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An Empirical Q-Matrix Validation Method for the Polytomous G-DINA Model

Published online by Cambridge University Press:  01 January 2025

Jimmy de la Torre ,
Xue-Lan Qiu  and
Kevin Carl Santos
Jimmy de la Torre*
Affiliation:
The University of Hong Kong
Xue-Lan Qiu
Affiliation:
The University of Hong Kong
Kevin Carl Santos
Affiliation:
University of the Philippines
*
Correspondence should be made to Jimmy de la Torre, Faculty of Education, The University of Hong Kong, Pokfulam Road, Pok Fu Lam, Hong Kong. Email: [email protected]
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Abstract

A number of empirically based Q-matrix validation methods are available in the literature, all of which were developed for cognitive diagnosis models (CDMs) involving dichotomous attributes. However, in many applications, it is more instructionally relevant to classify students into more than two categories (e.g., no mastery, basic mastery, and advanced mastery). To extend the practical utility of CDMs, methods for validating the Q-matrix for CDMs that measure polytomous attributes are needed. This study focuses on validating the Q-matrix of the generalized deterministic input, noisy, “and” gate model for polytomous attributes (pG-DINA). The pGDI, an extension of the G-DINA model discrimination index, is proposed for polytomous attributes. The pGDI serves as the basis of a validation method that can be used not only to identify potential misspecified q-entries, but also to suggest more appropriate attribute-level specifications. The theoretical properties of the pGDI are underpinned by several mathematical proofs, whereas its practical viability is examined using simulation studies covering various conditions. The results show that the method can accurately identify misspecified q-entries and suggest the correct attribute-level specifications, particularly when high-quality items are involved. The pGDI is applied to a proportional reasoning test that measures several polytomous attributes.

Keywords

cognitive diagnosis modelsG-DINAQ-matrix validationpolytomous attributes
Type
Theory and Methods
Information
Psychometrika , Volume 87 , Issue 2: Special Issue on Forecasting with Intensive Longitudinal Data , June 2022 , pp. 693 - 724
Copyright
Copyright © 2021 The Author(s) under exclusive licence to The Psychometric Society

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