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An IERI – International Educational Research Institute Journal

Table 1 Variable definitions for hierarchical models used in this paper

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

\({y}_{ij}\)

Student achievement, i.e., PISA competence (Math, Reading or Science)

\({x}_{ij}\)

Student socio-economic status, i.e., the PISA Economic, Social and Cultural Index (ESCS)

\({x}_{i}\)

The school’s socio-economic Index

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

Grand (i.e., overall) mean, intercept of the model

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

Fixed effect on student level

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

Fixed effect on school level

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

Residual

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

School random effect