International Scholarly Research Notices / 2012 / Article / Tab 1 / Research Article
A Gibbs Sampler for the Multidimensional Item Response Model Table 1 Posterior estimates and Gelman-Rubin
π
statistics for
πΌ
1
,
πΌ
2
,
π½
, and
π
1
2
when the specified intertrait correlation isβ0.2 (chain length = 10,000, burn-in = 5,000).
True Uniform priors Normal priors True Uniform priors Normal priors Estimate (
π
) Estimate (
π
) Estimate (
π
) Estimate (
π
)
πΌ
1
βββββ
π½
0.905 0.962 (1.036) 0.947 (1.223) β1.433 β1.593 (1.017) β1.553 (1.219) 0.310 0.229 (1.044) 0.237 (1.007) β1.552 β1.610 (1.027) β1.606 (1.010) 0.605 0.579 (1.068) 0.581 (1.007) β0.656 β0.627 (1.005) β0.626 (1.014) 0.117 0.082 (1.034) 0.091 (1.015) β0.146 β0.099 (1.011) β0.099 (1.010) 0.197 0.064 (1.008) 0.062 (1.003) β1.206 β1.176 (0.999) β1.169 (1.001) 0.498 0.517 (1.032) 0.518 (1.012) β1.457 β1.728 (1.100) β1.622 (1.021) 0.442 0.443 (1.043) 0.467 (1.085) 1.904 1.892 (1.025) 1.831 (1.057) 1.006 1.045 (1.008) 1.029 (1.117) 0.029 β0.046 (1.005) β0.045 (1.003) 1.881 1.903 (1.191) 1.837 (1.116) 0.805 0.758 (1.037) 0.737 (1.007) 0.733 0.838 (1.024) 0.828 (1.047) β1.267 β1.326 (1.037) β1.296 (1.049) 0.687 0.500 (1.012) 0.506 (1.042) 1.145 1.053 (1.021) 1.056 (1.024) 1.728 1.760 (1.090) 1.663 (1.148) β0.828 β0.898 (1.048) β0.861 (1.107) 1.429 1.582 (1.175) 1.450 (1.085) 0.786 0.948 (1.203) 0.876 (1.033) 0.888 0.895 (1.023) 0.893 (1.052) 1.116 1.137 (1.033) 1.135 (1.017) 1.223 1.346 (1.047) 1.301 (1.117) β0.197 β0.196 (1.005) β0.185 (1.010) 1.155 1.348 (1.028) 1.296 (1.049) 1.265 1.222 (1.260) 1.187 (1.052) 1.582 1.728 (1.085) 1.673 (1.170) β0.708 β0.856 (1.440) β0.838 (1.058) 1.427 1.097 (1.019) 1.084 (1.061) 0.513 0.426 (1.021) 0.424 (1.003)
πΌ
2
π
1
2
1.504 1.722 (1.049) 1.666 (1.079) 0.2 0.183 (1.199) 0.163 (1.038) 0.886 1.047 (1.029) 1.042 (1.022) 1.829 1.792 (1.089) 1.792 (1.033) 1.578 1.589 (1.036) 1.558 (1.023) 0.131 0.088 (1.018) 0.089 (1.007) 1.562 1.888 (1.095) 1.731 (1.019) 1.833 1.616 (1.215) 1.531 (1.008) 0.210 0.190 (1.115) 0.197 (1.023) 1.533 1.635 (1.175) 1.573 (1.003) 1.436 1.309 (1.090) 1.263 (1.057) 0.961 0.879 (1.091) 0.888 (1.039) 0.678 0.807 (1.130) 0.783 (1.106) 1.888 2.341 (1.281) 2.134 (1.055) 0.618 0.744 (1.106) 0.751 (1.013) 1.967 1.921 (1.076) 1.837 (1.034) 1.862 1.934 (1.142) 1.862 (1.060) 0.062 0.135 (1.169) 0.143 (1.060) 1.389 1.223 (1.137) 1.215 (1.041)
