Identifiability conditions in cognitive diagnosis: Implications for Q‐matrix estimation algorithms
Year: 2025
Type: article
Abstract: The Q-matrix of a cognitively diagnostic assessment (CDA), documenting the item-attribute associations, is a key component of any CDA. However, the true Q-matrix underlying a CDA is never known and must be estimated-typically by content experts. However, due to fallible human judgment, misspecifications of the Q-matrix may occur, resulting in the misclassification of examinees. In response to this challenge, algorithms have been developed to estimate the Q-matrix from item responses. Some algorithms impose identifiability conditions while others do not. The debate about which is "right" is ongoing; especially, since these conditions are sufficient but not necessary, which means viable alternative Q-matrix estimates may be ignored. In this study, the performance of Q-matrix estimation algorithms that impose identifiability conditions on the Q-matrix estimate was compared with that of estimation algorithms which do not impose such identifiability conditions. Large-scale simulations examined the impact of factors like sample size, test length, attributes, or error levels. The estimated Q-matrices were evaluated for meeting identifiability conditions and their accuracy in classifying examinees. The simulation results showed that for the various estimation algorithms studied here, imposing identifiability conditions on Q-matrix estimation did not change outcomes with respect to identifiability or examinee classification.
DOI: 10.1111/bmsp.70020
Authors: Hyunjoo Kim, Hans Friedrich Köhn, Chia‐Yi Chiu
Institutions: University of Illinois Urbana-Champaign, Columbia University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,400
OpenAlex ID: W4417289811