Bayesian Diagnostic Classification Models for a Partially Known Q-Matrix

This study proposes a Bayesian method for diagnostic classification models (DCMs) for a partially known Q-matrix setting between exploratory and confirmatory DCMs. This Q-matrix setting is practical and useful because test experts have pre-knowledge of the Q-matrix but cannot readily specify it completely. The proposed method employs priors for the Bayesian variable selection to simultaneously estimate the effects of active and nonactive attributes, and the simulations lead to appropriate attribute recovery rates. Furthermore, the proposed method recovers the attribute mastery of individuals at the same as for a fully known Q-matrix. In addition, the proposed methods can be used to estimate the unknown Q-matrix part. A real data example indicates that the proposed Bayesian estimation method for the partially known Q-matrix fits better than a fully specified Q-matrix. Finally, extensions and future research directions are discussed.