A New Class of Mixed Membership Models for Educational Testing: Partial-Mastery Cognitive Diagnosis Models

• Activity Number: 126 - Recent Advances in Bayesian Mixed Membership Modeling for Network, Longitudinal, and Multivariate Data
• Type: Topic Contributed
• Date/Time: Monday, August 3, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Elena A Erosheva* and Zhuoran Shang and Gongjun Xu
• Companies: University of Washington and University of Michingan and University of Michigan
• Keywords: constrained latent class models; bayesian estimation

Abstract

Cognitive diagnosis models (CDMs) are discrete latent attribute models used in educational and psychological assessments. CDMs aim to make inference on subjects' latent attributes given observed responses to a set of designed test items. The key assumption is that items require mastery of specific latent attributes and that each attribute is either fully mastered or not mastered by a given subject. We propose a new class of models, partial mastery (PM) CDMs, which generalizes the CDMs by allowing partial mastery for each attribute of interest. We show that PM-CDMs can be represented as restricted latent class models. Relying on this representation, we propose a Bayesian approach for estimation. On simulated data, we demonstrate parameter recovery and develop diagnostic tools that practitioners could use to decide between CDMs and PM-CDMs. Using real test data, we show that PM-CDMs do not only improve model fit, compared to CDMs, but also can make substantial difference in conclusions about attribute mastery. We conclude that PM-CDMs can lead to more effective remediation programs by providing detailed individual-level information about skills learned and skills that need to study.