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The Rating Scale Model

  • Erling B. Andersen
Chapter

Abstract

The rating scale model is a latent structure model for polytomous responses to a set of test items. The basic structure of the model is an extension of the Rasch model for dichotomous responses, suggested by Georg Rasch, 1961.

Keywords

Response Pattern Item Parameter Multinomial Distribution Category Score Score Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Andersen, E.B. (1972). The numerical solution of a set of conditional estimation equations. Journal of the Royal Statistical Society, B 34, 42–54.MATHGoogle Scholar
  2. Andersen, E.B. (1973). A goodness of fit test for the Rasch model. Psychometrika 38, 123–140.MathSciNetMATHCrossRefGoogle Scholar
  3. Andersen, E.B. (1977). Sufficient statistics and latent trait models. Psychometrika 42, 69–81.MathSciNetMATHCrossRefGoogle Scholar
  4. Andersen, E.B. (1983). A general latent structure model for contingency table data. In H. Wainer and S. Messick (Eds.), Principles of Modern Psychological Measurement (pp. 117–139 ). New Jersey: Lawrence Erlbaum Associates.Google Scholar
  5. Andersen, E.B. (1991). The Statistical Analysis of Categorical Data ( 2nd ed. ). Heidelberg: Springer-Verlag.CrossRefGoogle Scholar
  6. Andersen, E.B. (1995). Residual analysis in the polytomous Rasch model. Psychometrika 60, 375–393.MathSciNetMATHCrossRefGoogle Scholar
  7. Andrich, D. (1978a). A rating formulation for ordered response categories. Psychometrika 43, 561–573.MATHCrossRefGoogle Scholar
  8. Andrich, D. (1978b). Application of a psychometric rating model to ordered categories which are scored with successive integers. Applied Psychological Measurement 2, 581–594.CrossRefGoogle Scholar
  9. Andrich, D. (1982). An extension of the Rasch model to ratings providing both location and dispersion parameters. Psychometrika 47, 105–113.CrossRefGoogle Scholar
  10. Barndorff Nielsen, O. (1978). Information and Exponential Families in Statistical Theory. New York: Wiley and Sons.MATHGoogle Scholar
  11. Bech, P. (1990). Methodological problems in assessing quality of life as outcome in psychopharmacology: A multiaxial approach. In O. Benkert, W. Maier, and K. Rickels (Eds.), Methodology of the Evaluation of Psychotropic Drugs (pp. 79–110 ). Berlin-Heidelberg: Springer-Verlag.Google Scholar
  12. Bech, P., Allerup, P., Maier, W., Albus, M., Lavori, P., and Ayuso, J.L. (1992). The Hamilton scale and the Hopkins Symptom Checklist (SCL90): A cross-national validity study in patients with panic disorders. British Journal of Psychiatry 160, 206–211.Google Scholar
  13. Cressie, N. and Holland, P.W. (1983). Characterizing the manifest probabilities of latent trait models, Psychometrika 48, 129–141.MathSciNetMATHCrossRefGoogle Scholar
  14. de Leeuw, J. and Verhelst, N. (1986). Maximum likelihood estimation in generalized Rasch models. Journal of Educational Statistics 11, 183196.Google Scholar
  15. Derogatis, L.R., Lipman, R.S., Rickels, K., Uhlenhuth, E.H., and Covi, L. (1974). The Hopkins Symptom Checklist (HSCL). In P. Pichot (Ed.), Psychological Measurement in Psychopharmacology (pp. 79–110 ). Basel: Karger.Google Scholar
  16. Fischer, G.H. (1981). On the existence and uniqueness of maximum likelihood estimates in the Rasch model. Psychometrika 46, 59–77.MathSciNetMATHCrossRefGoogle Scholar
  17. Fischer, G.H. and Parzer, P. (1991). An extension of the rating scale model with an application to the measurement of change. Psychometrika 56, 637–651.MATHCrossRefGoogle Scholar
  18. Fischer, G.H. and Spada, H. (1973). Die Psychometrischen Grundlagen des Rorschachtests under der Holtzman Inkblot Technique. Bern: Huber.Google Scholar
  19. Glas, C.A.W. (1988a). The derivation of some tests for the Rasch model from the multinomial distribution. Psychometrika 53, 525–546.Google Scholar
  20. Glas, C.A.W. (1988b). The Rasch model and multistage testing. Journal of Educational Statistics 13, 45–52.CrossRefGoogle Scholar
  21. Glas, C.A.W. (1989). Contributions to Estimating and Testing Rasch Models. Doctoral dissertation, University of Twente, Enschede, The Netherlands.Google Scholar
  22. Mislevy, R.J. (1984). Estimating latent distributions. Psychometrika 49, 359–381.Google Scholar
  23. Rao, C.R. (1973). Linear Statistical Inference and Its Applications, 2nd Ed. New York: Wiley and Sons.MATHCrossRefGoogle Scholar
  24. Rasch, G. (1961). On general laws and the meaning of measurement in psychology, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 4, pp. 321–333 ). Berkeley: University of California Press.Google Scholar
  25. Tjur, T. (1982). A connection between Rasch’s item analysis model and a multiplicative Poisson model. Scandinavian Journal of Statistics 9, 23–30.MathSciNetMATHGoogle Scholar

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© Springer Science+Business Media New York 1997

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  • Erling B. Andersen

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