Skip to main content

Table 8 Application PISA 2015 Data—Model 1 \({y}_{ij}={\beta }_{0}+ {\tau }_{i}+ {\varepsilon }_{ij}\)

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

  \(\widehat{{\beta }_{0}}\) SE \(\widehat{{\beta }_{0}}\) \(\widehat{{\sigma }_{\varepsilon }^{2}}\) SE \(\widehat{{\sigma }_{\varepsilon }^{2}}\) \(\widehat{{\sigma }_{\tau }^{2}}\) SE \(\widehat{{\sigma }_{\tau }^{2}}\)
SAS
 No weights 508.28 4.49 5426.01 118.52 4013.66 272.93
 Unscaled weights 481.80 5.41 5079.08 132.86 3940.63 284.36
 Only school weights 483.83 5.37 5323.60 129.28 4042.81 331.98
 Only student weights 506.42 4.54 5174.72 115.51 3936.82 236.50
 Withincluster weights 484.43 5.34 5294.40 117.54 3987.60 307.94
 Scaled weights: cluster 483.83 5.37 5323.60 129.28 4042.81 331.98
 Scaled weights: ECluster 483.83 5.37 5323.60 129.28 4042.81 331.98
 Clustersum 503.40 4.68 5451.93 121.11 4027.00 282.90
 House weights 507.86 4.50 5421.13 121.32 4017.66 272.42
Mplus
 No weights 507.92 4.50 5412.54 117.97 4811.59 372.69
 Unscaled weights 483.67 5.34 5297.45 127.78 4865.75 454.33
 Only school weights 483.57 5.37 5294.79 127.64 4860.81 456.38
 Only student weights 507.81 4.50 5410.61 118.42 4818.42 373.28
 Withincluster weights 483.57 5.37 5294.79 127.64 4860.81 456.38
 Scaled weights: cluster 483.67 5.34 5297.45 127.78 4865.75 454.33
 Scaled Weights: ECluster 483.69 5.34 5297.98 127.86 4863.82 454.18
 Clustersum 504.26 4.61 5408.24 119.54 4760.76 373.38
 House weights 507.92 4.50 5412.54 117.97 4811.59 372.69
  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