An IERI – International Educational Research Institute Journal
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 |