Skip to main content
SpringerLink
Log in

A new approach to test score equating using item response theory with fixed C-parameters

  • Published:
Asia Pacific Education Review Aims and scope Submit manuscript

Abstract

Because parameter estimates from different calibration runs under the IRT model are linearly related, a linear equation can convert IRT parameter estimates onto another scale metric without changing the probability of a correct response (Kolen & Brennan, 1995, 2004). This study was designed to explore a new approach to finding a linear equation by fixing C-parameters for anchor items in IRT equating. A rationale for fixing C-parameters for anchor items in IRT equating can be established from the fact that the C-parameters are not affected by any linear transformation. This new approach can avoid the difficulty in getting accurate C-parameters for anchor items embedded in the application of the IRT model. Based upon our findings in this study, we would recommend using the new approach to fix C-parameters for anchor items in IRT equating.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Baker, F. B., & Al-Karni, A. (1991). A comparison of two procedures for computing IRT equating coefficients.Journal of Educational Measurement, 28, 147–162.

    Article  Google Scholar 

  • Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm.Psychometrika, 46, 443–459.

    Article  Google Scholar 

  • Bucket, G. R. (1996).PARDUXMX [Computer program]. Unpublished.

  • Bucket, G. R. (2000).PARDUXMJ [Computer program]. Unpublished.

  • Cook, L. L., & Eignor, D. R. (1991). An NCME instructional module on IRT equating methods.Educational Measurement: Issues and Practices, 10, 37–45.

    Article  Google Scholar 

  • Hambleton, R. K. (1989). Principles and selected applications of item response theory. In R.L. Linn (Ed.),Educational measurement (3rd ed.). Phoenix, AZ: Oryx Press.

    Google Scholar 

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

    Google Scholar 

  • Hanson, B. A., & Beguin, A. A. (2002). Obtaining a common scale for item response theory item parameters using separate versus concurrent estimation in the common-item equating design.Applied Psychological Measurement, 26, 3–24.

    Article  Google Scholar 

  • Hung, P., Wu, Y., & Chen, Y. (1991).IRT item parameter linking: Relevant issues for the purpose of item banking. Paper presented at the International Academic Symposium on Psychological Measurement, Tainan, Taiwan.

  • Kim, S.-H., & Cohen, A. S. (1992). Effects of linking methods on detection of DIF.Journal of Educational Measurement, 29, 51–66.

    Article  Google Scholar 

  • Kolen, M. J., & Brennan, R. L. (1995).Test equating: Methods and practices. New York: Springer-Verlag.

    Google Scholar 

  • Kolen, M. J., & Brennan, R. L. (2004).Test equating, scaling, and linking: Methods and practices (2nd ed.). New York: Springer.

    Google Scholar 

  • Lord, F. M. (1980).Applications of item response theory to practical testing problems._Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Loyd, B. H., & Hoover, H. D. (1980). Vertical equating using the Rasch model.Journal of Educational Measurement, 17, 179–193.

    Article  Google Scholar 

  • Marco, G. L. (1977). Item characteristic curve solutions to three intractable testing problems.Journal of Educational Measurement, 14, 139–160.

    Article  Google Scholar 

  • Ogasawara, H. (2001). Least squares estimation of item response theory linking coefficients.Applied Psychological Measurement, 25, 3–24.

    Article  Google Scholar 

  • Stocking, M. L., & Lord, F. M. (1983). Developing a common metric in item response theory.Applied Psychological Measurement, 7, 201–210.

    Article  Google Scholar 

  • Thissen, D. M., & Wainer, H. (1982). Some standard errors in item response theory.Psychometrika, 47, 397–412.

    Article  Google Scholar 

  • Way, W. D., & Tang, K. L. (1991).A comparison of four logistic model equating methods. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

  • Wingersky, M. S., Barton, M. A., & Lord, F. M. (1982).LOGIST users guide. Princeton, NJ: Educational Testing Service.

    Google Scholar 

  • Yen, W. (1990).CTB scaling specifications. Unpublished research paper.

Download references

Author information

Authors and Affiliations

  1. Department of Education, Yonsei University, 134 Shinchon-Dong, Seodaemoon-Ku, Seoul, Korea

    Guemin Lee & Anne R. Fitzpatrick

  2. Educational Testing Services, USA

    Anne R. Fitzpatrick

Authors
  1. Guemin Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anne R. Fitzpatrick
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guemin Lee.

Additional information

This work was supported by a Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, G., Fitzpatrick, A.R. A new approach to test score equating using item response theory with fixed C-parameters. Asia Pacific Educ. Rev. 9, 248–261 (2008). https://doi.org/10.1007/BF03026714

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03026714

Key words

Search

Navigation