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A Bayesian generalized multiple group IRT model with model-fit assessment tools

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  • Azevedo, Caio L.N.
  • Andrade, Dalton F.
  • Fox, Jean-Paul

Abstract

The multiple group IRT model (MGM) proposed by Bock and Zimowski (1997) provides a useful framework for analyzing item response data from clustered respondents. In the MGM, the selected groups of respondents are of specific interest such that group-specific population distributions need to be defined. The main goal is to explore the potentials of an MCMC estimation procedure and Bayesian model-fit tools for the MGM. We develop a full Gibbs sampling algorithm (FGSA) for estimation as well as a Metropolis-Hastings within Gibss sampling algorithm (MHWGS) in order to use non-conjugate priors. The FGSA is compared with Bilog–MG, which uses marginal maximum likelihood (MML) and marginal maximum a posteriori (MMAP) methods. That is; Bilog–MG provides maximum likelihood (ML) and expected a posteriori (EAP) estimates for both item and population parameters, and maximum a posteriori (MAP) estimates for the latent traits. We conclude that, in general, the results from our approach are slightly better than Bilog–MG. Besides a simultaneous MCMC estimation procedure, model-fit assessment tools are developed. Furthermore, the prior sensitivity is investigated with respect to the parameters of the latent population distributions. It will be shown that the FGSA provides a wide set of model-fit tools. The proposed model assessment tools can evaluate important model assumptions of (1) the item response function (IRF) and (2) the latent trait distributions. The utility of the proposed estimation and model-fit assessment methods will be shown using data from a longitudinal data study concerning first to fourth graders of sampled Brazilian public schools.

Suggested Citation

  • Azevedo, Caio L.N. & Andrade, Dalton F. & Fox, Jean-Paul, 2012. "A Bayesian generalized multiple group IRT model with model-fit assessment tools," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4399-4412.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4399-4412
    DOI: 10.1016/j.csda.2012.03.017
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    References listed on IDEAS

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    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. Tufi M. Soares & Flávio B. Gonçalves & Dani Gamerman, 2009. "An Integrated Bayesian Model for DIF Analysis," Journal of Educational and Behavioral Statistics, , vol. 34(3), pages 348-377, September.
    3. Jean-Paul Fox & Cees Glas, 2001. "Bayesian estimation of a multilevel IRT model using gibbs sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 271-288, June.
    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. da-Silva, C.Q. & Gomes, A.E., 2011. "Bayesian inference for an item response model for modeling test anxiety," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3165-3182, December.
    6. Roberto Leon Gonzalez, 2004. "Data Augmentation in the Bayesian Multivariate Probit Model," Working Papers 2004001, The University of Sheffield, Department of Economics, revised Jan 2004.
    7. 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.
    8. Bengt Muthén & James Lehman, 1985. "Multiple Group IRT Modeling: Applications to Item Bias Analysis," Journal of Educational and Behavioral Statistics, , vol. 10(2), pages 133-142, June.
    9. Robert Mislevy, 1986. "Bayes modal estimation in item response models," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 177-195, June.
    10. Jean‐Paul Fox & Cees A. W. Glas, 2005. "Bayesian modification indices for IRT models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 95-106, February.
    11. Robert Mislevy, 1984. "Estimating latent distributions," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 359-381, September.
    12. James H. Albert, 1992. "Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling," Journal of Educational and Behavioral Statistics, , vol. 17(3), pages 251-269, September.
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    Cited by:

    1. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    2. Mariagiulia Matteucci & Bernard Veldkamp, 2015. "The approach of power priors for ability estimation in IRT models," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 917-926, May.

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