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. Author manuscript; available in PMC: 2020 Oct 30.
Published in final edited form as: Stat Sci. 2020 Sep 11;35(3):375–390. doi: 10.1214/19-sts720

Table 5.

Bias and standard deviation (sd) for the estimated variance components σbj2, 0 ≤ j ≤ 3 and σϵ2 in the simulation study. n denotes sample size; T denotes total number of observations for each individual; GM denotes generative model. For GM 1 and GM 3, the model doesn’t include bi1 and bi3, so the corresponding entries in the table are left blank. The result is based on 1,000 replicates for each setting.

σb22 σb32 σb02 σb12 σϵ2
n T GM bias sd bias sd bias sd bias sd bias sd
30 0.024 0.400 - - −0.008 1.137 - - −0.003 0.049
50 0.013 0.300 - - −0.020 0.868 - - −0.002 0.035
1 10 100 0.017 0.210 - - −0.031 0.614 - - −0.001 0.024
200 0.004 0.151 - - −0.021 0.431 - - −0.000 0.017
30 0.012 0.319 - - −0.025 1.067 - - −0.003 0.032
50 0.010 0.246 - - −0.026 0.822 - - −0.001 0.023
1 20 100 0.008 0.174 - - −0.041 0.579 - - −0.001 0.016
200 0.004 0.126 - - −0.021 0.403 - - −0.000 0.011
30 0.003 0.293 - - −0.036 1.036 - - −0.002 0.025
50 0.001 0.232 - - −0.037 0.809 - - −0.001 0.018
1 30 100 0.008 0.163 - - −0.040 0.569 - - −0.001 0.013
200 0.000 0.116 - - −0.023 0.399 - - −0.000 0.009
30 0.047 0.498 −0.001 0.058 −0.003 1.238 −0.003 0.040 −0.003 0.048
50 0.048 0.392 −0.005 0.046 −0.057 0.935 −0.004 0.033 −0.001 0.038
2 10 100 0.000 0.260 −0.003 0.033 −0.019 0.646 −0.001 0.022 0.000 0.027
200 0.005 0.184 −0.003 0.021 −0.043 0.451 −0.001 0.015 −0.001 0.019
30 0.009 0.367 −0.003 0.043 −0.029 1.094 −0.003 0.032 −0.000 0.031
50 0.022 0.302 −0.003 0.033 −0.045 0.854 −0.002 0.025 0.000 0.025
2 20 100 0.002 0.200 −0.002 0.021 −0.016 0.597 −0.000 0.017 0.001 0.017
200 −0.001 0.142 −0.001 0.015 −0.029 0.418 −0.001 0.012 −0.001 0.012
30 0.001 0.334 −0.002 0.036 −0.045 1.065 −0.003 0.029 0.000 0.025
50 0.012 0.268 −0.003 0.027 −0.049 0.826 −0.002 0.022 0.000 0.019
2 30 100 0.002 0.183 −0.001 0.019 −0.028 0.584 0.000 0.016 0.000 0.013
200 −0.003 0.127 −0.001 0.013 −0.029 0.409 −0.001 0.011 −0.000 0.009
30 0.126 0.434 - - −0.710 1.159 - - 0.004 0.046
50 0.105 0.329 - - −0.771 0.860 - - 0.005 0.034
3 10 100 0.094 0.228 - - −0.810 0.604 - - 0.005 0.025
200 0.080 0.159 - - −0.796 0.429 - - 0.006 0.018
30 0.059 0.329 - - −0.380 1.056 - - 0.000 0.029
50 0.053 0.262 - - −0.428 0.800 - - 0.001 0.023
3 20 100 0.040 0.174 - - −0.429 0.575 - - 0.001 0.017
200 0.038 0.125 - - −0.430 0.406 - - 0.002 0.011
30 0.040 0.304 - - −0.268 1.029 - - −0.000 0.024
50 0.030 0.237 - - −0.296 0.782 - - −0.001 0.018
3 30 100 0.027 0.162 - - −0.306 0.569 - - 0.000 0.013
200 0.023 0.115 - - −0.299 0.395 - - 0.001 0.009