Hypothesis Testing of the Q-matrix

Psychometrika
Yuqi GuZhiliang Ying

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.

References

Nov 25, 2003·The British Journal of Mathematical and Statistical Psychology·Nikolaj Tollenaar, Ab Mooijaart
May 20, 2006·The British Journal of Mathematical and Statistical Psychology·Li CaiDavid Thissen
Sep 7, 2006·Psychological Methods·Jonathan L Templin, Robert A Henson
May 31, 2007·The British Journal of Mathematical and Statistical Psychology·Matthias von Davier
Aug 9, 2013·Applied Psychological Measurement·Jingchen LiuZhiliang Ying
May 9, 2014·Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability·Jingchen LiuZhiliang Ying
May 7, 2015·Psychometrika·Jimmy de la Torre, Chia-Yi Chiu
Aug 22, 2015·Journal of the American Statistical Association·Yunxiao ChenZhiliang Ying

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Citations

Jan 24, 2019·Psychometrika·Guanhua FangZhiliang Ying
Feb 7, 2019·The British Journal of Mathematical and Statistical Psychology·Wenchao Ma, Jimmy de la Torre
Jul 14, 2020·Educational and Psychological Measurement·Pablo NájeraFrancisco José Abad

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