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Bayesian estimation of a multilevel IRT model using gibbs sampling


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  • Jean-Paul Fox


  • Cees Glas
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    Bibliographic Info

    Article provided by Springer in its journal Psychometrika.

    Volume (Year): 66 (2001)
    Issue (Month): 2 (June)
    Pages: 271-288

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    Handle: RePEc:spr:psycho:v:66:y:2001:i:2:p:271-288

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    Keywords: Bayes estimates; Gibbs sampler; item response theory (IRT); Markov chain Monte Carlo; multilevel model; two-parameter normal ogive model;


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    1. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer, vol. 64(2), pages 153-168, June.
    2. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer, vol. 46(4), pages 443-459, December.
    3. Herbert Hojtink & Ivo Molenaar, 1997. "A multidimensional item response model: Constrained latent class analysis using the gibbs sampler and posterior predictive checks," Psychometrika, Springer, vol. 62(2), pages 171-189, June.
    4. Robert Gibbons & Donald Hedeker, 1992. "Full-information item bi-factor analysis," Psychometrika, Springer, vol. 57(3), pages 423-436, September.
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    Cited by:
    1. Li Cai, 2010. "High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm," Psychometrika, Springer, vol. 75(1), pages 33-57, March.
    2. R. Klein Entink & J.-P. Fox & W. Linden, 2009. "A Multivariate Multilevel Approach to the Modeling of Accuracy and Speed of Test Takers," Psychometrika, Springer, vol. 74(1), pages 21-48, March.
    3. Javier Revuelta, 2005. "An Item Response Model for Nominal Data Based on the Rising Selection Ratios Criterion," Psychometrika, Springer, vol. 70(2), pages 305-324, June.
    4. Michael Edwards, 2010. "A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis," Psychometrika, Springer, vol. 75(3), pages 474-497, September.
    5. Mariagiulia Matteucci & Bernard Veldkamp, 2013. "On the use of MCMC computerized adaptive testing with empirical prior information to improve efficiency," Statistical Methods and Applications, Springer, vol. 22(2), pages 243-267, June.
    6. Simon Hug & Richard Lukács, 2014. "Preferences or blocs? Voting in the United Nations Human Rights Council," The Review of International Organizations, Springer, vol. 9(1), pages 83-106, March.
    7. Cho, S.-J. & Rabe-Hesketh, S., 2011. "Alternating imputation posterior estimation of models with crossed random effects," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 12-25, January.
    8. Jeffrey Rouder & Dongchu Sun & Paul Speckman & Jun Lu & Duo Zhou, 2003. "A hierarchical bayesian statistical framework for response time distributions," Psychometrika, Springer, vol. 68(4), pages 589-606, December.
    9. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer, vol. 66(4), pages 541-561, December.
    10. Asim Ansari & Raghuram Iyengar, 2006. "Semiparametric Thurstonian Models for Recurrent Choices: A Bayesian Analysis," Psychometrika, Springer, vol. 71(4), pages 631-657, December.
    11. Heliton Tavares & Dalton Andrade, 2006. "Item response theory for longitudinal data: Item and population ability parameters estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 15(1), pages 97-123, June.
    12. Wim van der Linden, 2007. "A Hierarchical Framework for Modeling Speed and Accuracy on Test Items," Psychometrika, Springer, vol. 72(3), pages 287-308, September.
    13. Sophia Rabe-Hesketh & Anders Skrondal, 2007. "Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods," Psychometrika, Springer, vol. 72(2), pages 123-140, June.
    14. Jean-Paul Fox, . "Multilevel IRT Modeling in Practice with the Package mlirt," Journal of Statistical Software, American Statistical Association, vol. 20(i05).
    15. Jean-Paul Fox & Cees Glas, 2003. "Bayesian modeling of measurement error in predictor variables using item response theory," Psychometrika, Springer, vol. 68(2), pages 169-191, June.
    16. Azevedo, Caio L.N. & Bolfarine, Heleno & Andrade, Dalton F., 2011. "Bayesian inference for a skew-normal IRT model under the centred parameterization," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 353-365, January.
    17. Hong Jiao, 2011. "J.-P. FOX (2010) Bayesian Item Response Modeling: Theory and Applications," Psychometrika, Springer, vol. 76(2), pages 360-362, April.
    18. 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.
    19. Hanneke Geerlings & Cees Glas & Wim Linden, 2011. "Modeling Rule-Based Item Generation," Psychometrika, Springer, vol. 76(2), pages 337-359, April.


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