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Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 3 International ESCS component weights based on PCA

From: The measure of socio-economic status in PISA: a review and some suggested improvements

 

Number of countries in calibration

Factor loadings

Component weights (based on z-score transformed variables)

PARED

HISEI

HOMEPOS

PARED

HISEI

HOMEPOS

PISA 2015 (own computation, based on public-use files)

69

0.814

0.815

0.776

0.422

0.422

0.402

PISA 2015 (own computation, OECD countries)

35

0.810

0.817

0.758

0.427

0.430

0.399

PISA 2015 (technical report)

 

0.812

0.796

0.783

0.457

0.464

0.446

PISA 2012

 

0.815

0.836

0.722

0.431

0.451

0.394

PISA 2009

 

0.810

0.805

0.735

0.436

0.436

0.393

PISA 2006

 

0.810

0.798

0.742

0.436

0.432

0.397

PISA 2003

 

0.795

0.794

0.756

0.432

0.432

0.404

  1. Factor loadings, divided by the square root of the eigenvalue (first principal component)
  2. Factor loadings from the original principal component analysis are not (always) available in technical reports. The factor loadings in this table are therefore computed as correlation coefficients between the ESCS composite and its components across all students with at least two valid component measures in the public-use file, using senate weights across all countries (2015) or OECD countries only (2003–2012); they may differ from the original factor loadings due to differences in the estimation sample and weighting or in the imputation of the missing component (original imputed values were not available). Component weights are by definition equal to factor scores divided by the eigenvalue of the first principal component, which in turn equals the sum of squared factor loadings. The values reported here are computed as regression coefficients from the regression of ESCS on its standardised components and therefore reflect the original loadings; they may be slightly inconsistent with factor loadings reported elsewhere in this table. In all cases, the R2 coefficient from the regression was close to 100% (the difference could be easily explained by rounding). Prior to the regression, components were standardised using senate weights across all countries (2015) or OECD countries only (2003–2012); imputed component scores were not included in the standardisation, nor in the regression
  3. For PISA 2015, the factor loadings and component weights reported in the first two lines of this table are based on all countries included in public-use files, except Lebanon, Spain (QES and ESP) and Latvia. Indeed, for these three countries, the values of PARED in the database were corrected after the principal component analysis had been completed
  4. In PISA 2000, ESCS was built as a composite score of five components
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