Modeling relative competence in PISA: a compositional multiple factor analysis approach

This study presents a novel approach to analyzing student performance data from the
OECD-PISA assessments, emphasizing relative variability over absolute achievement
levels. Traditional analyses tend to focus on rankings and scale construction,
often neglecting the underlying components of performance. In contrast, the proposed
method adopts a compositional perspective to investigate how various cognitive
domains contribute to individual outcomes, revealing patterns of association
and trade-offs between areas. To effectively handle the complex structure of PISA
microdata, typically provided as multiple sets of plausible values, the ratio-based
approach is combined with Multiple Factor Analysis. This integration enables a
streamlined and coherent treatment of multivariate uncertainty. A case study from
the Italian region of Campania illustrates how the proposed framework improves
interpretability by offering new insights into the composition of students’ overall
competence and supporting the development of bipolar skill indexes. Group-level
socio-biographical differences are also explored to enrich the analysis.