This Chapter explains the Rasch model for ordered response categories by demonstrating the latent response structure and process compatible with the model. This is necessary because there is some confusion in the interpretation of the parameters and the possible response process characterized by the model. The confusion arises from two main sources. First, the model has the initially counterintuitive properties that (i) the values of the estimates of the thresholds defining the boundaries between the categories on the latent continuum can be reversed relative to their natural order, and (ii) that adjacent categories cannot be combined in the sense that their probabilities can be summed to form a new category. Second, two identical models at the level of a single person responding to a single item, the so called rating and partial credit models, have been portrayed as being different in the response structure and response process compatible with the model. This Chapter studies the structure and process compatible with the Rasch model, in which subtle and unusual distinctions need to be made between the values and structure of response probabilities and between compatible and determined relationships. The Chapter demonstrates that the response process compatible with the model is one of classification in which a response in any category implies a latent response at every threshold. The Chapter concludes with an example of a response process that is compatible with the model and one that is incompatible.

Key words

rating credit models partial credit models Guttman structure combing categories 


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5. References

  1. Adams, R.J., Wilson, M., and Wang. W. (1997) The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1–23.Google Scholar
  2. Andersen, E.B. (1977). Sufficient statistics and latent trait models. Psychometrika, 42, 69–81.Google Scholar
  3. Andrich, D. (1978a). A rating formulation for ordered response categories. Psychometrika, 43, 357–374.Google Scholar
  4. Andrich, D. (1978b). Application of a psychometric rating model to ordered categories which are scored with successive integers. Applied Psychological Measurement. 2, 581–94Google Scholar
  5. Andrich, D. (1995). Models for measurement, precision and the non-dichotomization of graded responses. Psychometrika, 60, 7–26.Google Scholar
  6. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F.M, Lord and M.R. Novick, Statistical theories of mental test scores (pp. 397–545). Reading, Mass.: Addison-Wesley.Google Scholar
  7. Guttman, L. (1950). The basis for scalogram analysis. In S.A. Stouffer, L. Guttman, E.A. Suchman, P.F. Lazarsfeld, S.A. Star and J.A. Clausen (Eds.), Measurement and Prediction, pp.60–90. New York: Wiley.Google Scholar
  8. Harris, J. (1991). Consequences for social measurement of collapsing adjacent categories with three or more ordered categories. Unpublished Master of Education Dissertation, Murdoch University, Western Australia.Google Scholar
  9. Jansen P.G.W. & Roskam, E.E. (1986). Latent trait models and dichotomization of graded responses. Psychometrika, 51(1), 69–91.Google Scholar
  10. Luo, G. & Andrich, D. (2004). Estimation in the presence of null categories in the reparameterized Rasch model. Journal of Applied Measurement, Under review.Google Scholar
  11. Masters, G.N. and Wright, B.D. (1997) The partial credit model. In W.J. van der Linden and R.K. Hambleton (Eds.) Handbook of Item Response Theory, (pp. 101–121). New York. Springer.Google Scholar
  12. Rasch, G. (1966). An individualistic approach to item analysis. In P.F. Lazarsfeld and N.W. Henry, (Eds.). Readings in Mathematical Social Science (pp.89–108). Chicago: Science Research Associates.Google Scholar
  13. Wright, B.D. & Masters, G.N. (1982). Rating Scale Analysis: Rasch Measurement. Chicago: MESA Press.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • David Andrich
    • 1
  1. 1.Murdoch UniversityAustralia

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