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2019 | OriginalPaper | Buchkapitel

Comparison of Hyperpriors for Modeling the Intertrait Correlation in a Multidimensional IRT Model

verfasst von : Meng-I Chang, Yanyan Sheng

Erschienen in: Quantitative Psychology

Verlag: Springer International Publishing

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Abstract

Markov chain Monte Carlo (MCMC) algorithms have made the estimation of multidimensional item response theory (MIRT) models possible under a fully Bayesian framework. An important goal in fitting a MIRT model is to accurately estimate the interrelationship among multiple latent traits. In Bayesian hierarchical modeling, this is realized through modeling the covariance matrix, which is typically done via the use of an inverse Wishart prior distribution due to its conjugacy property. Studies in the Bayesian literature have pointed out limitations of such specifications. The purpose of this study is to compare the inverse Wishart prior with other alternatives such as the scaled inverse Wishart, the hierarchical half-t, and the LKJ priors on parameter estimation and model adequacy of one form of the MIRT model through Monte Carlo simulations. Results suggest that the inverse Wishart prior performs worse than the other priors on parameter recovery and model-data adequacy across most of the simulation conditions when variance for person parameters is small. Findings from this study provide a set of guidelines on using these priors in estimating the Bayesian MIRT models.

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Alvarez, I., Niemi, J., & Simpson, M. (2014). Bayesian inference for a covariance matrix. arXiv preprint arXiv:1408.4050.

Barnard, J., McCulloch, R., & Meng, X. L. (2000). Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statistica Sinica, 10(4), 1281–1311. Retrieved from http://www.jstor.org/stable/24306780.

Béguin, A. A., & Glas, C. A. W. (2001). MCMC estimation and some model-fit analysis of multidimensional IRT models. Psychometrika, 66(4), 541–561. https://doi.org/10.1007/BF02296195.MathSciNetCrossRefMATH

Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46(4), 443–459. https://doi.org/10.1007/BF02293801.MathSciNetCrossRef

Bolt, D. M., & Lall, V. F. (2003). Estimation of compensatory and noncompensatory multidimensional item response models using Markov chain Monte Carlo. Applied Psychological Measurement, 27(6), 395–414. https://doi.org/10.1177/0146621603258350.MathSciNetCrossRef

Bouriga, M., & Féron, O. (2013). Estimation of covariance matrices based on hierarchical inverse-Wishart priors. Journal of Statistical Planning and Inference, 143, 795–808. https://doi.org/10.1016/j.jspi.2012.09.006.MathSciNetCrossRefMATH

Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7(4), 434–455.MathSciNet

Carpenter, B., et al. (2016). Stan: A probabilistic programming language. Journal of Statistical Software, 76(1), 1–32. http://dx.doi.org/10.18637/jss.v076.i01.

Chang, M. I., & Sheng, Y. (2016). A comparison of two MCMC algorithms for the 2PL IRT model. In The Annual Meeting of the Psychometric Society (pp. 71–79). Springer, Cham.

Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. The American Statistician, 49(4), 327–335.

Dawber, T., Rogers, W. T., & Carbonaro, M. (2009). Robustness of Lord’s formulas for item difficulty and discrimination conversions between classical and item response theory models. Alberta Journal of Educational Research, 55(4), 512–533.

Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195, 216–222. https://doi.org/10.1016/0370-2693(87)91197-X.MathSciNetCrossRef

Fox, J. P., & Glas, C. A. W. (2001). Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66(2), 271–288. https://doi.org/10.1007/BF02294839.MathSciNetCrossRefMATH

Geisser, S., & Eddy, W. F. (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74(365), 153–160.

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (Comment on an Article by Browne and Draper). Bayesian Analysis, 1(3), 515–533.MathSciNetCrossRefMATH

Gelman, A. (2014). Bayesian data analysis (3rd ed.). Boca Raton: CRC Press.

Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge ; New York : Cambridge University Press, 2007.

Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4), 457–472.CrossRefMATH

Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721–741. https://doi.org/10.1109/TPAMI.1984.4767596.CrossRefMATH

Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory: Newbury Park, Calif.: Sage Publications.

Harwell, M., Stone, C. A., Hsu, T. C., & Kirisci, L. (1996). Monte Carlo studies in item response theory. Applied Psychological Measurement, 20(2), 101–125. https://doi.org/10.1177/014662169602000201.CrossRef

Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109. https://doi.org/10.1093/biomet/57.1.97.MathSciNetCrossRefMATH

Hemker, B. T., Sijtsma, K., & Molenaar, I. W. (1995). Selection of unidimensional scales from a multidimensional item bank in the polytomous Mokken IRT model. Applied Psychological Measurement, 19(4), 337–352. https://doi.org/10.1177/014662169501900404.CrossRef

Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(1), 1593–1623.MathSciNetMATH

Huang, A. & Wand, M. P. (2013). Simple marginally noninformative prior distributions for covariance matrices. Bayesian Analysis, 8(2), 439–452.

Kieftenbeld, V., & Natesan, P. (2012). Recovery of graded response model parameters: A comparison of marginal maximum likelihood and Markov chain Monte Carlo estimation. Applied Psychological Measurement, 36(5), 399–419. https://doi.org/10.1177/0146621612446170.CrossRef

Kim, S. H. (2007). Some posterior standard deviations in item response theory. Educational and Psychological Measurement, 67(2), 258–279. https://doi.org/10.1177/00131644070670020501.MathSciNetCrossRef

Lewandowski, D., Kurowicka, D., & Joe, H. (2009). Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis, 100(9), 1989–2001.MathSciNetCrossRefMATH

Liu, H., Zhang, Z., & Grimm, K. J. (2016). Comparison of inverse Wishart and separation-strategy priors for Bayesian estimation of covariance parameter matrix in growth curve analysis. Structural Equation Modeling: A Multidisciplinary Journal, 23(3), 354–367. https://doi.org/10.1080/10705511.2015.1057285.MathSciNetCrossRef

Lord, F. M. (1980). Applications of item response theory to practical testing problems: Hillsdale, N.J.: L. Erlbaum Associates.

Luo, U., & Al-Harbi, K. (2017). Performances of LOO and WAIC as IRT model selection methods. Psychological Test and Assessment Modeling, 59(2), 183–205.

Mislevy, R. J. (1986). Bayes modal estimation in item response models. Psychometrika, 51(2), 177–195. https://doi.org/10.1007/BF02293979.MathSciNetCrossRefMATH

O’Malley, A., & Zaslavsky, A. (2008). Domain-level covariance analysis for survey data with structured nonresponse. Journal of the American Statistical Association, 103(484), 1405–1418. https://doi.org/10.1198/016214508000000724.MathSciNetCrossRefMATH

Patz, R. J., & Junker, B. W. (1999). A straightforward approach to Markov chain Monte Carlo methods for item response models. Journal of Educational and Behavioral Statistics, 24(2), 146–178. https://doi.org/10.3102/10769986024002146.CrossRef

Reckase, M. D. (1997). The past and future of multidimensional item response theory. Applied Psychological Measurement, 21(1), 25–36. https://doi.org/10.1177/0146621697211002.CrossRef

Roberts, J., & Thompson, V. (2011). Marginal maximum a posteriori item parameter estimation for the generalized graded unfolding model. Applied Psychological Measurement, 35(4), 259–279. https://doi.org/10.1177/0146621610392565.CrossRef

Schuurman, N. K., Grasman, R. P. P. P., & Hamaker, E. L. (2016). A comparison of inverse-Wishart prior specifications for covariance matrices in multilevel autoregressive models. Multivariate Behavioral Research, 51(2–3), 185–206. https://doi.org/10.1080/00273171.2015.1065398.CrossRef

Sheng, Y. (2010). A sensitivity analysis of Gibbs sampling for 3PNO IRT models: Effects of prior specifications on parameter estimates. Behaviormetrika, 37(2), 87–110. https://doi.org/10.2333/bhmk.37.87.CrossRefMATH

Sheng, Y., & Wikle, C. K. (2007). Comparing multiunidimensional and unidimensional item response theory models. Educational and Psychological Measurement, 67(6), 899–919. https://doi.org/10.1177/0013164406296977.MathSciNetCrossRef

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), 583–639.

Stan Development Team. (2017). Stan modeling language users guide and reference manual, Version 2.15.0.

Swaminathan, H., & Gifford, J. A. (1982). Bayesian estimation in the Rasch model. Journal of Educational Statistics, 7(3), 175–191. https://doi.org/10.2307/1164643.CrossRef

Swaminathan, H., & Gifford, J. A. (1983). Estimation of parameters in the three-parameter latent trait model. New Horizon Testing, 13–30. https://doi.org/10.1016/b978-0-12-742780-5.50009-3.

Tokuda, T., Goodrich, B., Van Mechelen, I., Gelman, A., & Tuerlinckx, F. (2011). Visualizing distributions of covariance matrices. Unpublished manuscript. http://www.stat.columbia.edu/gelman/research/unpublished/Visualization.pdf.

Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27(5), 1413–1432. https://doi.org/10.1007/s11222-016-9696-4.MathSciNetCrossRefMATH

Watanabe, S. (2010, December). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11, 3571–3594.

Wollack, J. A., Bolt, D. M., Cohen, A. S., & Lee, Y. S. (2002). Recovery of item parameters in the nominal response model: A comparison of marginal maximum likelihood estimation and Markov chain Monte Carlo estimation. Applied Psychological Measurement, 26(3), 339–352. https://doi.org/10.1177/0146621602026003007.MathSciNetCrossRef

Titel: Comparison of Hyperpriors for Modeling the Intertrait Correlation in a Multidimensional IRT Model
verfasst von: Meng-I Chang
Yanyan Sheng
Verlag: Springer International Publishing
Buch: Quantitative Psychology
Print ISBN: 978-3-030-01309-7

Electronic ISBN: 978-3-030-01310-3

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-01310-3_19

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