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Gibbs sampling using the data augmentation scheme for higher-order item response models

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  • Fu, Zhihui
  • Zhang, Xue
  • Tao, Jian

Abstract

Many latent traits in the human sciences have a hierarchical structure. This article will focus on a higher-order item response theory ( HO-IRT) model, which integrates a single overall ability and several domain-specific abilities in the same model to improve the parameter estimation of assessment data. A DAGS-based (data augmentation scheme) Gibbs sampler procedure to analyze HO-IRT models with three-parameter logistic link will be introduced. This procedure is a generalization of Maris and Maris (2002)’s sampling based Bayesian technique, called the DA-T-Gibbs sampler, are suitable for a wide variety of IRT models. With the introduction of the two latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. The performance of the proposed DAGS-based Bayesian procedure is evaluated via a simulation study and compared with the M–H algorithm. Results indicate that the proposed DAGS-based Bayesian procedure is more efficient and flexible than the M–H algorithm. Finally, applications to a real dataset are conducted to demonstrate the efficiency and utility of the proposed method.

Suggested Citation

  • Fu, Zhihui & Zhang, Xue & Tao, Jian, 2020. "Gibbs sampling using the data augmentation scheme for higher-order item response models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s037843711932059x
    DOI: 10.1016/j.physa.2019.123696
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    References listed on IDEAS

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    1. Yiu-Fai Yung & David Thissen & Lori McLeod, 1999. "On the relationship between the higher-order factor model and the hierarchical factor model," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 113-128, June.
    2. Gunter Maris & Eric Maris, 2002. "A MCMC-method for models with continuous latent responses," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 335-350, September.
    3. Jimmy Torre & Jeffrey Douglas, 2004. "Higher-order latent trait models for cognitive diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 333-353, September.
    4. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    5. Andrade, Dalton F. & Tavares, Heliton R., 2005. "Item response theory for longitudinal data: population parameter estimation," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 1-22, July.
    6. Zhehan Jiang & Jonathan Templin, 2019. "Gibbs Samplers for Logistic Item Response Models via the Pólya–Gamma Distribution: A Computationally Efficient Data-Augmentation Strategy," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 358-374, June.
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