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Fig. 1 | Large-scale Assessments in Education

Fig. 1

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

Fig. 1Fig. 1Fig. 1

Simulation outcomes for data mirroring the German PISA population. 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 \({y}_{ij}={\beta }_{0}+ {\beta }_{1}*{x}_{ij}+{\beta }_{2}*{x}_{i}+ {\tau }_{i}+ {\varepsilon }_{ij}\). The median, the 25% and 75% quartiles, minimum and maximum for each model estimator are presented in boxplots. No outliers are displayed. The true population values for each estimate are marked as red line. Simulation variation is displayed with the different weighting approaches combined with different estimation algorithms implemented in the two examined software packages

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