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Table 3 Simulation scenarios including varying ICCs, three investigated hierarchical models and different weighting approaches combined with different estimation algorithms implemented in the two examined software packages

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

ICC Model Software package Weighting scenario
0.52/0.05/0.79 Model 1 MPLUS No weights
Unscaled weights
Only student weights
Only school weights
Scaled weights: cluster
Scaled weights: ECluster
Withincluster weights
House weights
Clustersum
SAS No weights
Unscaled weights
Only student weights
Only school weights
Scaled weights: cluster
Scaled weights: ECluster
Withincluster weights
House weights
Clustersum
Model 2 MPLUS No weights
Unscaled weights
Only student weights
Only school weights
Scaled weights: cluster
Scaled weights: ECluster
Withincluster We
ights
House weights
Clustersum
SAS No weights
Unscaled weights
Only student weights
Only school weights
Scaled weights: cluster
Scaled weights: ECluster
Withincluster weights
House weights
Clustersum
Model 3 MPLUS No weights
Unscaled Weights
Only student weights
Only school weights
Scaled weights: cluster
Scaled weights: ECluster
Withincluster weights
House weights
Clustersum
SAS No weights
Unscaled weights
Only student weights
Only school weights
Scaled weights: cluster
Scaled weights: ECluster
Withincluster weights
House weights
Clustersum
  1. Model 1 is declared as \({y}_{ij}={\beta }_{0}+ {\tau }_{i}+ {\varepsilon }_{ij}\), Model 2 as \({y}_{ij}={\beta }_{0}+ {\beta }_{1}*{x}_{ij}+ {\tau }_{i}+ {\varepsilon }_{ij}\) and Model 3 as \({y}_{ij}={\beta }_{0}+ {\beta }_{1}*{x}_{ij}+{\beta }_{2}*{x}_{i}+ {\tau }_{i}+ {\varepsilon }_{ij}\)