### Abstract

Parametric likelihood estimation is the prevailing method for fitting cognitive diagnosis models—also called diagnostic classification models (DCMs). Nonparametric concepts and methods that do not rely on a parametric statistical model have been proposed for cognitive diagnosis. These methods are particularly useful when sample sizes are small. The general nonparametric classification (GNPC) method for assigning examinees to proficiency classes can accommodate assessment data conforming to any diagnostic classification model that describes the probability of a correct item response as an increasing function of the number of required attributes mastered by an examinee (known as the “monotonicity assumption”). Hence, the GNPC method can be used with any model that can be represented as a general DCM. However, the statistical properties of the estimator of examinees’ proficiency class are currently unknown. In this article, the consistency theory of the GNPC proficiency-class estimator is developed and its statistical consistency is proven.

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

Pages (from-to) | 830-845 |

Number of pages | 16 |

Journal | Psychometrika |

Volume | 84 |

Issue number | 3 |

DOIs | |

State | Published - Sep 15 2019 |

### Fingerprint

### Keywords

- DINA model
- DINO model
- G-DINA model
- Q-matrix
- cognitive diagnosis
- general DCM
- general nonparametric classification method
- nonparametric classification

### ASJC Scopus subject areas

- Psychology(all)
- Applied Mathematics

### Cite this

*Psychometrika*,

*84*(3), 830-845. https://doi.org/10.1007/s11336-019-09660-x

**Consistency Theory for the General Nonparametric Classification Method.** / Chiu, Chia Yi; Koehn, Hans Friedrich.

Research output: Contribution to journal › Article

*Psychometrika*, vol. 84, no. 3, pp. 830-845. https://doi.org/10.1007/s11336-019-09660-x

}

TY - JOUR

T1 - Consistency Theory for the General Nonparametric Classification Method

AU - Chiu, Chia Yi

AU - Koehn, Hans Friedrich

PY - 2019/9/15

Y1 - 2019/9/15

N2 - Parametric likelihood estimation is the prevailing method for fitting cognitive diagnosis models—also called diagnostic classification models (DCMs). Nonparametric concepts and methods that do not rely on a parametric statistical model have been proposed for cognitive diagnosis. These methods are particularly useful when sample sizes are small. The general nonparametric classification (GNPC) method for assigning examinees to proficiency classes can accommodate assessment data conforming to any diagnostic classification model that describes the probability of a correct item response as an increasing function of the number of required attributes mastered by an examinee (known as the “monotonicity assumption”). Hence, the GNPC method can be used with any model that can be represented as a general DCM. However, the statistical properties of the estimator of examinees’ proficiency class are currently unknown. In this article, the consistency theory of the GNPC proficiency-class estimator is developed and its statistical consistency is proven.

AB - Parametric likelihood estimation is the prevailing method for fitting cognitive diagnosis models—also called diagnostic classification models (DCMs). Nonparametric concepts and methods that do not rely on a parametric statistical model have been proposed for cognitive diagnosis. These methods are particularly useful when sample sizes are small. The general nonparametric classification (GNPC) method for assigning examinees to proficiency classes can accommodate assessment data conforming to any diagnostic classification model that describes the probability of a correct item response as an increasing function of the number of required attributes mastered by an examinee (known as the “monotonicity assumption”). Hence, the GNPC method can be used with any model that can be represented as a general DCM. However, the statistical properties of the estimator of examinees’ proficiency class are currently unknown. In this article, the consistency theory of the GNPC proficiency-class estimator is developed and its statistical consistency is proven.

KW - DINA model

KW - DINO model

KW - G-DINA model

KW - Q-matrix

KW - cognitive diagnosis

KW - general DCM

KW - general nonparametric classification method

KW - nonparametric classification

UR - http://www.scopus.com/inward/record.url?scp=85061250293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061250293&partnerID=8YFLogxK

U2 - 10.1007/s11336-019-09660-x

DO - 10.1007/s11336-019-09660-x

M3 - Article

C2 - 30725333

AN - SCOPUS:85061250293

VL - 84

SP - 830

EP - 845

JO - Psychometrika

JF - Psychometrika

SN - 0033-3123

IS - 3

ER -