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Article . 2021
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British Journal of Mathematical and Statistical Psychology
Article . 2020 . Peer-reviewed
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Balancing fit and parsimony to improve Q‐matrix validation

Authors: Pablo Nájera; Miguel A. Sorrel; Jimmy de la Torre; Francisco José Abad;

Balancing fit and parsimony to improve Q‐matrix validation

Abstract

The Q‐matrix identifies the subset of attributes measured by each item in the cognitive diagnosis modelling framework. Usually constructed by domain experts, the Q‐matrix might contain some misspecifications, disrupting classification accuracy. Empirical Q‐matrix validation methods such as the general discrimination index (GDI) and Wald have shown promising results in addressing this problem. However, a cut‐off point is used in both methods, which might be suboptimal. To address this limitation, the Hull method is proposed and evaluated in the present study. This method aims to find the optimal balance between fit and parsimony, and it is flexible enough to be used either with a measure of item discrimination (the proportion of variance accounted for , PVAF) or a coefficient of determination (pseudo‐ R 2 ). Results from a simulation study showed that the Hull method consistently showed the best performance and shortest computation time, especially when used with the PVAF. The Wald method also performed very well overall, while the GDI method obtained poor results when the number of attributes was high. The absence of a cut‐off point provides greater flexibility to the Hull method, and it places it as a comprehensive solution to the Q‐matrix specification problem in applied settings. This proposal is illustrated using real data.

Country
Spain
Related Organizations
Keywords

validation, Models, Statistical, PVAF, Psychometrics, CDM, Psicología, Hull method, Q-matrix, R-squared, Research Design, Computer Simulation, G-DINA

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
26
Top 10%
Top 10%
Top 10%
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