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Table 2 Population specifications

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

Population Parameters

Scenario 1—PISA

Scenario 2—low

Scenario 3—high

\({y}_{ij}\)

\(\sim N\left(\mathrm{505,101}\right)\)

\(\sim N\left(\mathrm{500,97}\right)\)

\(\sim N\left(\mathrm{468,148}\right)\)

\({x}_{ij}\)

\(\sim N\left(\mathrm{0,1}\right)\)

\(\sim N\left(\mathrm{0,0.89}\right)\)

\(\sim N\left(\mathrm{0.16,1.20}\right)\)

\({x}_{i}\)

\(\sim N\left(\mathrm{0,0.59}\right)\)

\(\sim N\left(\mathrm{0,0.36}\right)\)

\(\sim N\left(-\mathrm{0.10,0.89}\right)\)

\({\beta }_{0}\)

476/ 479/ 494

500/500/500

421/429/449

\({\beta }_{1}\)

–/29/28

–/27/26

–/35/35

\({\beta }_{2}\)

–/–/40

–/–/7

–/–/65

\({\varepsilon }_{ij}\)

5005/4022/4027

8994/8421/8419

5012/4420/4420

\({\tau }_{i}\)

5053/4240/ 2417

530/299/266

16,100/12,541/8191

ICC

0.52

0.05

0.79