| | |
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
|
- *: Since m was large relative to the sample size (N = 2n), modeling with large number of parameters was discarded