Some matrices with Padovan Q-matrix property

2017 ◽  
Author(s):  
Supunnee Sompong ◽  
Natthaphat Wora-Ngon ◽  
Areeya Piranan ◽  
Natnapa Wongkaentow
Keyword(s):  
Matrix Property ◽  
Q Matrix

A New Method of Q-matrix Validation Based on DINA Model

2013 ◽  
Vol 44 (4) ◽  
pp. 558-568 ◽  
Author(s):  
Dong-Bo TU ◽  
Yan CAI ◽  
Hai-Qi DAI
Keyword(s):  
New Method ◽  
Dina Model ◽  
Q Matrix

scholarly journals A Residual-Based Approach to Validate Q-Matrix Specifications

2017 ◽  
Vol 41 (4) ◽  
pp. 277-293 ◽  
Author(s):  
Jinsong Chen
Keyword(s):  
Real Life ◽  
Attribute Level ◽  
Simulation Studies ◽  
Cognitive Diagnosis Models ◽  
Modeling Process ◽  
Response Formats ◽  
Item Level ◽  
Q Matrix ◽  
Matrix Construction ◽  
Test Level

Q-matrix validation is of increasing concern due to the significance and subjective tendency of Q-matrix construction in the modeling process. This research proposes a residual-based approach to empirically validate Q-matrix specification based on a combination of fit measures. The approach separates Q-matrix validation into four logical steps, including the test-level evaluation, possible distinction between attribute-level and item-level misspecifications, identification of the hit item, and fit information to aid in item adjustment. Through simulation studies and real-life examples, it is shown that the misspecified items can be detected as the hit item and adjusted sequentially when the misspecification occurs at the item level or at random. Adjustment can be based on the maximum reduction of the test-level measures. When adjustment of individual items tends to be useless, attribute-level misspecification is of concern. The approach can accommodate a variety of cognitive diagnosis models (CDMs) and be extended to cover other response formats.

Tracking Knowledge Proficiency of Students with Calibrated Q-Matrix

2021 ◽  
pp. 116454
Author(s):  
Wentao Wang ◽  
Huifang Ma ◽  
Yan Zhao ◽  
Zhixin Li ◽  
Xiangchun He
Keyword(s):  
Q Matrix

scholarly journals Q-Matrix Refinement Based on Item Fit Statistic RMSEA

2018 ◽  
Vol 43 (7) ◽  
pp. 527-542 ◽  
Author(s):  
Chunhua Kang ◽  
Yakun Yang ◽  
Pingfei Zeng
Keyword(s):  
Search Algorithm ◽  
Delta Method ◽  
Mean Square ◽  
Simulation Studies ◽  
Response Data ◽  
Item Fit ◽  
Dina Model ◽  
Q Matrix ◽  
Diagnosis Model ◽  
Effectiveness And Efficiency

A Q-matrix, which reflects how attributes are measured for each item, is necessary when applying a cognitive diagnosis model to an assessment. In most cases, the Q-matrix is constructed by experts in the field and may be subjective and incorrect. One efficient method to refine the Q-matrix is to employ a suitable statistic that is calculated using response data. However, this approach is limited by its need to estimate all items in the Q-matrix even if only some are incorrect. To address this challenge, this study proposes an item fit statistic root mean square error approximation (RMSEA) for validating a Q-matrix with the deterministic inputs, noisy, “and” (DINA) model. Using a search algorithm, two simulation studies were performed to evaluate the effectiveness and efficiency of the proposed method at recovering Q-matrices. Results showed that using RMSEA can help define attributes in a Q-matrix. A comparison with the existing Delta method and residual sum of squares (RSS) method revealed that the proposed method had higher mean recovery rates and can be used to identify and correct Q-matrix misspecifications. When no error exists in the Q-matrix, the proposed method does not modify the correct Q-matrix.

scholarly journals Counterexamples to Q-matrix conjectures

1988 ◽  
Vol 111 ◽  
pp. 135-145 ◽  
Author(s):  
Walter D. Morris
Keyword(s):  
Q Matrix

scholarly journals The Q-matrix completion problem

2009 ◽  
Vol 18 ◽  
Author(s):  
Luz DeAlba, ◽  
Leslie Hogben ◽  
Bhaba Sarma
Keyword(s):  
Matrix Completion ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
Q Matrix

scholarly journals Generalization of real interval matrices to other fields

2019 ◽  
Vol 35 ◽  
pp. 285-296
Author(s):  
Elena Rubei
Keyword(s):  
Full Rank ◽  
Maximal Rank ◽  
Interval Matrix ◽  
Real Interval ◽  
Rational Matrix ◽  
Rank One ◽  
Rational Rank ◽  
Q Matrix ◽  
Rational Interval ◽  
Rank Of A Matrix

An interval matrix is a matrix whose entries are intervals in $\R$. This concept, which has been broadly studied, is generalized to other fields. Precisely, a rational interval matrix is defined to be a matrix whose entries are intervals in $\Q$. It is proved that a (real) interval $p \times q$ matrix with the endpoints of all its entries in $\Q$ contains a rank-one matrix if and only if it contains a rational rank-one matrix, and contains a matrix with rank smaller than $\min\{p,q\}$ if and only if it contains a rational matrix with rank smaller than $\min\{p,q\}$; from these results and from the analogous criterions for (real) inerval matrices, a criterion to see when a rational interval matrix contains a rank-one matrix and a criterion to see when it is full-rank, that is, all the matrices it contains are full-rank, are deduced immediately. Moreover, given a field $K$ and a matrix $\al$ whose entries are subsets of $K$, a criterion to find the maximal rank of a matrix contained in $\al$ is described.

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