How school leadership and innovation shape instructional pathways to student achievement across nations: Evidence from multilevel structural equation modeling and decision tree analysis

Educational leadership, innovation and teaching play essential roles in shaping student achievement. However, extant literature primarily has relied on linear modelling approaches and has not focused on substantively testing a theory. The present study employs multilevel structural equation modelling (ML-SEM) and multilevel decision trees (MLM trees) to investigate associations between school leadership, team innovation, cognitive activation and student achievement using PISA-TALIS 2018 linked data across seven countries: Australia; Colombia; Czech Republic; Denmark; Georgia; Malta; and Türkiye. The ML-SEM findings indicated no significant indirect effects from leadership on achievement. The MLM trees highlighted country-specific patterns in associations between school leadership, innovation and student achievement, revealing potential nonlinear relationships. These findings suggest that the relationship between leadership, instructional practices and achievement is highly context-dependent. The study contributes to the literature by offering a comparative analysis of ML-SEM and MLM trees, highlighting traditional linear models’ limitations in educational research. • No indirect leadership effects on achievement via teaching found in linear models. • Nonlinear tree models uncover diverse leadership–teaching–achievement patterns. • High achievement occurs despite low leadership and teaching innovation. • Leadership and teaching effects on achievement vary across educational systems. • Findings call for context-aware, nonlinear research on leadership and teaching.