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This study employs Invariant Risk Minimization (IRM) to identify stable causal mediators of educational inequity across social, ethnic, gender, and treatment dimensions using PISA 2022 Australian data (N=13,021). Integrating Bourdieu's theory with machine learning methods, we reveal that home ICT access and school attendance consistently mediate achievement gaps across equity dimensions. Domain-specific mechanisms emerged: social equity was mediated through behavioral patterns (tardiness), ethnic equity through digital access and linguistic factors, and gender equity through psychological mediators including career aspiration clarity. Simulation-based interventions demonstrate that improving ICT access from none to one device yields 48-point gains, while regular attendance produces 34-point improvements. These findings challenge deficit-based explanations by revealing how structural disadvantage operates through relational mechanisms, offering evidence-based targets for equity interventions.