Measuring Skill Growth and Evaluating Change: Unconditional and Conditional Approaches to Latent Growth Cognitive Diagnostic Models.

During the past decade, cognitive diagnostic models (CDMs) have become prevalent in providing diagnostic information for learning. Cognitive diagnostic models have generally focused on single cross-sectional time points. However, longitudinal assessments have been commonly used in education to assess students' learning progress as well as evaluating intervention effects. Thus, it becomes natural to identify longitudinal growth in skills profiles mastery, which can yield meaningful inferences on learning. This study proposes longitudinal CDMs that incorporate latent growth curve modeling and covariate extensions, with the aim to measure the growth of skills mastery and to evaluate attribute-level intervention effects over time. Using real-world data, this study demonstrates applications of unconditional and conditional latent growth CDMs. Simulation studies show stable parameter recovery and classification of latent classes for different sample sizes. These findings suggest that building on the well-established growth modeling frameworks, applications of covariate-based longitudinal CDM can help understand the effect of explanatory factors and intervention on the change of attribute mastery.