Identifiability of the latent attribute space and conditions of Q-matrix completeness for attribute hierarchy models

Hans Friedrich Koehn, Chia Yi Chiu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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. Different approaches have been discussed in the literature; among them the proposition to impose a hierarchical structure so that mastery of one or more 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. In this article, the conditions of identifiability of the latent space if attributes are hierarchically organized and the conditions of completeness of the Q-matrix are studied.

Original languageEnglish (US)
Title of host publicationQuantitative Psychology - The 82nd Annual Meeting of the Psychometric Society, Zurich, Switzerland, 2017
EditorsJorge Gonzalez, Rianne Janssen, Marie Wiberg, Dylan Molenaar, Steven Culpepper
PublisherSpringer New York LLC
Pages363-375
Number of pages13
ISBN (Print)9783319772486
DOIs
StatePublished - Jan 1 2018
Event82nd Annual meeting of the Psychometric Society, 2017 - Zurich, Switzerland
Duration: Jul 17 2017Jul 21 2017

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume233
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other82nd Annual meeting of the Psychometric Society, 2017
CountrySwitzerland
CityZurich
Period7/17/177/21/17

Fingerprint

Q-matrix
Identifiability
Completeness
Attribute
Model
Hierarchical Structure
Hierarchy
Performance Test
Complications
Proposition
Diagnostics

Keywords

  • Attribute hierarchy
  • Cognitive diagnosis
  • Completeness
  • DINA model
  • Latent attribute space
  • Q-matrix

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Koehn, H. F., & Chiu, C. Y. (2018). Identifiability of the latent attribute space and conditions of Q-matrix completeness for attribute hierarchy models. In J. Gonzalez, R. Janssen, M. Wiberg, D. Molenaar, & S. Culpepper (Eds.), Quantitative Psychology - The 82nd Annual Meeting of the Psychometric Society, Zurich, Switzerland, 2017 (pp. 363-375). (Springer Proceedings in Mathematics and Statistics; Vol. 233). Springer New York LLC. https://doi.org/10.1007/978-3-319-77249-3_30

Identifiability of the latent attribute space and conditions of Q-matrix completeness for attribute hierarchy models. / Koehn, Hans Friedrich; Chiu, Chia Yi.

Quantitative Psychology - The 82nd Annual Meeting of the Psychometric Society, Zurich, Switzerland, 2017. ed. / Jorge Gonzalez; Rianne Janssen; Marie Wiberg; Dylan Molenaar; Steven Culpepper. Springer New York LLC, 2018. p. 363-375 (Springer Proceedings in Mathematics and Statistics; Vol. 233).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Koehn, HF & Chiu, CY 2018, Identifiability of the latent attribute space and conditions of Q-matrix completeness for attribute hierarchy models. in J Gonzalez, R Janssen, M Wiberg, D Molenaar & S Culpepper (eds), Quantitative Psychology - The 82nd Annual Meeting of the Psychometric Society, Zurich, Switzerland, 2017. Springer Proceedings in Mathematics and Statistics, vol. 233, Springer New York LLC, pp. 363-375, 82nd Annual meeting of the Psychometric Society, 2017, Zurich, Switzerland, 7/17/17. https://doi.org/10.1007/978-3-319-77249-3_30
Koehn HF, Chiu CY. Identifiability of the latent attribute space and conditions of Q-matrix completeness for attribute hierarchy models. In Gonzalez J, Janssen R, Wiberg M, Molenaar D, Culpepper S, editors, Quantitative Psychology - The 82nd Annual Meeting of the Psychometric Society, Zurich, Switzerland, 2017. Springer New York LLC. 2018. p. 363-375. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-77249-3_30
Koehn, Hans Friedrich ; Chiu, Chia Yi. / Identifiability of the latent attribute space and conditions of Q-matrix completeness for attribute hierarchy models. Quantitative Psychology - The 82nd Annual Meeting of the Psychometric Society, Zurich, Switzerland, 2017. editor / Jorge Gonzalez ; Rianne Janssen ; Marie Wiberg ; Dylan Molenaar ; Steven Culpepper. Springer New York LLC, 2018. pp. 363-375 (Springer Proceedings in Mathematics and Statistics).
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