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Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design

The design of test Q matrix can directly influence the classification accuracy of a cognitive diagnostic assessment. In this paper, we focus on Q matrix design when attribute hierarchies are known prior to test development. A complete Q matrix design is proposed and theorems are presented to demonst...

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Detalles Bibliográficos
Autores principales: Cai, Yan, Tu, Dongbo, Ding, Shuliang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6092632/
https://www.ncbi.nlm.nih.gov/pubmed/30135672
http://dx.doi.org/10.3389/fpsyg.2018.01413
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author Cai, Yan
Tu, Dongbo
Ding, Shuliang
author_facet Cai, Yan
Tu, Dongbo
Ding, Shuliang
author_sort Cai, Yan
collection PubMed
description The design of test Q matrix can directly influence the classification accuracy of a cognitive diagnostic assessment. In this paper, we focus on Q matrix design when attribute hierarchies are known prior to test development. A complete Q matrix design is proposed and theorems are presented to demonstrate that it is a necessary and sufficient condition to guarantee the identifiability of ideal response patterns. A simulation study is also conducted to detect the effects of the proposed design on a family of conjunctive diagnostic models. The results revealed that the proposed Q matrix design is the key condition for guaranteeing classification accuracy. When only one type of item pattern in R matrix is missing from the associated test Q matrix, the related attribute-wise agreement rate will decrease dramatically. When the entire R matrix is missing, both the pattern-wise and attribute-wise agreement rates will decrease sharply. This indicates that the proposed procedures for complete Q matrix design with attribute hierarchies can serve as guidelines for test blueprint development prior to item writing in a cognitive diagnostic assessment.
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spelling pubmed-60926322018-08-22 Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design Cai, Yan Tu, Dongbo Ding, Shuliang Front Psychol Psychology The design of test Q matrix can directly influence the classification accuracy of a cognitive diagnostic assessment. In this paper, we focus on Q matrix design when attribute hierarchies are known prior to test development. A complete Q matrix design is proposed and theorems are presented to demonstrate that it is a necessary and sufficient condition to guarantee the identifiability of ideal response patterns. A simulation study is also conducted to detect the effects of the proposed design on a family of conjunctive diagnostic models. The results revealed that the proposed Q matrix design is the key condition for guaranteeing classification accuracy. When only one type of item pattern in R matrix is missing from the associated test Q matrix, the related attribute-wise agreement rate will decrease dramatically. When the entire R matrix is missing, both the pattern-wise and attribute-wise agreement rates will decrease sharply. This indicates that the proposed procedures for complete Q matrix design with attribute hierarchies can serve as guidelines for test blueprint development prior to item writing in a cognitive diagnostic assessment. Frontiers Media S.A. 2018-08-08 /pmc/articles/PMC6092632/ /pubmed/30135672 http://dx.doi.org/10.3389/fpsyg.2018.01413 Text en Copyright © 2018 Cai, Tu and Ding. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Psychology
Cai, Yan
Tu, Dongbo
Ding, Shuliang
Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design
title Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design
title_full Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design
title_fullStr Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design
title_full_unstemmed Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design
title_short Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design
title_sort theorems and methods of a complete q matrix with attribute hierarchies under restricted q-matrix design
topic Psychology
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6092632/
https://www.ncbi.nlm.nih.gov/pubmed/30135672
http://dx.doi.org/10.3389/fpsyg.2018.01413
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