An IERI – International Educational Research Institute Journal
Table 4 Weighting approaches for the simulation study and their application and formulas for the different levels of the hierarchies
From: Sampling weights in multilevel modelling: an investigation using PISA sampling structures
Weighting approaches | School level | Student level |
|---|---|---|
No weights | – | – |
Unscaled weights | \({w}_{i}\) | \({w}_{ij}\) |
Only student weights | \({w}_{ij}\) | |
Only school weights | \({w}_{i}\) | |
Scaled weights: Cluster | \({w}_{i}\) | \({w}_{ij }\frac{{n}_{i}}{\sum_{j=1}^{{n}_{i}}{w}_{ij}}\) |
Scaled weights: ECluster | \({w}_{i}\) | \({w}_{ij }\frac{{{n}^{*}}_{i }}{\sum_{j=1}^{{n}_{i }}{w}_{ij}}\) |
Withincluster weights | \({{w}_{i }}^{*}\) | \({{w}_{j }}^{*}\) |
House weights | \({w}_{ij }\frac{n}{\sum_{j=1}^{n}{w}_{ij}}\) | |
Clustersum | \(\sum_{j=1}^{{n}_{i}}{w}_{ij}\) | \({w}_{ij }\frac{{n}_{i}}{\sum_{j=1}^{{n}_{i}}{w}_{ij}}\) |