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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 |