Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 110, Issue 510, Pages 850-866Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2014.934827
Keywords
Diagnostic classification models; Identifiability; Latent variable selection
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Funding
- NSF [SES-1323977, DMS-1308566]
- NIH [R37GM047845]
- Army Research Laboratory [W911NF-14-1-0020]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1308566] Funding Source: National Science Foundation
- Divn Of Social and Economic Sciences
- Direct For Social, Behav & Economic Scie [1323977] Funding Source: National Science Foundation
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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).
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