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

Abstract 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.