Asia Pacific Education Review

, Volume 8, Issue 1, pp 41–55 | Cite as

Evaluation of linking methods for multidimensional irt calibrations

  • Kyung-Seok Min
Articles and reports


Most researchers agree that psychological/educational tests are sensitive to multiple traits, implying the need for a multidimensional item response theory (MIRT). One limitation of applying a MIRT in practice is the difficulty in establishing equivalent scales of multiple traits. In this study, a new MIRT linking method was proposed and evaluated by comparison with two existing methods. The results showed that the new method was more acceptable in transforming item parameters and maintaining dimensional structures. Limitations and cautions in using multidimensional linking techniques were also discussed.

Key words

Linking multidimensional item response theory orthogonal Procrustes rotation scale indeterminacy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ackerman, T. A. (1996). Graphical representation of multidimensional item response theory analyses.Applied Psychological Measurement, 20, 311–329.CrossRefGoogle Scholar
  2. Fraser, C. (1988).NOHARM: A computer program for fitting both unidimensional and multidimensional normal ogive models of latent trait theory. Armidale, Australia: University of New EnglandGoogle Scholar
  3. Harman, H. (1976).Modern Factor Analysis (3rd ed.). Chicago: University of Chicago Press.Google Scholar
  4. Harris, D. J., & Crouse, J. D. (1993). A study of criteria used in equating.Applied Measurement in Education, 6, 195–240.CrossRefGoogle Scholar
  5. Hirsch, T. M. (1989). Multidimensional equating.Journal of Educational Measurement, 26, 337–349.CrossRefGoogle Scholar
  6. Lee, K., & Oshima, T. C. (1996).IPLINK: Multidimensional and unidimensional item parameter equating in item response theory.Applied Psychological Measurement, 20, 230.CrossRefGoogle Scholar
  7. Li, Y. H. (1996).MDEQUATE [Computer software]. Upper Marlboro MD: Author.Google Scholar
  8. Li, Y. H., and Lissitz, R. W. (2000). An evaluation of the accuracy of multidimensional IRT equating.Applied Psychological Measurement, 24, 115 - 138.Google Scholar
  9. Lord, F. M. (1980).Applications of item response theory to practical testing problems. New Jersey: Lawrence.Google Scholar
  10. MathWork, Inc. (1995).MATLAB: The ultimate computing environment for technical education. Englewood Cliffs, NJ: Prentice-Hall, Inc.Google Scholar
  11. Min, K. S. and Kim, J. P. (2003). A comparison of two linking methods for multidimensional IRT Scale Transformation.ACT Research Report Series 2003-6. Iowa City, Iowa: American College Testing.Google Scholar
  12. Oshima, T. C., Davey, T. C., and Lee, K. (2000). Multidimensional equating: Four practical approaches.Journal of Educational Measurement, 37, 357–373.CrossRefGoogle Scholar
  13. Reckase, M. D. (1995). A linear logistic multidimensional model for dichotomous item response data. In W. J. van der Linden and Hambleton Linden (Ed.),Handbook of Modern Item Response Theory. NY: Springer.Google Scholar
  14. Reckase, M. D., and Mckinley, R. L. (1991). The discriminating power of items that measure more than one dimension.Applied Psychological Measurement.14, 361–373.CrossRefGoogle Scholar
  15. Rencher, A. C.(1995).Methods of Multivariate Analysis. New York, Wiley.Google Scholar
  16. Roussos, L. A., Stout, W. F., and Marden, J. I. (1998). Using new proximity measures with hierarchical cluster analysis to detect multidimensionality.Journal of Educational Measurement, 35, 1–30.CrossRefGoogle Scholar
  17. Schönemann, P. H., and Carroll, R. M. (1970). Fitting one matrix to another under choice of a central dilation and a rigid motion.Psychometrica, 35, 245–255.CrossRefGoogle Scholar
  18. Stocking, M. L. and Lord, F. M. (1983). Developing a common metric in item response theory.Applied Psychological Measurement, 7, 201–210.CrossRefGoogle Scholar
  19. Sympson, J. B. (1978). A model for testing with multidimensional items. In D. J. Weiss (Ed.),proceedings of the 1977 computerized adaptive testing conference (pp. 82–98). Minneapolis: University of Minnesota.Google Scholar
  20. Thompson, T. (2003).GENDATS: A computer program for generating multidimensional item response data.Google Scholar
  21. Thompson, T., Nering, M., and Davey, T. (1997).Multidimensional IRT scale linking without common items or common examinees. Paper presented at the annual meeting of the psychometric society, TN: Gatlinburg,.Google Scholar

Copyright information

© Education Research Institute 2007

Authors and Affiliations

  1. 1.Office for the College Scholastic Ability TestKorea Institute of Curriculum & EvaluationKorea

Personalised recommendations