Statistical Analysis of Q-Matrix Based Diagnostic Classification Models

• 成果类型: Article
• 署名作者: Chen, Yunxiao; Liu, Jingchen; Xu, Gongjun; Ying, Zhiliang
• 署名单位: Columbia University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.934827
• 发表日期: 2015
• 页码: 850-866
• 关键词: nonconcave penalized likelihood; dina model; cognitive assessment; variable selection; linear-models

摘要

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).