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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