Abstract
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.
Highlights
Growth of knowledge and skills are important indicators of learning, which commonly results from the implementation of interventions such as course materials, instructional curriculum, teaching methods, and policies
Motivated from latent growth curve models and Reparameterized DINA (RDINA) model with covariate extensions, we propose two latent growth curve cognitive diagnostic models (CDMs) (LG-CDMs) using unconditional and conditional approaches to track the changes in examinees’ latent attributes as well as evaluating the effects of covariate at the latent attributes level
This study focuses on applying the latent growth curve model into the attribute-level of CDM to analyze how the attributes mastery change over time
Summary
Growth of knowledge and skills are important indicators of learning, which commonly results from the implementation of interventions such as course materials, instructional curriculum, teaching methods, and policies. For educational systems and educators, it is important to understand the changes in learning by evaluating the intervention effects. To quantify these effects, longitudinal assessments or pre-and post-test designs have been widely used and the raw score has been examined to reveal the progress in learning. Longitudinal assessment designs involve repeated observations of variables over a period of time while pre-and post-test designs focus on two measurements that are taken before and after a treatment. Item response theory (IRT) allows psychometrically specifying students’ ability as continues latent variables and has a tradition to employ longitudinal models to assess the growth in ability (Andersen, 1985; Fischer, 1989; Embretson, 1991). The multidimensional IRT models are useful to measure how the unidimensional ability increase over a period of time, yet it is hard to diagnose the increment when the latent constructs are correlated with one another over repeated measures
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