Development of the Random Effect Diagnostic Classification Multilevel Growth Curve Model

Learning diagnosis is essential for effective education, with formative assessments shown to significantly enhance academic performance. Diagnostic classification models have been developed to assess students' learning status and provide remedial instruction. However, the impact of mastery or non-mastery of specific attributes on long-term learning development remains uncertain. If certain non-mastered attributes hinder the growth of mathematical ability, early intervention becomes essential. In this study, we developed a random-effects diagnostic classification for a multilevel growth curve (RDC–MGC) model to identify the specific effects of attribute mastery on individual-level mathematics ability growth. The simulation studies showed that the Bayesian estimation procedure provided appropriate parameter recovery and coverage probabilities, whereas ignoring the multilevel structure resulted in biased parameter estimates. The model was applied to arithmetic test data from second- to sixth-grade elementary school students. Diagnosis was conducted in the second grade, and the effects of mastery on mathematics ability growth from the third to sixth grades were assessed. The results showed that attribute mastery in second grade was associated with both the intercept and slope of individual ability growth, suggesting the potential importance of early-stage diagnostic information for understanding later mathematical development. Potential extensions of the proposed RDC–MGC model are also discussed.