Identification and Estimation of Dynamic Restricted Latent Class Models for Cognitive Diagnosis

This research project will advance dynamic, cognitive diagnostic assessments for tracking student skill acquisition as an alternative approach to the static classification of student skill mastery. Existing formative assessment frameworks require extensive prior content knowledge and theory concerning the nature of student skill mastery and the process by which skills are joined to determine cognitive performance.

This project will provide researchers with new tools for inferring the learning process from dynamic, longitudinal data on student performance and offer a framework for evaluating substantive theory for how students learn. A central concern in the educational sciences is formulating and evaluating interventions. The project will develop accurate methods for researchers to gain a fine-grained understanding as to the effectiveness of learning interventions.

The new methods will leverage student responses to longitudinal assessments to offer educators and policymakers with insights regarding the status and timing of student mastery of educational content. The methods also will shed light on the effectiveness of educational interventions with the goal of establishing strategies for formulating personalized learning interventions to accelerate student learning.

To achieve these aims, the project will advance fundamental theory in statistics and psychometrics. In addition to broadening methodological theory, the project will strengthen the educational assessment infrastructure. The research to be conducted will create a robust foundation for the development and administration of real-time formative assessments that adapt to the needs of students and provide educators with timely information to inform instructional decisions.

Graduate students will be involved in the discovery process, and theoretical developments will be incorporated into the graduate curriculum. Publicly available software will be created to provide researchers and decision makers with cutting-edge tools.

This research project will consider statistical problems at the heart of the social, behavioral, and health sciences, and will highlight the interplay among the fields of psychometrics, latent class modeling, longitudinal data analysis, and Bayesian statistics. The project will involve complex statistical modeling and will addresses issues related to computational complexity.

New methods and algorithms for dynamic restricted latent class models (D-RLCMs) will be developed. Novel Bayesian methods will be used to deploy D-RLCMs to classify student mastery over time. The longitudinal skill classifications will provide educators and stakeholders with a fine-grained trajectory of student performance and learning.

The project will deploy a hidden Markov model (HMM) framework that enables precise information regarding the probability students transition into states with greater content mastery. The mathematical theory of HMMs will be advanced in the project by establishing new identifiability theory to accurately infer student longitudinal skill profiles and learning trajectories.

Methods will be developed to provide a powerful evaluation of the role of contextual factors in learning environments, such as student or school characteristics and pedagogical techniques. The methods to be developed will harvest the wealth of longitudinal student response data to provide decision makers and educators with actionable evidence to improve student learning outcomes.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.