Bayesian Estimation of the DINA Q matrix

• DOI: 10.1007/s11336-017-9579-4
• Publication Date: 2017-08-31T20:29:27Z
• Authors: Yinghan Chen; Steven Andrew Cul...; Yuguo Chen; Jeffrey Douglas
• Keywords: Models, Statistical; Psychometrics; 0504 sociology; 05 social sciences; Bayes Theorem; Computer Simulation; Monte Carlo Method; Algorithms

Cognitive diagnosis models are partially ordered latent class models and are used to classify students into skill mastery profiles. The deterministic inputs, noisy “and” gate model (DINA) is a popular psychometric model for cognitive diagnosis. Application of the DINA model requires content expert knowledge of a Q matrix, which maps the attributes or skills needed to master a collection of items. Misspecification of Q has been shown to yield biased diagnostic classifications. We propose a Bayesian framework for estimating the DINA Q matrix. The developed algorithm builds upon prior research (Chen, Liu, Xu, & Ying, in J Am Stat Assoc 110(510):850–866, 2015) and ensures the estimated Q matrix is identified. Monte Carlo evidence is presented to support the accuracy of parameter recovery. The developed methodology is applied to Tatsuoka’s fraction-subtraction dataset.