An IERI – International Educational Research Institute Journal
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 |