Statistical Analysis of Q-Matrix Based Diagnostic Classification Models

Abstract

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).

• Diagnostic classification models
• Identifiability
• Latent variable selection.

Additional information

Notes on contributors

Yunxiao Chen

Yunxiao Chen (E-mail: [email protected])

Jingchen Liu

Jingchen Liu (E-mail: [email protected])

Gongjun Xu

Zhiliang Ying (E-mail: [email protected]), Department of Statistics, 1255 Amsterdam Avenue, Columbia University, New York, NY 10027.

Zhiliang Ying

Gongjun Xu is Professor, Department of Statistics, University of Minnesota, Minneapolis, MN 55455 (E-mail: [email protected]).