Psychometrika

, Volume 42, Issue 4, pp 631–634 | Cite as

The rasch model, the law of comparative judgment and additive conjoint measurement

  • H. E. Brogden
Notes And Comments

Abstract

Relationships between the Rasch model and both the law of comparative judgment and additive conjoint measurement are discussed. The distance between the ability of Persona and the difficult of Itemi is, in the Rasch model, the baseline value corresponding to the probability thata will respond correctly toi, where this probability is interpreted as the area under a logistic curve (which is substantially equivalent to the normal curve) and is thus an application of the law of comparative judgment. Under certain assumptions, the Rasch model is also a special case of additive conjoint measurement and, properly reinterpreted, may be usefully applied in contexts other than individual differences.

Key words

measurement theory Rasch model test theory ability inverse logistic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Birnbaum, A. Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M. and Novick, R. N. (Eds.),Statistical theories of mental test scores. Reading: Addison-Wesley Publishing Company, 1968.Google Scholar
  2. Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W.Discrete multivariate analysis: Theory and practice. Cambridge: The MIT Press, 1975.Google Scholar
  3. Lord, F. M., & Novick, R. N.Statistical theories of mental test scores. Reading: Addison-Wesley Publishing Company, 1968.Google Scholar
  4. Luce, R. D., & Tukey, J. W. Simultaneous conjoint measurement: A new type fundamental measurement.Journal of Mathematical Psychology, 1964,1, 1–27.Google Scholar
  5. Rasch, G. An individualistic approach to item analysis. In P. F. Lazarsfeld and N. W. Henry (Eds.),Readings in mathematical social science. Chicago: Science Research Associates, 1966.Google Scholar

Copyright information

© Psychometric Society 1977

Authors and Affiliations

  • H. E. Brogden
    • 1
  1. 1.Department of Psychological SciencesPurdue UniversityWest Lafayette

Personalised recommendations