Machine learning and latent profiles of mathematics achievement in nine European countries

Abstract

Mathematics achievement is associated with interacting individual and contextual factors, but these associations are often examined separately. As a result, existing research may overlook how affective characteristics combine within students and how these configurations are distributed across school settings. This study aimed to investigate the multilevel predictors of mathematics achievement by integrating machine learning and latent variable approaches using PISA 2022 data from nine European countries. The analysis was conducted in a sequence of stages, summarised in Fig. 1. First, predictive models were used to identify the most important predictors of mathematics achievement. Second, Latent Profile Analysis was performed to classify students based on key socioeconomic and affective indicators. Third, a two-stage multilevel approach—a separate latent profile analysis of school-level indicators, linked to the student profiles through mixed-effects models—was used to identify school climate profiles and examine cross-level associations between school contexts and student profile membership. Tree-based algorithms outperformed regularised linear models, indicating that mathematics achievement was characterised by complex and non-linear relationships among predictors. Socioeconomic resources and mathematics-related affective beliefs emerged as the strongest predictors. The analyses identified six student profiles and three school climate profiles, with marked differences in achievement across student groups. Student profiles were not randomly distributed across schools; instead, they were systematically associated with distinct school climates. These findings suggest that mathematics achievement is associated with synergistic combinations of individual and contextual factors, highlighting the importance of personalised interventions and equity-oriented policies that account for school-level selectivity.