 0.043 | 0.059 |
0.25 | 0.010 | 0.200 | 0.217 | 0.453 | 0.189 | 0.078 | 0.423 | 0.134 | 0.385 | 0.121 | 0.065 | 0.271 | 0.277 | 0.500 | 0.266 | 0.090 | |
0.35 | 0.020 | 0.636 | 0.652 | 0.772 | 0.580 | 0.152 | 0.689 | 0.401 | 0.600 | 0.327 | 0.107 | 0.815 | 0.814 | 0.879 | 0.786 | 0.279 | |
(10,30) | 0 | 0 | 0.063 | 0.076 | 0.086 | 0.062 | 0.039 | 0.268 | 0.053 | 0.093 | 0.049 | 0.039 | 0.040 | 0.043 | 0.092 | 0.038 | 0.045 |
0.25 | 0.010 | 0.507 | 0.517 | 0.570 | 0.488 | 0.197 | 0.621 | 0.310 | 0.385 | 0.278 | 0.136 | 0.709 | 0.714 | 0.898 | 0.697 | 0.341 | |
0.35 | 0.020 | 0.979 | 0.979 | 1.000 | 0.974 | 0.715 | 0.949 | 0.824 | 0.879 | 0.764 | 0.420 | 1.000 | 1.000 | 1.000 | 0.999 | 0.959 | |
(10,50) | 0 | 0 | 0.055 | 0.058 | 0.067 | 0.054 | 0.049 | 0.257 | 0.051 | 0.061 | 0.049 | 0.041 | 0.048 | 0.048 | 0.067 | 0.056 | 0.054 |
0.25 | 0.010 | 0.716 | 0.718 | 0.725 | 0.712 | 0.310 | 0.752 | 0.484 | 0.500 | 0.428 | 0.204 | 0.893 | 0.896 | 0.940 | 0.893 | 0.603 | |
0.35 | 0.020 | 0.999 | 0.996 | 1.000 | 0.999 | 0.958 | 0.993 | 0.961 | 0.970 | 0.941 | 0.684 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | |
(20,5) | 0 | 0 | 0.062 | 0.070 | --* | 0.054 | --† | 0.369 | 0.066 | --* | 0.054 | --† | 0.049 | 0.050 | --* | 0.050 | --† |
0.25 | 0.005 | 0.203 | 0.218 | --* | 0.164 | --† | 0.462 | 0.098 | --* | 0.076 | --† | 0.235 | 0.241 | --* | 0.242 | --† | |
0.35 | 0.010 | 0.619 | 0.621 | --* | 0.529 | --† | 0.606 | 0.265 | --* | 0.1208 | --† | 0.700 | 0.711 | --* | 0.706 | --† | |
(20,10) | 0 | 0 | 0.065 | 0.069 | --* | 0.058 | --† | 0.378 | 0.056 | --* | 0.046 | --† | 0.040 | 0.040 | --* | 0.040 | --† |
0.25 | 0.005 | 0.394 | 0.394 | --* | 0.380 | --† | 0.530 | 0.171 | --* | 0.143 | --† | 0.469 | 0.472 | --* | 0.481 | --† | |
0.35 | 0.010 | 0.901 | 0.902 | --* | 0.870 | --† | 0.790 | 0.472 | --* | 0.394 | --† | 0.960 | 0.961 | --* | 0.961 | --† | |
(20,30) | 0 | 0 | 0.047 | 0.050 | 0.173 | 0.049 | 0.057 | 0.369 | 0.051 | 0.179 | 0.045 | 0.049 | 0.049 | 0.049 | 0.178 | 0.051 | 0.061 |
0.25 | 0.005 | 0.794 | 0.794 | 0.888 | 0.789 | 0.223 | 0.705 | 0.355 | 0.435 | 0.327 | 0.111 | 0.920 | 0.920 | 1.000 | 0.918 | 0.392 | |
0.35 | 0.010 | 1.000 | 1.000 | 1.000 | 1.000 | 0.857 | 0.977 | 0.889 | 0.940 | 0.832 | 0.293 | 1.000 | 1.000 | 1.000 | 1.000 | 0.985 | |
(20,50) | 0 | 0 | 0.047 | 0.049 | 0.102 | 0.045 | 0.043 | 0.360 | 0.045 | 0.098 | 0.034 | 0.039 | 0.046 | 0.047 | 0.104 | 0.049 | 0.046 |
0.25 | 0.005 | 0.979 | 0.976 | 1.000 | 0.942 | 0.441 | 0.849 | 0.567 | 0.628 | 0.479 | 0.154 | 1.000 | 1.000 | 1.000 | 0.993 | 0.775 | |
0.35 | 0.010 | 1.000 | 1.000 | 1.000 | 1.000 | 0.996 | 1.000 | 0.991 | 1.000 | 0.975 | 0.628 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
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 |
Between-subjects (group) effect
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 |
Illustrative examples
Example 1: Pituitary-pteryomaxillary distance data
Effect | |||||||
---|---|---|---|---|---|---|---|
Method | no | Structure | Group | Time | Group × Time | AIC | BIC |
LMM with Random intercept | 1 | IND | 0.005 | < 0.001 | 0.014 | 445.76 | 461.62 |
2 | AR1 | 0.006 | < 0.001 | 0.012 | 447.71 | 466.22 | |
3 | UNS | 0.007 | < 0.001 | 0.009 | 450.17 | 481.90 | |
LMM with Random intercept and slope | 4 | IND | 0.009 | < 0.001 | 0.026 | 448.58 | 469.74 |
5 | AR1 | 0.015 | < 0.001 | 0.021 | 446.81 | 470.61 | |
6 | UNS | 0.010 | < 0.001 | 0.009 | 454.12 | 491.14 | |
SMA | 7 | - | 0.005 | < 0.001 | 0.019 | - | - |
UMA | 8 | - | 0.005 | < 0.001 | 0.070 | - | - |
Example 2: Change in lung NO metabolites level data
Effect | |||||||
---|---|---|---|---|---|---|---|
Method | no | Structure | Group | Time | Group × Time | AIC | BIC |
LMM with Random intercept | 1 | IND | 0.264 | < 0.001 | < 0.001 | 121.38 | 148.31 |
2 | AR1 | 0.248 | < 0.001 | 0.026 | 58.77 | 89.06 | |
3 | UNS | 0.175 | < 0.001 | < 0.001 | 10.91 | 344.14 | |
LMM with Random intercept and slope | 4 | IND | 0.212 | < 0.001 | 0.236 | 4.51 | 38.17 |
5 | AR1 | 0.209 | < 0.001 | 0.234 | 5.90 | 42.93 | |
6 | UNS | < 0.001 | < 0.001 | 0.262 | -0.57 | 339.39 | |
SMA | 7 | - | 0.273 | < 0.001 | 0.241 | - | - |