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.