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Title: Attribute hierarchy models in cognitive diagnosis: Identifiability of the latent attribute space and the Q-matrix Authors:  Hans Friedrich Koehn - University of Illinois, Urbana-Champaign (United States) [presenting]
Abstract: Educational researchers have argued that a realistic view of the role of attributes in cognitively diagnostic modeling should account for the possibility that attributes are not isolated entities but interdependent in their effect on test performance. (``Attributes'' is a collective term in cognitive diagnosis for any cognitive characteristic required to perform tasks.) Different approaches to modeling possible attribute interdependency have been discussed in the literature; among them the proposition to impose a hierarchical structure so that mastery of certain attributes is a prerequisite of mastering one or more other attributes. A hierarchical organization of attributes constrains the latent attribute space such that several proficiency classes, as they exist if attributes are not hierarchically organized, are no longer defined because the corresponding attribute combinations cannot occur with the given attribute hierarchy. Hence, the identification of the latent attribute space is often difficult--especially, if the number of attributes is large. As an additional complication, constructing a complete Q-matrix may not at all be straightforward if the attributes underlying the test items are supposed to have a hierarchical structure. A framework based on lattice theory is proposed for examining the conditions of identifiability of the latent space and of completeness of the Q-matrix if attributes are hierarchically organized.