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**Statistical analysis of \(Q\)-matrix based diagnostic classification models.**
*(English)*
Zbl 1373.62565

Summary: 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).

### MSC:

62P15 | Applications of statistics to psychology |

62P25 | Applications of statistics to social sciences |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |