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A Note on the Invariance of the DINA Model Parameters
Author(s) -
De La Torre Jimmy,
Lee YoungSun
Publication year - 2010
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/j.1745-3984.2009.00102.x
Subject(s) - item response theory , invariant (physics) , computer science , measurement invariance , property (philosophy) , noise (video) , artificial intelligence , cognition , noisy data , domain (mathematical analysis) , machine learning , mathematics , psychology , statistics , psychometrics , structural equation modeling , mathematical analysis , philosophy , image (mathematics) , epistemology , confirmatory factor analysis , neuroscience , mathematical physics
Cognitive diagnosis models (CDMs), as alternative approaches to unidimensional item response models, have received increasing attention in recent years. CDMs are developed for the purpose of identifying the mastery or nonmastery of multiple fine‐grained attributes or skills required for solving problems in a domain. For CDMs to receive wider use, researchers and practitioners need to understand the basic properties of these models. The article focuses on one CDM, the deterministic inputs, noisy “and” gate (DINA) model, and the invariance property of its parameters. Using simulated data involving different attribute distributions, the article demonstrates that the DINA model parameters are absolutely invariant when the model perfectly fits the data. An additional example involving different ability groups illustrates how noise in real data can contribute to the lack of invariance in these parameters. Some practical implications of these findings are discussed .