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Hypothesis Testing of the Q-matrix

Published online by Cambridge University Press:  01 January 2025

Yuqi Gu ,
Jingchen Liu ,
Gongjun Xu  and
Zhiliang Ying
Yuqi Gu
Affiliation:
University of Michigan
Jingchen Liu
Affiliation:
Columbia University
Gongjun Xu*
Affiliation:
University of Michigan
Zhiliang Ying
Affiliation:
Columbia University
*
Correspondence should be made to Gongjun Xu, Department of Statistics, University of Michigan, 456 West Hall,1085 South University, Ann Arbor, MI 48109, USA. Email: gongjun@umich.edu
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Abstract

The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method.

Keywords

Q-matrixdiagnostic classification modelshypothesis testing

Information

Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 3 , September 2018 , pp. 515 - 537
Copyright
Copyright © The Psychometric Society 2018

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-9629-6) contains supplementary material, which is available to authorized users.

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