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Parameter Invariance and Skill Attribute Continuity in the DINA Model
Author(s) -
Bolt Daniel M.,
Kim JeeSeon
Publication year - 2018
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/jedm.12175
Subject(s) - measurement invariance , differential (mechanical device) , binary number , differential item functioning , cognition , item response theory , computer science , dreyfus model of skill acquisition , econometrics , cognitive psychology , psychology , mathematics , machine learning , structural equation modeling , statistics , psychometrics , confirmatory factor analysis , arithmetic , neuroscience , economic growth , engineering , economics , aerospace engineering
Cognitive diagnosis models (CDMs) typically assume skill attributes with discrete (often binary) levels of skill mastery, making the existence of skill continuity an anticipated form of model misspecification. In this article, misspecification due to skill continuity is argued to be of particular concern for several CDM applications due to the lack of invariance it yields in CDM skill attribute metrics, or what in this article are viewed as the “thresholds” applied to continuous attributes in distinguishing masters from nonmasters. Using the deterministic input noisy and (DINA) model as an illustration, the effects observed in real data are found to be systematic, with higher thresholds for mastery tending to emerge in higher ability populations. The results are shown to have significant implications for applications of CDMs that rely heavily upon the parameter invariance properties of the models, including, for example, applications toward the measurement of growth and differential item functioning analyses.