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Table 9 Application PISA 2015 Data – Model 2 \({y}_{ij}={\beta }_{0}+ {\beta }_{1}*{x}_{ij}+ {\tau }_{i}+ {\varepsilon }_{ij}\)

From: Sampling weights in multilevel modelling: an investigation using PISA sampling structures

  \(\widehat{{\beta }_{0}}\) SE \(\widehat{{\beta }_{0}}\) \(\widehat{{\beta }_{1}}\) SE \(\widehat{{\beta }_{1}}\) \(\widehat{{\sigma }_{\varepsilon }^{2}}\) SE \(\widehat{{\sigma }_{\varepsilon }^{2}}\) \(\widehat{{\sigma }_{\tau }^{2}}\) SE \(\widehat{{\sigma }_{\tau }^{2}}\)
SAS
 No weights 509.57 4.06 15.87 1.21 5233.28 112.71 2670.31 181.69
 Unscaled weights 484.76 5.14 11.31 1.54 4990.11 131.10 2239.82 143.37
 Only school weights 487.12 5.02 13.62 1.37 5246.73 125.43 4149.08 414.42
 Only student weights 507.36 4.20 13.12 1.20 5049.22 111.51 2229.14 125.10
 Withincluster weights 487.64 4.96 13.96 1.19 5159.23 113.60 4219.66 404.56
 Scaled weights: cluster 487.12 5.02 13.62 1.37 5246.73 125.43 4149.08 414.42
 Scaled weights: ECluster 487.12 5.02 13.62 1.37 5246.73 125.43 4149.08 414.42
 Clustersum 505.08 4.26 15.28 1.25 5300.05 116.11 3880.08 333.45
 House weights 508.83 4.10 15.26 1.24 5293.84 117.33 3886.28 325.77
Mplus
 No weights 509.19 4.10 15.10 1.20 5313.87 116.12 3876.26 324.59
 Unscaled weights 487.20 4.99 13.60 1.37 5247.64 125.27 4141.49 411.45
 Only school weights 487.11 5.01 13.61 1.37 5246.64 125.17 4151.67 414.03
 Only student weights 509.15 4.10 15.12 1.21 5316.13 116.62 3877.56 325.67
 Withincluster weights 487.11 5.01 13.61 1.37 5246.64 125.17 4151.67 414.03
 Scaled weights: cluster 487.20 4.99 13.60 1.37 5247.64 125.27 4141.49 411.45
 Scaled weights: ECluster 487.22 4.99 13.61 1.37 5248.73 125.38 4137.74 410.98
 Clustersum 506.06 4.18 15.41 1.24 5304.56 116.65 3816.42 323.59
 House weights 509.19 4.10 15.10 1.20 5313.87 116.12 3876.26 324.59
  1. Classifying the results of the simulation study to application data, the different weighting approaches combined with different estimation algorithms implemented in the two examined software packages are displayed