Skip to main content

Non-Rasch Measurement Models for Ordered Response Categories

  • Chapter
  • First Online:
A Course in Rasch Measurement Theory

Part of the book series: Springer Texts in Education ((SPTE))

  • 66k Accesses

Abstract

There are non-Rasch models used for analysing responses to items with ordered categories. Their application follows the item response theory, rather than the Rasch measurement theory, paradigm. There are two classes of models used. The first class specializes algebraically to the PRM; the second class is structurally different from the PRM.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Andersen, E. B. (1977). Sufficient statistics and latent trait models. Psychometrika,42, 69–81.

    Article  Google Scholar 

  • Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika,43(4), 561–574.

    Article  Google Scholar 

  • Andrich, D. (2011). Rating scales and Rasch measurement. Expert Review of Pharmacoeconomics & Outcomes Research,11(5), 571–585.

    Article  Google Scholar 

  • Andrich, D., & Luo, G. (2003). Conditional pairwise estimation in the Rasch model for ordered response categories using principal components. Journal of Applied Measurement,4(3), 205–221.

    Google Scholar 

  • Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 397–545). Reading, Massachusetts: Addison-Wesley.

    Google Scholar 

  • Bock, R. D. (1972). Estimating item parameters and latent ability when response are scored in two or more nominal categories. Psychometrika,37, 29–51.

    Article  Google Scholar 

  • Bock, R. D. (1975). Multivariate statistical methods in behavioral research. New York: McGraw-Hill.

    Google Scholar 

  • Edwards, A. L., & Thurstone, L. L. (1952). An internal consistency check for scale values determined by the method of successive intervals. Psychometrika,17, 169–180.

    Article  Google Scholar 

  • Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement,16(2), 159–176.

    Article  Google Scholar 

  • Muraki, E. & Muraki, M. (2016). Generalized partial credit model. In W. J. van der Linden (Ed.), Handbook of item response theory: Models (Vol. 1, Chapter 8, pp. 127–137). Boca Raton, Florida: Taylor and Francis.

    Google Scholar 

  • Rasch, G. (1961). On general laws and the meaning of measurement in psychology. In J. Neyman (Ed.), Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 4, pp. 321–333). Berkeley, California: University of California Press. Reprinted in Bartholomew, D. J. (Ed.) (2006). Measurement: Sage benchmarks in social research methods (Vol. I, pp. 319–334). London: Sage Publications.

    Google Scholar 

  • Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometric Monographs,34(2, No.17).

    Google Scholar 

  • Samejima, F. (2016). Graded response models. In W. J. van der Linden (Ed.), Handbook of item response theory: Models (Vol. 1, Chapter 6, pp. 95–108). Boca Raton, Florida: Taylor and Francis.

    Google Scholar 

  • Thurstone, L. L. (1928). The measurement of opinion. Journal of Abnormal and Social Psychology,22, 415–430.

    Article  Google Scholar 

Further Reading

  • Andrich, D. (1995). Distinctive and incompatible properties of two common classes of IRT models for graded responses. Applied Psychological Measurement,19(1), 101–119.

    Article  Google Scholar 

  • Nering, M., & Ostini, R. (Eds.). (2010). Handbook of polytomous item response theory models: Developments and applications. Mahwah, New Jersey: Lawrence Erlbaum Associates Inc.

    Google Scholar 

  • Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models. Psychometrika,51, 567–577.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David Andrich .

Exercises

Exercises

Describe, in one paragraph each, two differences between the Rasch and non-Rasch models used for analysing items with ordered categories.

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Andrich, D., Marais, I. (2019). Non-Rasch Measurement Models for Ordered Response Categories. In: A Course in Rasch Measurement Theory. Springer Texts in Education. Springer, Singapore. https://doi.org/10.1007/978-981-13-7496-8_28

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-7496-8_28

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-7495-1

  • Online ISBN: 978-981-13-7496-8

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics