Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T14:20:33.580Z Has data issue: false hasContentIssue false
  • English
  • Français

A Rasch Model for Continuous Ratings

Published online by Cambridge University Press:  01 January 2025

Hans Müller
Hans Müller*
Affiliation:
Johann Wolfgang Goethe-Universität
*
Requests for reprints should be sent to Hans Müller, Institut für Psychologie, Johann Wolfgang Goethe-Universität, Mertonstr. 17, D-6000 Frankfurt am Main 11, FEDERAL REPUBLIC OF GERMANY.
Get access Rights & Permissions [Opens in a new window]

Abstract

A unidimensional latent trait model for continuous ratings is developed. This model is an extension of Andrich's rating formulation which assumes that the response process at latent thresholds is governed by the dichotomous Rasch model. Item characteristic functions and information functions are used to illustrate that the model takes ceiling and floor effects into account. Both the dichotomous Rasch model and a linear model with normally distributed error can be derived as limiting cases. The separability of the structural and incidental parameters is demonstrated and a procedure for estimating the parameters is outlined.

Keywords

latent traitRasch modelthresholdsrating scalescontinuous responsesceiling and floor effectsnormal distribution
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 2 , March 1987 , pp. 165 - 181
Copyright
Copyright © 1987 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

The author wishes to thank the three anonymous reviewers for several valuable suggestions and Rose Marie Bambach for improving the English manuscript.

References

Andersen, E. B. (1977). Sufficient statistics and latent trait models. Psychometrika, 42, 69–81.CrossRefGoogle Scholar
Andersen, E. B. (1980). Discrete statistical models with social science applications, Amsterdam: North-Holland.Google Scholar
Anderson, N. H. (1982). Methods of information integration theory, New York: Academic Press.Google Scholar
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.CrossRefGoogle Scholar
Andrich, D. (1978). Application of a psychometric rating model to ordered categories which are scored with successive integers. Applied Psychological Measurement, 2, 581–594.CrossRefGoogle Scholar
Andrich, D. (1982). An extension of the Rasch model for ratings providing both location and dispersion parameters. Psychometrika, 47, 105–113.CrossRefGoogle Scholar
Andrich, D., De'Ath, G., Lyne, A., Hill, P., Jennings, J. (1982). DISLOC: A Fortran IV program for a Rasch model which has both a location and a scale parameter for subtests, Nedlands: Department of Education, The University of Western Australia and the State Education Department, Western Australia.Google Scholar
Bejar, I. I. (1977). An application of the continuous response level model to personality measurement. Applied Psychological Measurement, 1, 509–521.CrossRefGoogle Scholar
Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (Eds.), Statistical theories of mental test scores (pp. 395–479). Reading, MA: Addison-Wesley.Google Scholar
Bock, R. D., Jones, L. V. (1968). The measurement and prediction of judgment and choice, San Francisco: Holden-Day.Google Scholar
Champney, H. (1941). The measurement of parent behavior. Child Development, 12, 131–166.Google Scholar
Freyd, M. (1923). The graphic rating scale. Journal of Educational Psychology, 14, 83–102.CrossRefGoogle Scholar
Isaacson, E., Keller, H. B. (1966). Analysis of numerical methods, New York: Wiley.Google Scholar
Johnson, N. L., Kotz, S. (1970). Distributions in statistics, Vol. 2: Continuous univariate distributions-1, New York: Houghton Mifflin.Google Scholar
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.CrossRefGoogle Scholar
Masters, G. N., Wright, B. D. (1984). The essential process in a family of measurement models. Psychometrika, 49, 529–544.CrossRefGoogle Scholar
Maxwell, C. (1978). Sensitivity and accuracy of the visual analogue scale: A psycho-physical classroom experiment. British Journal of Clinical Pharmacology, 6, 15–24.CrossRefGoogle ScholarPubMed
McKelvie, S. J. (1978). Graphic rating scales—How many categories?. British Journal of Psychology, 69, 185–202.CrossRefGoogle Scholar
Mood, A. M., Graybill, F. A., Boes, D. C. (1974). Introduction to the theory of statistics 3rd ed.,, New York: McGraw-Hill.Google Scholar
Moosbrugger, H., Müller, H. (1982). A classical latent additive test model (CLA model). German Journal of Psychology, 6, 145–149.Google Scholar
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests, Copenhagen: Pædagogiske Institut.Google Scholar
Rasch, G. (1961). On general laws and the meaning of measurement in psychology. In Neyman, J. (Eds.), Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (pp. 321–333). Berkeley: University of California Press.Google Scholar
Rasch, G. (1977). On specific objectivity: An attempt at formalizing the request for generality and validity of scientific statements. Danish Yearbook of Philosophy, 14, 58–94.CrossRefGoogle Scholar
Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests, Chicage: University of Chicago Press.Google Scholar
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph No. 17, 34(4, Pt. 2).Google Scholar
Samejima, F. (1973). Homogeneous case of the continuous response model. Psychometrika, 38, 203–219.CrossRefGoogle Scholar
Samejima, F. (1974). Normal ogive model on the continuous response level in the multidimensional latent space. Psychometrika, 39, 111–121.CrossRefGoogle Scholar
Scheiblechner, H. (1979). Specifically objective stochastic latency mechanisms. Journal of Mathematical Psychology, 19, 18–38.CrossRefGoogle Scholar
Searle, S. R. (1971). Linear models, New York: Wiley.Google Scholar
Wright, B. D., Masters, G. N. (1982). Rating scale analysis, Chicago: MESA Press.Google Scholar