Identifiability of the Latent Attribute Space and Conditions of Q-Matrix Completeness for Attribute Hierarchy Models

The higher-order structure and attribute hierarchical structure are two popular approaches to defining the latent attribute space in cognitive diagnosis models. However, to our knowledge, it is still impossible to integrate them to accommodate the higher-order latent trait and hierarchical attributes simultaneously. To address this issue, this article proposed a sequential higher-order latent structural model (LSM) by incorporating various hierarchical structures into a higher-order latent structure. The feasibility of the proposed higher-order LSM was examined using simulated data. Results indicated that, in conjunction with the deterministic-inputs, noisy “and” gate model, the sequential higher-order LSM produced considerable improvement in person classification accuracy compared with the conventional higher-order LSM, when a certain attribute hierarchy existed. An empirical example was presented as well to illustrate the application of the proposed LSM.

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Cognitive Diagnostic Models With Attribute Hierarchies: Model Estimation With a Restricted Q-Matrix Design

Applied Psychological Measurement ◽

10.1177/0146621618765721 ◽

2018 ◽

Vol 43 (4) ◽

pp. 255-271 ◽

Cited By ~ 4

Author(s):

Dongbo Tu ◽

Shiyu Wang ◽

Yan Cai ◽

Jeff Douglas ◽

Hua-Hua Chang

Keyword(s):

Classification Accuracy ◽

Latent Class ◽

Estimation Procedure ◽

Syllogistic Reasoning ◽

Estimation Methods ◽

Diagnostic Models ◽

Cognitive Diagnostic Models ◽

Attribute Hierarchy ◽

Q Matrix ◽

Matrix Design

Attribute hierarchy is a common assumption in the educational context, where the mastery of one attribute is assumed to be a prerequisite to the mastery of another one. The attribute hierarchy can be incorporated through a restricted Q matrix that implies the specified structure. The latent class–based cognitive diagnostic models (CDMs) usually do not assume a hierarchical structure among attributes, which means all profiles of attributes are possible in a population of interest. This study investigates different estimation methods to the classification accuracy for a family of CDMs when they are combined with a restricted Q-matrix design. A simulation study is used to explain the misclassification caused by an unrestricted estimation procedure. The advantages of the restricted estimation procedure utilizing attribute hierarchies for increased classification accuracy are also further illustrated through a real data analysis on a syllogistic reasoning diagnostic assessment. This research can provide guidelines for educational and psychological researchers and practitioners when they use CDMs to analyze the data with a restricted Q-matrix design and make them be aware of the potentially contaminated classification results if ignoring attribute hierarchies.

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Assessing the Dimensionality of the Latent Attribute Space in Cognitive Diagnosis Through Testing for Conditional Independence

Springer Proceedings in Mathematics & Statistics - Quantitative Psychology ◽

10.1007/978-3-030-01310-3_17 ◽

2019 ◽

pp. 183-194

Author(s):

Youn Seon Lim ◽

Fritz Drasgow

Keyword(s):

Conditional Independence ◽

Cognitive Diagnosis ◽

Latent Attribute ◽

Attribute Space

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Complete Q-Matrices in General Attribute Structure Models

10.31234/osf.io/k82a5 ◽

2019 ◽

Author(s):

Jürgen Heller

Keyword(s):

Partial Order ◽

Necessary Conditions ◽

Knowledge Structure ◽

Diagnostic Assessment ◽

Structure Theory ◽

Cognitive Diagnostic Assessment ◽

Attribute Hierarchy ◽

Sufficient And Necessary Conditions ◽

Q Matrix ◽

Observed Behavior

In cognitive diagnostic assessment a property of the Q-matrix, usually referred to as completeness, warrants that the cognitive attributes underlying the observed behavior can be assessed uniquely. Characterizations of completeness were first derived under the assumption of independent attributes, and are currently under investigation for interdependent attributes. The dominant approach considers so-called attribute hierarchies, which are conceptualized through a partial order on the set of attributes. The present paper corrects and extends previously published results on this issue obtained for conjunctive attribute hierarchy models. Drawing upon results from knowledge structure theory it provides novel sufficient and necessary conditions for completeness of the $Q$-matrix, not only for conjunctive models on attribute hierarchies, but also on more general attribute structures.

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Development and Application of an Exploratory Reduced Reparameterized Unified Model

Journal of Educational and Behavioral Statistics ◽

10.3102/1076998618791306 ◽

2018 ◽

Vol 44 (1) ◽

pp. 3-24 ◽

Cited By ~ 5

Author(s):

Steven Andrew Culpepper ◽

Yinghan Chen

Keyword(s):

Bayesian Methods ◽

Unified Model ◽

Cognitive Diagnosis ◽

Simulation Studies ◽

Binary Matrix ◽

Data Set ◽

Cognitive Diagnosis Models ◽

Item Parameters ◽

Attribute Hierarchy ◽

Q Matrix

Exploratory cognitive diagnosis models (CDMs) estimate the Q matrix, which is a binary matrix that indicates the attributes needed for affirmative responses to each item. Estimation of Q is an important next step for improving classifications and broadening application of CDMs. Prior research primarily focused on an exploratory version of the restrictive deterministic-input, noisy-and-gate model, and research is needed to develop exploratory methods for more flexible CDMs. We consider Bayesian methods for estimating an exploratory version of the more flexible reduced reparameterized unified model (rRUM). We show that estimating the rRUM Q matrix is complicated by a confound between elements of Q and the rRUM item parameters. A Bayesian framework is presented that accurately recovers Q using a spike–slab prior for item parameters to select the required attributes for each item. We present Monte Carlo simulation studies, demonstrating the developed algorithm improves upon prior Bayesian methods for estimating the rRUM Q matrix. We apply the developed method to the Examination for the Certificate of Proficiency in English data set. The results provide evidence of five attributes with a partially ordered attribute hierarchy.

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