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On Equivalence between a Partial Credit Item and a Set of Independent Rasch Binary Items

Published online by Cambridge University Press:  01 January 2025

Huynh Huynh
Huynh Huynh*
Affiliation:
University of South Carolina
*
Requests for reprints should be sent to Huynh Huynh, College of Education, University of South Carolina, Columbia, SC 29208.
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Abstract

Given a Masters partial credit item with n known step difficulties, conditions are stated for the existence of a set of (locally) independent Rasch binary items such that their raw score and the partial credit raw score have identical probability density functions. The conditions are those for the existence of n positive values with predetermined elementary symmetric functions and include the requirement that the n step difficulties form an increasing sequence.

Keywords

elementary symmetric functionsfree-response itemgraded response modelpartial credit modelperformance assessmentopen-ended itemRasch model
Type
Article
Information
Psychometrika , Volume 59 , Issue 1 , March 1994 , pp. 111 - 119
Copyright
Copyright © 1994 The Psychometric Society

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Footnotes

The author wishes to thank an anonymous reviewer for several thoughtful comments and for providing references to earlier works by Andersen and Rasch on unidimensional models for polytomous items.

References

Andersen, E. B. (1966). Den diskrete malingsmodel af endelig orden med anvendelse pa et socialpsykologisk materiale [A discrete latent trait model for ordered categories with applications to social psychology data], Kobenhavn, Denmark: Statens Trykningskontor.Google Scholar
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.CrossRefGoogle Scholar
Andrich, D. (1985). A latent trait model for items with response dependencies: Implications for test construction and analysis. In Embretson, S. (Eds.), Test design: Contributions from psychology, education and psychometrics (pp. 245–273). New York: Academic Press.CrossRefGoogle Scholar
Baxter, G. P., Shavelson, R. J., Goldman, S. R., Pine, J. (1992). Evaluation of procedure-based scoring for hands-on science assessment. Journal of Educational Measurement, 29, 1–17.CrossRefGoogle Scholar
Beckenbach, E. F., Bellman, R. (1965). Inequalities (Second Revised Printing), Berlin: Springer-Verlag.Google Scholar
Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more latent categories. Psychometrika, 37, 29–51.CrossRefGoogle Scholar
Brent, R. P. (1971). An algorithm with guaranteed convergence for finding a zero of a function. The Computer Journal, 14, 422–425.CrossRefGoogle Scholar
Burnside, W. S., Panton, A. W. (1892). Theory of equations 3rd ed.,, Dublin: Dublin University Press Series.Google Scholar
David, F. N., Kendall, M. G., Barton, D. E. (1966). Symmetric functions and allied tables, London: Cambridge University Press.Google Scholar
Fischer, G. H. (1974). Einfuhrung in die theorie psychologisher tests. Grundlagen und Anwendungen [Introduction to the theory of psychological tests. Foundations and applications], Bern: Huber.Google Scholar
Haney, W., Madaus, G. (1989). Searching for alternatives to standardized tests: Whys, whats, and withers. Phi Delta Kappan, 70, 683–687.Google Scholar
Holland, P. W. (1990). On the sampling theory foundation of item response theory models. Psychometrika, 55, 577–601.CrossRefGoogle Scholar
Huynh, H. & Ferrara, S. F. (in press). A comparison of equal percentile and partial credit equatings for performance-based assessments comprised of free-response items. Journal of Educational Measurement.Google Scholar
IMSL (1987). User's manual: Math/library—FORTRAN subroutines for mathematical applications, Houston: Author.Google Scholar
Macdonald, I. G. (1979). Symmetric functions and Hall polynomials, Oxford: Clarendon Press.Google Scholar
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.CrossRefGoogle Scholar
Mehrens, W. A. (1992). Using performance assessment for accountability purposes. Educational Measurement: Issues and practice, 11, 3–9.CrossRefGoogle Scholar
Muraki, E. (1990). Fitting a polytomous item response model to Likert-type data. Applied Psychological Measurement, 14, 59–71.CrossRefGoogle Scholar
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.CrossRefGoogle Scholar
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests, Copenhagen: Danish Institute for Educational Research.Google Scholar
Rasch, G. (1961). On general laws and the meaning of measurement in psychology, Berkeley: University of California Press.Google Scholar
Rasch, G. (1967). An informal report on a theory of objectivity in comparisons. In van der Kamp, L. J. Th., Vlek, C. A. J. (Eds.), Measurement theory, Leyden: University of Leyden.Google Scholar
Rasch, G. (1967). An individual-centered approach to item analysis with two categories of answers. In van der Kamp, L. J. Th., Vlek, C. A. J. (Eds.), Measurement theory, Leyden: University of Leyden.Google Scholar
Samejima, F. (1972). A general model for free-response data. Psychometric Monograph No. 18, 37(1, Pt. 2).Google Scholar
Serret, J. A. (1928). Cours d'algèbre supérieure 7th ed.,, Paris, France: Gauthier-Villars.Google Scholar
Smith, B. T. (1967). ZERPOL, A zero finding algorithm for polynomials using Laguerre's method, Toronto: University of Toronto, Department of Computer Science.Google Scholar
Thissen, D., Steinberg, L. (1984). A response model for multiple-choice items. Psychometrika, 49, 501–519.CrossRefGoogle Scholar
Thissen, D., Steinberg, L., Mooney, J. (1989). Trace lines for testlets: A use of multiple-categorical response models. Journal of Educational Measurement, 26, 247–260.CrossRefGoogle Scholar
Wainer, H., Sireci, S. G., Thissen, D. (1991). Differential testlet functioning definitions and detection. Journal of Educational Measurement, 28, 197–219.CrossRefGoogle Scholar
Wilson, M. (1988). Detecting and interpreting local item dependence using a family of Rasch models. Applied Psychological Measurement, 12, 353–364.CrossRefGoogle Scholar
Wright, B. D., Masters, G. N. (1982). Rating scale analysis, Chicago: Mesa Press.Google Scholar