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Original Articles

Discrimination with unidimensional and multidimensional item response theory models for educational data

ORCID Icon & ORCID Icon
Pages 2992-3012 | Received 18 Jun 2019, Accepted 11 Dec 2019, Published online: 30 Dec 2019

References

  • Adams, R. J., M. Wilson, and W.-C. Wang. 1997. The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement 21 (1):1–23. doi:10.1177/0146621697211001.
  • Baker, F. B., and S.-H. Kim. 2004. Item response theory: Parameter estimation techniques. CRC Press.
  • Berger, M. P. F., and W.-K. Wong. 2005. Applied optimal designs. West Sussex: John Wiley & Sons.
  • Bock, R. D., R. Gibbons, and E. Muraki. 1988. Full-information item factor analysis. Applied psychological measurement 12 (3):261–80. doi:10.1177/014662168801200305.
  • Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference – a practical information-theoretic approach. New York: Springer.
  • Buyske, S. 2005. Optimal designs in educational testing. In Applied optimal designs, eds. M. P. F. Berger and W. K. Wong. Chichester, UK: John Wiley & Sons, Ltd.
  • Chalmers, R. P. 2012. mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software 48 (6):1–29. doi:10.18637/jss.v048.i06.
  • Childs, R. A., and S. H. Oppler. 1999. Practical implications of test dimensionality for item response theory calibration of the medical college admission test. MCAT Monograph. Washington, DC: ERIC.
  • Conway, J. M., and A. I. Huffcutt. 2003. A review and evaluation of exploratory factor analysis practices in organizational research. Organizational Research Methods 6 (2):147–68. doi:10.1177/1094428103251541.
  • De La Torre, J., and R. J. Patz. 2005. Making the most of what we have: A practical application of multidimensional item response theory in test scoring. Journal of Educational and Behavioral Statistics 30 (3):295–311. doi:10.3102/10769986030003295.
  • Drasgow, F., and C. K. Parsons. 1983. Application of unidimensional item response theory models to multidimensional data. Applied Psychological Measurement 7 (2):189–99. doi:10.1177/014662168300700207.
  • Fabrigar, L. R., D. T. Wegener, R. C. MacCallum, and E. J. Strahan. 1999. Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods 4 (3):272–99. doi:10.1037//1082-989X.4.3.272.
  • Finkelman, M., G. Hooker, and Z. Wang. 2010. Prevalence and magnitude of paradoxical results in multidimensional item response theory. Journal of Educational and Behavioral Statistics 35 (6):744–61. doi:10.3102/1076998610381402.
  • Garrido, L. E., F. J. Abad, and V. Ponsoda. 2013. A new look at Horn’s parallel analysis with ordinal variables. Psychological Methods 18 (4):454–74. doi:10.1037/a0030005.
  • Gorsuch, R. L. 1983. Factor analysis. 2nd ed. London: Lawrence Erlbaum Associates.
  • Guttman, L. 1954. Some necessary conditions for common-factor analysis. Psychometrika 19 (2):149–61. doi:10.1007/BF02289162.
  • Hambleton, R. K., H. Swaminathan, and H. J. Rogers. 1991. Fundamentals of item response theory. Newbury Park, CA: Sage Publications.
  • Harrison, D. A. 1986. Robustness of IRT parameter estimation to violations of the unidimensionality assumption. Journal of Educational Statistics 11 (2):91–115. doi:10.3102/10769986011002091.
  • Hartig, J., and J. Höhler. 2009. Multidimensional IRT models for the assessment of competencies. Studies in Educational Evaluation 35 (2/3):57–63. doi:10.1016/j.stueduc.2009.10.002.
  • Hayton, J. C., D. G. Allen, and V. Scarpello. 2004. Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational Research Methods 7 (2):191–205. doi:10.1177/1094428104263675.
  • Henson, R. K., and J. K. Roberts. 2006. Use of exploratory factor analysis in published research common errors and some comment on improved practice. Educational and Psychological Measurement 66 (3):393–416. doi:10.1177/0013164405282485.
  • Hooker, G. 2010. On separable test, correlated priors, and paradoxical results in multidimensional item response theory. Psychometrika 75 (4):694–707. doi:10.1007/s11336-010-9181-5.
  • Hooker, G., M. Finkelman, and A. Schwartzman. 2009. Paradoxical results in multidimensional item response theory. Psychometrika 74 (3):419–42. doi:10.1007/s11336-009-9111-6.
  • Horn, J. L. 1965. A rationale and test for the number of factors in factor analysis. Psychometrika 30 (2):179–85. doi:10.1007/BF02289447.
  • Jordan, P., and M. Spiess. 2012. Generalization of paradoxical results in multidimensional item response theory. Psychometrika 77 (1):127–52. doi:10.1007/s11336-011-9243-3.
  • Jordan, P., and M. Spiess. 2018. A new explanation and proof of the paradoxical scoring results in multidimensional item response models. Psychometrika 83 (4):831–46. doi:10.1007/s11336-017-9588-3.
  • Kaiser, H. F. 1960. The application of electronic computers to factor analysis. Educational and Psychological Measurement 20 (1):141–51. doi:10.1177/001316446002000116.
  • Kirisci, L., T.-C. Hsu, and L. Yu. 2001. Robustness of item parameter estimation programs to assumptions of unidimensionality and normality. Applied Psychological Measurement 25 (2):146–62. doi:10.1177/01466210122031975.
  • Kose, I. A., and N. C. Demirtasli. 2012. Comparison of unidimensional and multidimensional models based on item response theory in terms of both variables of test length and sample size. Procedia - Social and Behavioral Sciences 46:135–40. doi:10.1016/j.sbspro.2012.05.082.
  • Lee, S., and R. Terry. 2005. MDIRT-FIT: SAS macros for fitting multidimensional item response. Paper presented at the SUGI 31st Conference, Cary.
  • Li, Y., H. Jiao, and R. W. Lissitz. 2012. Applying multidimensional item response theory models in validating test dimensionality: An example of k–12 large-scale science assessment. Journal of Applied Testing Technology 13 (2):1–27.
  • Magis, D. 2013. A note on the item information function of the four-parameter logistic model. Applied Psychological Measurement 37 (4):304–15. doi:10.1177/0146621613475471.
  • Magis, D., and G. Raîche. 2012. Random generation of response patterns under computerized adaptive testing with the r package catr. Journal of Statistical Software 48 (8):1–31. doi:10.18637/jss.v048.i08.
  • Peres-Neto, P. R., D. A. Jackson, and K. M. Somers. 2005. How many principal components? Stopping rules for determining the number of non-trivial axes revisited. Computational Statistics & Data Analysis 49 (4):974–97. doi:10.1016/j.csda.2004.06.015.
  • Reckase, M. D. 1979. Unifactor latent trait models applied to multifactor tests: Results and implications. Journal of Educational Statistics 4 (3):207–30. doi:10.3102/10769986004003207.
  • Reckase, M. D. 1997. High dimensional analysis of the contents of an achievement test battery: Are 50 dimensions too many? Paper presented at the meeting of the Society for Multivariate Experimental Psychology, Scottsdale, AZ.
  • Reckase, M. D. 2007. Multidimensional item response theory. In: Handbook of statistics 26: Psychometrics, ed. C. R. Rao and S. Sinharay, 607–42. Amsterdam, Netherlands: Elsevier.
  • Reckase, M. D. 2009. Multidimensional item response theory. Springer, New York.
  • Reckase, M., and X. Luo. 2015. A paradox by another name is good estimation. In Quantitative psychology research. Springer proceedings in mathematics & statistics, R. Millsap, D. Bolt, L. van der Ark, and W. C. Wang, vol. 89, 465–86. Cham: Springer.
  • Reckase, M. D., and R. L. McKinley. 1991. The discriminating power of items that measure more than one dimension. Applied Psychological Measurement 15 (4):361–73. doi:10.1177/014662169101500407.
  • Reckase, M. D. 1985. Models for multidimensional tests and hierarchically structured training materials. Technical report, American Coll Testing Program IOWA city IA test development div.
  • Rizopoulos, D. 2006. ltm: An R package for latent variable modeling and item response theory analyses. Journal of Statistical Software 17 (5):1–25. doi:10.18637/jss.v017.i05.
  • Ruscio, J., and B. Roche. 2012. Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure. Psychological Assessment 24 (2):282–92. doi:10.1037/a0025697.
  • Samejima, F. 1969. Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Psychometrika 34 (4):100. doi:10.1007/BF03372160.
  • Sheng, Y., and C. K. Wikle. 2007. Comparing multiunidimensional and unidimensional item response theory models. Educational and Psychological Measurement 67 (6):899–919. doi:10.1177/0013164406296977.
  • Spencer, S. G. 2004. The strength of multidimensional item response theory in exploring construct space that is multidimensional and correlated. Ph. D. thesis., Doctoral Dissertation, Brigham Young University-Provo.
  • van der Linden, W. J. 2012. On compensation in multidimensional response modeling. Psychometrika 77 (1):21–30. doi:10.1007/s11336-011-9237-1.
  • van Rijn, P. W., and F. Rijmen. 2012. A note on explaining away and paradoxical results in multidimensional item response theory. Technical report, Princeton, New Jersey: Educational Testing Service. doi:10.1002/j.2333-8504.2012.tb02295.x.
  • Velicer, W. F., C. A. Eaton, and J. L. Fava. 2000. Construct explication through factor or component analysis: A review and evaluation of alternative procedures for determining the number of factors or components. In Problems and solutions in human assessment, 41–71. Boston: Springer.
  • Verma, N., and M. K. Markey. 2014. Item response analysis of Alzheimer’s disease assessment scale. In Engineering in medicine and biology society (EMBC), 2014 36th annual international conference of the IEEE, 2476–2479. Chicago: IEEE.
  • Way, W. D., T. N. Ansley, and R. A. Forsyth. 1988. The comparative effects of compensatory and noncompensatory two-dimensional data on unidimensional IRT estimates. Applied Psychological Measurement 12 (3):239–52. doi:10.1177/014662168801200303.
  • Wiberg, M. 2012. Can a multidimensional test be evaluated with unidimensional item response theory? Educational Research and Evaluation 18 (4):307–20. doi:10.1080/13803611.2012.670416.
  • Yang, S. 2007. A comparison of unidimensional and multidimensional RASCH models using parameter estimates and fit indices when assumption of unidimensionality is violated. Ph. D. thesis, doctoral dissertation, The Ohio State University.
  • Yen, W. M. 1984. Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement 8 (2):125–45. doi:10.1177/014662168400800201.
  • Zwick, W. R., and W. F. Velicer. 1986. Comparison of five rules for determining the number of components to retain. Psychological Bulletin 99 (3):432–42. doi:10.1037//0033-2909.99.3.432.