Dichotomous and Polytomous Q Matrix Theory

Ding, Shuliang; Luo, Fen; Wang, Wenyi; Xiong, Jian

doi:10.1007/978-3-319-38759-8_21

Cited by 8 publications

(4 citation statements)

References 7 publications

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“…Based on the studies by Ding et al ( 2008 , 2012 , 2016 ), we formally define a complete Q matrix design in a more general framework when an attribute hierarchy exits. The proposed complete Q matrix design can be easily constructed from an R matrix, which reflects the direct and indirect relationships between attributes.…”

Section: Discussionmentioning

confidence: 99%

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

Cai

Ding

2018

Front. Psychol.

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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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Section: Discussionmentioning

confidence: 99%

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

Cai

Ding

2018

Front. Psychol.

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“…The fact illustrated in Example 2 is that any columns of the W 1 can be expressed by the columns of the W 2 under the logical OR operation for the disjunctive model. This is also because the augmented algorithm proposed by Ding et al ( 2008 , 2009 ) in the generalized Q-matrix theory (Ding et al, 2015 ) provided the useful fact that any columns of the reduced Q-matrix can be expressed by the columns of the reachability matrix under the logical OR operation. The following theorem gives the precise statement.…”

Section: Model and Methodsmentioning

confidence: 99%

A Semi-supervised Learning Method for Q-Matrix Specification Under the DINA and DINO Model With Independent Structure

et al. 2020

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Cognitive diagnosis assessment (CDA) can be regarded as a kind of formative assessments because it is intended to promote assessment for learning and modify instruction and learning in classrooms by providing the formative diagnostic information about students' cognitive strengths and weaknesses. CDA has two phases, like a statistical pattern recognition. The first phase is feature generation, followed by classification stage. A Q-matrix, which describes the relationship between items and latent skills, corresponds to the feature generation phase in statistical pattern recognition. Feature generation is of paramount importance in any pattern recognition task. In practice, the Q-matrix is difficult to specify correctly in cognitive diagnosis and misspecification of the Q-matrix can seriously affect the accuracy of the classification of examinees. Based on the fact that any columns of a reduced Q-matrix can be expressed by the columns of a reachability R matrix under the logical OR operation, a semi-supervised learning approach and an optimal design for examinee sampling were proposed for Q-matrix specification under the conjunctive and disjunctive model with independent structure. This method only required subject matter experts specifying a R matrix corresponding to a small part of test items for the independent structure in which the R matrix is an identity matrix. Simulation and real data analysis showed that the new method with the optimal design is promising in terms of correct recovery rates of q-entries.

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“…A heuristic method for test construction based on CDI (Henson & Douglas, ) was chosen to assemble the second test with a relative simple Q ‐matrix, because it has been found that the CDI tends to select items measuring a small number of attributes, particularly the single‐attribute items (Kuo et al., ). The third test with a simple Q ‐matrix was constructed by selecting one or more five‐by‐five identity matrices (IMs); as the reachability matrix for independent attribute structure, the IM plays an important role in diagnostic test design (Chiu et al., ; Ding, Luo, Wang, & Xiong, ). Given the simulated Q ‐matrix, item parameters, and attribute patterns, the item response data was generated using the DINA model.…”

Section: Simulation Studymentioning

confidence: 99%

An Item‐Level Expected Classification Accuracy and Its Applications in Cognitive Diagnostic Assessment

Wang

Song

Chen

et al. 2019

J Educational Measurement

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Most of the existing classification accuracy indices of attribute patterns lose effectiveness when the response data is absent in diagnostic testing. To handle this issue, this article proposes new indices to predict the correct classification rate of a diagnostic test before administering the test under the deterministic noise input “and” gate (DINA) model. The new indices include an item‐level expected classification accuracy (ECA) for attributes and a test‐level ECA for attributes and attribute patterns, and both of them are calculated based solely on the known item parameters and Q‐matrix. Theoretical analysis showed that the item‐level ECA could be regarded as a measure of correct classification rates of attributes contributed by an item. This article also illustrates how to apply the item‐level ECA for attributes to estimate the correct classification rate of attributes patterns at the test level. Simulation results showed that two test‐level ECA indices, ECA_I_W (an index based on the independence assumption and the weighted sum of the item‐level ECAs) and ECA_C_M (an index based on Gaussian Copula function that incorporates the dependence structure of the events of attribute classification and the simple average of the item‐level ECAs), could make an accurate prediction for correct classification rates of attribute patterns.

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Dichotomous and Polytomous Q Matrix Theory

Cited by 8 publications

References 7 publications

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

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

A Semi-supervised Learning Method for Q-Matrix Specification Under the DINA and DINO Model With Independent Structure

An Item‐Level Expected Classification Accuracy and Its Applications in Cognitive Diagnostic Assessment

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