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Table 10 Application PISA 2015 Data – Model 3 \({y}_{ij}={\beta }_{0}+ {\beta }_{1}*{x}_{ij}+{\beta }_{2}*{x}_{i}+ {\tau }_{i}+ {\varepsilon }_{ij}\)

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

  \(\widehat{{\beta }_{0}}\) SE \(\widehat{{\beta }_{0}}\) \(\widehat{{\beta }_{1}}\) SE \(\widehat{{\beta }_{1}}\) \(\widehat{{\beta }_{2}}\) SE \(\widehat{{\beta }_{2}}\) \(\widehat{{\sigma }_{\varepsilon }^{2}}\) SE \(\widehat{{\sigma }_{\varepsilon }^{2}}\) \(\widehat{{\sigma }_{\tau }^{2}}\) SE \(\widehat{{\sigma }_{\tau }^{2}}\)
SAS
 No weights 516.04 2.40 12.89 1.18 49.50 2.32 5316.47 116.13 1176.65 143.61
 Unscaled weights 506.36 4.35 11.33 1.54 43.26 6.35 4972.29 130.45 1093.40 138.68
 Only school weights 509.08 3.57 11.34 1.30 47.43 4.14 5256.11 126.86 1399.36 262.86
 Only student weights 514.61 2.56 13.06 1.20 48.47 3.10 5049.66 111.53 1051.45 97.37
 Withincluster weights 509.43 3.50 12.99 1.18 46.62 4.12 5170.39 114.15 1492.50 254.13
 Scaled weights: cluster 509.08 3.57 11.34 1.30 47.43 4.14 5256.11 126.86 1399.36 262.86
 Scaled weights: ECluster 509.08 3.57 11.34 1.30 47.43 4.14 5256.11 126.86 1399.36 262.86
 Clustersum 515.11 2.52 13.02 1.21 48.04 2.78 5300.28 116.20 1218.51 166.33
 House weights 515.81 2.42 13.07 1.20 48.79 2.53 5285.94 116.88 1222.41 156.36
Mplus
 No weights 515.96 2.40 12.91 1.18 49.48 2.32 5320.55 116.31 1201.40 148.93
 Unscaled weights 509.17 3.50 11.32 1.30 47.48 4.13 5271.26 127.35 1401.29 261.30
 Only school weights 509.06 3.57 11.34 1.30 47.39 4.15 5270.65 127.31 1413.88 267.75
 Only student weights 515.91 2.39 12.93 1.18 49.55 2.33 5322.62 116.78 1198.43 148.23
 Withincluster weights 509.06 3.57 11.34 1.30 47.39 4.15 5270.65 127.31 1413.88 267.75
 Scaled weights: cluster 509.17 3.50 11.32 1.30 47.48 4.13 5271.26 127.35 1401.29 261.30
 Scaled weights: ECluster 509.19 3.50 11.32 1.30 47.49 4.12 5272.64 127.49 1396.79 259.89
 Clustersum 515.41 2.46 13.13 1.20 47.86 2.79 5315.53 117.16 1210.36 160.83
 House weights 515.96 2.40 12.91 1.18 49.48 2.32 5320.55 116.31 1201.40 148.93
  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