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An IERI – International Educational Research Institute Journal

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 \({y}_{ij}={\beta }_{0}+ {\beta }_{1}*{x}_{ij}+{\beta }_{2}*{x}_{i}+ {\tau }_{i}+ {\varepsilon }_{ij}\)