### Abstract

The Q-matrix of a cognitively diagnostic test is said to be complete if it allows for the identification of all possible proficiency classes among examinees. Completeness of the Q-matrix is therefore a key requirement for any cognitively diagnostic test. However, completeness of the Q-matrix is often difficult to establish, especially, for tests with a large number of items involving multiple attributes. As an additional complication, completeness is not an intrinsic property of the Q-matrix, but can only be assessed in reference to a specific cognitive diagnosis model (CDM) supposed to underly the data—that is, the Q-matrix of a given test can be complete for one model but incomplete for another. In this article, a method is presented for assessing whether a given Q-matrix is complete for a given CDM. The proposed procedure relies on the theoretical framework of general CDMs and is therefore legitimate for CDMs that can be reparameterized as a general CDM.

Original language | English (US) |
---|---|

Pages (from-to) | 112-132 |

Number of pages | 21 |

Journal | Psychometrika |

Volume | 82 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2017 |

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### Keywords

- G-DINA
- LCDM
- Q-matrix
- cognitive diagnosis
- completeness
- general cognitive diagnostic models

### ASJC Scopus subject areas

- Psychology(all)
- Applied Mathematics

### Cite this

*Psychometrika*,

*82*(1), 112-132. https://doi.org/10.1007/s11336-016-9536-7

**A Procedure for Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Tests.** / Köhn, Hans Friedrich; Chiu, Chia Yi.

Research output: Contribution to journal › Article

*Psychometrika*, vol. 82, no. 1, pp. 112-132. https://doi.org/10.1007/s11336-016-9536-7

}

TY - JOUR

T1 - A Procedure for Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Tests

AU - Köhn, Hans Friedrich

AU - Chiu, Chia Yi

PY - 2017/3/1

Y1 - 2017/3/1

N2 - The Q-matrix of a cognitively diagnostic test is said to be complete if it allows for the identification of all possible proficiency classes among examinees. Completeness of the Q-matrix is therefore a key requirement for any cognitively diagnostic test. However, completeness of the Q-matrix is often difficult to establish, especially, for tests with a large number of items involving multiple attributes. As an additional complication, completeness is not an intrinsic property of the Q-matrix, but can only be assessed in reference to a specific cognitive diagnosis model (CDM) supposed to underly the data—that is, the Q-matrix of a given test can be complete for one model but incomplete for another. In this article, a method is presented for assessing whether a given Q-matrix is complete for a given CDM. The proposed procedure relies on the theoretical framework of general CDMs and is therefore legitimate for CDMs that can be reparameterized as a general CDM.

AB - The Q-matrix of a cognitively diagnostic test is said to be complete if it allows for the identification of all possible proficiency classes among examinees. Completeness of the Q-matrix is therefore a key requirement for any cognitively diagnostic test. However, completeness of the Q-matrix is often difficult to establish, especially, for tests with a large number of items involving multiple attributes. As an additional complication, completeness is not an intrinsic property of the Q-matrix, but can only be assessed in reference to a specific cognitive diagnosis model (CDM) supposed to underly the data—that is, the Q-matrix of a given test can be complete for one model but incomplete for another. In this article, a method is presented for assessing whether a given Q-matrix is complete for a given CDM. The proposed procedure relies on the theoretical framework of general CDMs and is therefore legitimate for CDMs that can be reparameterized as a general CDM.

KW - G-DINA

KW - LCDM

KW - Q-matrix

KW - cognitive diagnosis

KW - completeness

KW - general cognitive diagnostic models

UR - http://www.scopus.com/inward/record.url?scp=84990848104&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990848104&partnerID=8YFLogxK

U2 - 10.1007/s11336-016-9536-7

DO - 10.1007/s11336-016-9536-7

M3 - Article

C2 - 27714544

AN - SCOPUS:84990848104

VL - 82

SP - 112

EP - 132

JO - Psychometrika

JF - Psychometrika

SN - 0033-3123

IS - 1

ER -