Statistical Analysis of Q-Matrix Based Diagnostic Classification Models

Diagnostic classification models (DMCs) have recently gained prominence in educational assessment, psychiatric evaluation, and many other disciplines. Central to the model specification is the so-called Q-matrix that provides a qualitative specification of the item-attribute relationship. In this article, we develop theories on the identifiability for the Q-matrix under the DINA and the DINO models. We further propose an estimation procedure for the Q-matrix through the regularized maximum likelihood. The applicability of this procedure is not limited to the DINA or the DINO model and it can be applied to essentially all Q-matrix based DMCs. Simulation studies show that the proposed method admits high probability recovering the true Q-matrix. Furthermore, two case studies are presented. The first case is a dataset on fraction subtraction (educational application) and the second case is a subsample of the National Epidemiological Survey on Alcohol and Related Conditions concerning the social anxiety disorder (psychiatric application).