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. 2013 Feb 28;8(2):e57279. doi: 10.1371/journal.pone.0057279

Table 1. Variance of the group effect estimated in the simulation study (Inline graphic) and using the Cramer-Rao’s bound (Inline graphic) for different values of the group effect (Inline graphic), the sample size in each group (Inline graphic), the variance of the latent variable (Inline graphic), the number of items (Inline graphic), the spacing regularity of the items and the gap between the global mean of the latent variable and the mean of the distribution of the item difficulties (Inline graphic).

J = 5 J = 10
Normal distribution Mixture of normal distributions Normal distribution Mixture of normal distributions
Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic Inline graphic Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic Inline graphic/Inline graphic
0 50 0.25 0.045/0.045 0.047/0.047 0.052/0.052 0.046/0.046 0.047/0.047 0.052/0.052 0.028/0.028 0.028/0.030 0.031/0.033 0.028/0.028 0.029/0.029 0.031/0.032
1 0.082/0.082 0.088/0.089 0.113/0.113 0.085/0.085 0.088/0.088 0.107/0.107 0.062/0.062 0.065/0.067 0.078/0.081 0.063/0.063 0.065/0.066 0.075/0.077
4 0.225/0.226 0.252/0.251 0.368/0.367 0.232/0.232 0.242/0.242 0.318/0.318 0.195/0.196 0.210/0.211 0.272/0.275 0.198/0.199 0.204/0.205 0.250/0.252
9 0.458/0.459 0.520/0.521 0.782/0.777 0.466/0.467 0.493/0.493 0.645/0.641 0.413/0.413 0.447/0.447 0.589/0.595 0.417/0.418 0.432/0.433 0.520/0.518
100 0.25 0.022/0.022 0.023/0.023 0.026/0.026 0.023/0.023 0.023/0.023 0.026/0.026 0.014/0.014 0.014/0.015 0.016/0.016 0.014/0.014 0.014/0.015 0.016/0.016
1 0.041/0.041 0.044/0.044 0.056/0.056 0.042/0.042 0.044/0.044 0.053/0.053 0.031/0.031 0.033/0.033 0.039/0.040 0.031/0.032 0.032/0.033 0.037/0.038
4 0.113/0.113 0.126/0.126 0.184/0.183 0.116/0.116 0.121/0.121 0.159/0.159 0.097/0.098 0.105/0.105 0.136/0.137 0.099/0.099 0.102/0.102 0.125/0.125
9 0.229/0.229 0.260/0.259 0.389/0.388 0.233/0.233 0.246/0.246 0.321/0.320 0.206/0.207 0.223/0.224 0.294/0.294 0.208/0.209 0.216/0.216 0.259/0.259
200 0.25 0.011/0.011 0.012/0.012 0.013/0.013 0.011/0.011 0.012/0.012 0.013/0.013 0.007/0.007 0.007/0.007 0.008/0.008 0.007/0.007 0.007/0.007 0.008/0.008
1 0.020/0.020 0.022/0.022 0.028/0.028 0.021/0.021 0.022/0.022 0.027/0.027 0.015/0.015 0.016/0.016 0.019/0.020 0.016/0.016 0.016/0.016 0.019/0.019
4 0.056/0.056 0.063/0.063 0.092/0.092 0.058/0.058 0.061/0.061 0.079/0.079 0.049/0.049 0.052/0.052 0.068/0.068 0.049/0.050 0.051/0.051 0.062/0.062
9 0.114/0.114 0.130/0.130 0.194/0.194 0.116/0.116 0.123/0.123 0.161/0.161 0.103/0.103 0.112/0.112 0.147/0.147 0.104/0.104 0.108/0.108 0.129/0.129
300 0.25 0.007/0.007 0.008/0.008 0.009/0.009 0.008/0.008 0.008/0.008 0.009/0.009 0.005/0.005 0.005/0.005 0.005/0.005 0.005/0.005 0.005/0.005 0.005/0.005
1 0.014/0.014 0.015/0.015 0.019/0.019 0.014/0.014 0.015/0.015 0.018/0.018 0.010/0.010 0.011/0.011 0.013/0.013 0.010/0.011 0.011/0.011 0.012/0.013
4 0.038/0.038 0.042/0.042 0.061/0.061 0.039/0.039 0.040/0.040 0.053/0.053 0.032/0.032 0.035/0.035 0.045/0.045 0.033/0.033 0.034/0.034 0.042/0.042
9 0.076/0.076 0.086/0.087 0.129/0.129 0.078/0.078 0.082/0.082 0.107/0.107 0.069/0.069 0.074/0.074 0.098/0.098 0.069/0.069 0.072/0.072 0.086/0.086
500 0.25 0.004/0.004 0.005/0.005 0.005/0.005 0.005/0.005 0.005/0.005 0.005/0.005 0.003/0.003 0.003/0.003 0.003/0.003 0.003/0.003 0.003/0.003 0.003/0.003
1 0.008/0.008 0.009/0.009 0.011/0.011 0.008/0.008 0.009/0.009 0.011/0.011 0.006/0.006 0.006/0.007 0.008/0.008 0.006/0.006 0.006/0.007 0.007/0.008
4 0.023/0.023 0.025/0.025 0.037/0.037 0.023/0.023 0.024/0.024 0.032/0.032 0.019/0.019 0.021/0.021 0.027/0.027 0.020/0.020 0.020/0.020 0.025/0.025
9 0.046/0.046 0.052/0.052 0.078/0.078 0.047/0.047 0.049/0.049 0.064/0.064 0.041/0.041 0.045/0.045 0.059/0.059 0.042/0.042 0.043/0.043 0.052/0.052
0.2 50 0.25 0.045/0.045 0.045/0.047 0.045/0.053 0.045/0.046 0.045/0.047 0.045/0.052 0.028/0.029 0.028/0.030 0.028/0.033 0.028/0.029 0.028/0.029 0.028/0.032
1 0.082/0.082 0.089/0.089 0.113/0.113 0.085/0.085 0.088/0.088 0.107/0.107 0.062/0.062 0.065/0.067 0.078/0.081 0.063/0.064 0.065/0.066 0.075/0.077
4 0.226/0.226 0.225/0.252 0.225/0.371 0.225/0.232 0.226/0.242 0.225/0.318 0.195/0.196 0.195/0.211 0.195/0.276 0.195/0.198 0.195/0.205 0.195/0.252
9 0.458/0.457 0.458/0.519 0.458/0.783 0.458/0.466 0.458/0.492 0.458/0.644 0.413/0.413 0.413/0.449 0.413/0.591 0.413/0.418 0.413/0.432 0.413/0.519
100 0.25 0.022/0.022 0.022/0.023 0.022/0.026 0.022/0.023 0.022/0.023 0.022/0.026 0.014/0.014 0.014/0.015 0.014/0.016 0.014/0.014 0.014/0.015 0.014/0.016
1 0.041/0.041 0.044/0.044 0.056/0.056 0.042/0.042 0.044/0.044 0.053/0.053 0.031/0.031 0.033/0.033 0.039/0.040 0.032/0.032 0.032/0.033 0.037/0.038
4 0.113/0.113 0.113/0.126 0.113/0.184 0.113/0.116 0.113/0.121 0.113/0.158 0.097/0.098 0.097/0.105 0.097/0.137 0.097/0.099 0.097/0.102 0.097/0.125
9 0.229/0.229 0.229/0.259 0.229/0.389 0.229/0.233 0.229/0.246 0.229/0.320 0.206/0.206 0.206/0.224 0.206/0.294 0.206/0.208 0.206/0.216 0.206/0.259
200 0.25 0.011/0.011 0.011/0.012 0.011/0.013 0.011/0.011 0.011/0.012 0.011/0.013 0.007/0.007 0.007/0.007 0.007/0.008 0.007/0.007 0.007/0.007 0.007/0.008
1 0.020/0.020 0.022/0.022 0.028/0.028 0.021/0.021 0.022/0.022 0.027/0.027 0.015/0.015 0.016/0.016 0.019/0.020 0.016/0.016 0.016/0.016 0.019/0.019
4 0.056/0.056 0.056/0.063 0.056/0.092 0.056/0.058 0.056/0.061 0.056/0.079 0.049/0.049 0.049/0.052 0.049/0.068 0.049/0.049 0.049/0.051 0.049/0.062
9 0.114/0.114 0.114/0.130 0.114/0.194 0.114/0.117 0.114/0.123 0.114/0.161 0.103/0.103 0.103/0.112 0.103/0.147 0.103/0.104 0.103/0.108 0.103/0.129
300 0.25 0.007/0.007 0.007/0.008 0.007/0.009 0.007/0.008 0.007/0.008 0.007/0.009 0.005/0.005 0.005/0.005 0.005/0.005 0.005/0.005 0.005/0.005 0.005/0.005
1 0.014/0.014 0.015/0.015 0.019/0.019 0.014/0.014 0.015/0.015 0.018/0.018 0.010/0.010 0.011/0.011 0.013/0.013 0.011/0.011 0.011/0.011 0.012/0.013
4 0.038/0.038 0.038/0.042 0.038/0.061 0.038/0.039 0.038/0.040 0.038/0.053 0.032/0.032 0.032/0.035 0.032/0.045 0.032/0.033 0.032/0.034 0.032/0.042
9 0.076/0.076 0.076/0.086 0.076/0.129 0.076/0.078 0.076/0.082 0.076/0.107 0.069/0.069 0.069/0.075 0.069/0.098 0.069/0.069 0.069/0.072 0.069/0.086
500 0.25 0.004/0.004 0.004/0.005 0.004/0.005 0.004/0.005 0.004/0.005 0.004/0.005 0.003/0.003 0.003/0.003 0.003/0.003 0.003/0.003 0.003/0.003 0.003/0.003
1 0.008/0.008 0.009/0.009 0.011/0.011 0.008/0.008 0.009/0.009 0.011/0.011 0.006/0.006 0.007/0.007 0.008/0.008 0.006/0.006 0.006/0.007 0.007/0.008
4 0.023/0.023 0.023/0.025 0.023/0.037 0.023/0.023 0.023/0.024 0.023/0.032 0.019/0.019 0.019/0.021 0.019/0.027 0.019/0.020 0.019/0.020 0.019/0.025
9 0.046/0.046 0.046/0.052 0.046/0.078 0.046/0.047 0.046/0.049 0.046/0.064 0.041/0.041 0.041/0.045 0.041/0.059 0.041/0.042 0.041/0.043 0.041/0.052