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**Bayesian estimation of the DINA \(Q\) matrix.**
*(English)*
Zbl 1402.62302

Summary: Cognitive diagnosis models are partially ordered latent class models and are used to classify students into skill mastery profiles. The deterministic inputs, noisy “and” gate model (DINA) is a popular psychometric model for cognitive diagnosis. Application of the DINA model requires content expert knowledge of a \(Q\) matrix, which maps the attributes or skills needed to master a collection of items. Misspecification of \(Q\) has been shown to yield biased diagnostic classifications. We propose a Bayesian framework for estimating the DINA \(Q\) matrix. The developed algorithm builds upon prior research [Y. Chen et al., J. Am. Stat. Assoc. 110, No. 510, 850–866 (2015; Zbl 1373.62565)] and ensures the estimated \(Q\) matrix is identified. Monte Carlo evidence is presented to support the accuracy of parameter recovery. The developed methodology is applied to Tatsuoka’s fraction-subtraction dataset.

### MSC:

62P15 | Applications of statistics to psychology |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

91E10 | Cognitive psychology |

### Keywords:

cognitive diagnosis models; deterministic inputs; noisy “and” gate (DINA) model; \(Q\) matrix; Bayesian statistics; fraction-subtraction data### Citations:

Zbl 1373.62565
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\textit{Y. Chen} et al., Psychometrika 83, No. 1, 89--108 (2018; Zbl 1402.62302)

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### References:

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