162
Views
1
CrossRef citations to date
0
Altmetric
Research Article

The Hellinger Distance within Posterior Predictive Assessment for Investigating Multidimensionality in IRT Models

&

References

  • Adams, R. J., Wilson, M., & Wang, W.-C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21(1), 1–23. doi: 10.1177/0146621697211001
  • Agresti, A. (2002). Categorical data analysis. Wiley. doi:10.1002/0471249688
  • Albert, J. H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics, 17(3), 251–269. doi:10.3102/10769986017003251
  • Bhattacharyya, A. (1943). On a measure of divergence between two statistical populations defined by their probability distributions. Bulletin of Calcutta Mathematical Society, 35, 99–109.
  • Béguin, A. A., & Glas, C. A. W. (2001). MCMC estimation and some fit analysis of multidimensional IRT models. Psychometrika, 66(4), 541–488. doi:10.1007/BF02296195
  • Bernini, C., Matteucci, M., & Mignani, S. (2015). Investigating heterogeneity in residents’ attitudes toward tourism with an IRT multidimensional approach. Quality & Quantity, 49(2), 805–826. doi:10.1285/i20705948v11n2p427
  • de la Torre, J., & Song, H. (2009). Simultaneous estimation of overall and domain abilities: A higher-order IRT model approach. Applied Psychological Measurement, 33(8), 620–639. doi:10.1177/0146621608326423
  • Fontanella, L., Fontanella, S., Valentini, P., & Trendafilov, N. (2019). Simple structure detection through Bayesian exploratory multidimensional IRT models. Multivariate Behavioral Research, 54(1), 100–112. doi:10.1080/00273171.2018.1496317
  • Gelman, A., Meng, X. L., & Stern, H. S. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6, 733–807.
  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2014). Bayesian data analysis (3rd ed). CRC Press.
  • Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(6), 721–741. doi:10.1109/TPAMI.1984.4767596
  • Gibbons, R. D., & Hedeker, D. R. (1992). Full-information item bi-factor analysis. Psychometrika, 57(3), 423–436. doi:10.1007/BF02295430
  • Gibbons, R. D., Immekus, J. C., & Bock, R. D. (2007). The added value of multidimensional IRT models. Multidimensional and hierarchical modeling monograph 1. Center for Health Statistics, University of Illinois.
  • Glas, C. A. W., & Meijer, R. R. (2003). A Bayesian approach to person fit analysis in item response theory models. Applied Psychological Measurement, 27(3), 217–233. doi:10.1177/0146621603027003003
  • Hellinger, E. (1909). Neue Begrundung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)), 1909(136), 210–271. doi:10.1515/crll.1909.136.210
  • Hoijtink, H. (2001). Conditional independence and differential item functioning in the two-parameter logistic model. In A. Boomsma, M. A. J. van Duijn, & T. A. B. Snijders (Eds.), Essays in item response theory. Springer-Verlag. doi:10.1007/978-1-4613-0169-1_6
  • Huo, Y., de la Torre, J., Mun, E.-Y., Kim, S.-Y., Ray, A. E., Jiao, Y., & White, H. R. (2015). A hierarchical multi-unidimensional IRT approach for analyzing sparse, multi-group data for integrative data analysis. Psychometrika, 80(3), 834–855. doi:10.1007/s11336-014-9420-2
  • Ip, E. H. (2010). Empirically indistinguishable multidimensional IRT and locally dependent unidimensional item response models. British Journal of Mathematical and Statistical Psychology, 63(2), 395–416. doi:10.1348/000711009X466835
  • Kang, H.-A., & Chang, H.-H. (2016). Parameter drift detection in multidimensional computerized adaptive testing based on informational distance/divergence measures. Applied Psychological Measurement, 40(7), 534–550. doi:10.1177/0146621616663676
  • Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22(1), 79–86. doi:10.1214/aoms/1177729694
  • Levy, R. (2011). Posterior predictive model checking for conjunctive multidimensionality in item response theory. Journal of Educational and Behavioral Statistics, 36(5), 672–694. doi:10.3102/1076998611410213
  • Levy, R., & Svetina, D. (2011). A generalized dimensionality discrepancy measure for dimensionality assessment in multidimensional item response theory. British Journal of Mathematical and Statistical Psychology, 64(2), 208–232. doi:10.1348/000711010X500483
  • Levy, R., Mislevy, R. J., & Sinharay, S. (2009). Posterior predictive model checking for multidimensionality in item response theory. Applied Psychological Measurement, 33(7), 519–537. doi:10.1177/0146621608329504
  • Levy, R., Xu, Y., Yel, N., & Svetina, D. (2015). A standardized generalized dimensionality discrepancy measure and a standardized model-based covariance for dimensionality assessment for multidimensional models. Journal of Educational Measurement, 52(2), 144–158. doi:10.1111/jedm.12070
  • Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Addison-Wesley.
  • Reckase, M. (1997). A linear logistic multidimensional model for dichotomous item response data. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 271–286). Springer-Verlag. doi:10.1007/978-1-4757-2691-6
  • Reckase, M. (2009). Multidimensional item response theory. Springer-Verlag. doi:10.1007/978-0-387-89976-3
  • Rubin, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applies statistician. The Annals of Statistics, 12(4), 1151–1172. doi:10.1214/aos/1176346785
  • Sheng, Y. (2008a). Markov chain Monte Carlo estimation of normal ogive IRT models in MATLAB. Journal of Statistical Software, 25(8), 1–15. doi:10.18637/jss.v025.i08
  • Sheng, Y. (2008b). A MATLAB package for Markov chain Monte Carlo with a multi-unidimensional IRT model. Journal of Statistical Software, 28(10), 1–20. doi:10.18637/jss.v028.i10
  • Sheng, Y. (2010). Bayesian estimation of MIRT models with general and specific latent traits in MATLAB. Journal of Statistical Software, 34(3), 1–27. doi:10.18637/jss.v034.i03
  • Sheng, Y., & Wikle, C. (2007). Comparing multiunidimensional and unidimensional item response theory models. Educational and Psychological Measurement, 67(6), 899–919. doi:10.1177/0013164406296977
  • Sheng, Y., & Wikle, C. (2008). Bayesian multidimensional IRT models with an hierarchical structure. Educational and Psychological Measurement, 68(3), 413–430. doi:10.1177/0013164407308512
  • Sheng, Y., & Wikle, C. (2009). Bayesian IRT models incorporating general and specific abilities. Behaviormetrika, 36(1), 27–48. doi:10.2333/bhmk.36.27
  • Sinharay, S. (2005). Assessing fit of unidimensional item response theory models using a Bayesian approach. Journal of Educational Measurement, 42(4), 375–394. doi:10.1111/j.1745-3984.2005.00021.x
  • Sinharay, S. (2006). Bayesian item fit analysis for unidimensional item response theory models. British Journal of Mathematical and Statistical Psychology, 59(2), 429–449. doi:10.1348/000711005X66888
  • Sinharay, S., Johnson, M. S., & Stern, H. S. (2006). Posterior predictive assessment of item response theory models. Applied Psychological Measurement, 30(4), 298–321. doi:10.1177/0146621605285517
  • van der Linden, W. J., & Hambleton, R. K. (1997). Handbook of modern item response theory. Springer-Verlag. doi:10.1007/978-1-4757-2691-6
  • Wang, W.-C., Chen, P.-H., & Cheng, Y.-Y. (2004). Improving measurement precision of test batteries using multidimensional item response models. Psychological Methods, 9(1), 116–136. doi:10.1037/1082-989X.9.1.116
  • Wu, H., Yuen, K. V., & Leung, S. O. (2014). A novel relative entropy-posterior predictive model checking approach with limited information statistics for latent trait models in sparse 2k contingency tables. Computational Statistics & Data Analysis, 79, 261–276. doi:10.1016/j.csda.2014.06.004
  • Yen, W. (1993). Scaling performance assessments: Strategies for managing local item dependence. Journal of Educational Measurement, 30(3), 187–213. doi:10.1111/j.1745-3984.1993.tb00423.x
  • Zhang, J., & Stout, W. (1999). Conditional covariance structure of generalized compensatory multidimensional items. Psychometrika, 64(2), 129–152. doi:10.1007/BF02294532
  • Zhu, X., & Stone, C. A. (2011). Assessing fit of unidimensional graded response models using Bayesian methods. Journal of Educational Measurement, 48(1), 81–97. doi:10.1111/j.1745-3984.2011.00132.x

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.