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Some Improved Diagnostics for Failure of the Rasch Model

Published online by Cambridge University Press:  01 January 2025

Ivo W. Molenaar
Ivo W. Molenaar*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Ivo W. Molenaar, Fac. Soc. Wet., Oude Boteringestraat 23, 9712 GC Groningen, Netherlands.
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Abstract

Although several goodness of fit tests have been developed for the Rasch model for dichotomous items, most of them are of a global, asymptotic, and confirmatory type. This paper, based on ideas from a recent thesis by Van den Wollenberg, offers some suggestions for local, small sample, and exploratory techniques: difficulty plots for person groups scoring right and wrong on a specific item, a slope test per item based on a binomial distribution per score group, and a unidimensionality check based on an extended hypergeometric distribution per score group.

Keywords

logistic latent trait modelRasch assumptionsexploration of model fit
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 1 , March 1983 , pp. 49 - 72
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

This paper owes much to the inspiring and pioneering work of Arnold Van den Wollenberg, of which only minor aspects are criticized. Thanks go to Charles Lewis for stimulating discussions and for solutions to some programming problems.

References

Reference Notes

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Andersen, E. B. Latent trait models and ability parameter estimation. Applied Psychological Measurement, 1982, to be published.CrossRefGoogle Scholar
Fischer, G. H. Einführung in die Theorie Psychologischer Tests. Grundlagen und Anwendungen, Bern: Huber, 1974.Google Scholar
Fischer, G. H. & Scheiblechner, H. Algorithmen und Programma für das probabilistische Testmodell von Rasch. Psychologische Beiträge, 1970, 12, 23–51.Google Scholar
Formann, A. K. Über die Verwendung von Items als Teilungskriterium für Modellkontrollen im Modell von Rasch. Zeitschrift für Experimentelle und Angewandte Psychologie, 1981, 28, 541–560.Google Scholar
Gustafsson, J. E. Testing and obtaining fit of data to the Rasch model. British Journal of Mathematical and Statistical Psychology, 1980, 33, 205–233.CrossRefGoogle Scholar
Harkness, W. L. Properties of the Extended Hypergeometric distribution. Annals of Mathematical Statistics, 1965, 36, 938–945.CrossRefGoogle Scholar
Lehmann, E. L. Testing Statistical Hypotheses, Wiley: New York, 1959.Google Scholar
Lord, F. M. Applications of item response theory to practical testing. Erlbaum, Hillsdale N.J., 1981.Google Scholar
Patil, G. G. & Joshi, S. W. A dictionary and bibliography of discrete distributions, Edinburgh: Oliver & Boyd, 1968.Google Scholar
Van den Wollenberg, A. L. The Rasch model and time-limit tests, Ph.D. thesis, University of Nijmegen, 1979.Google Scholar
Van den Wollenberg, A. L. Two new test statistics for the Rasch model. Psychometrika, 1982, 47, 123–140.CrossRefGoogle Scholar
Wainer, H., Morgan, A. & Gustafsson, J. E. A review of estimation procedures for the Rasch model with an eye toward longish tests. Journal of Educational Statistics, 1980, 5, 35–64.CrossRefGoogle Scholar
Wallis, W. A. Compounding probabilities from independent significance tests. Econometrica, 1942, 10, 229–248.CrossRefGoogle Scholar
Wright, B. D. & Panchapakesan, N. A procedure for sample-free item analysis. Educational and Psychological Measurement, 1969, 28, 23–48.CrossRefGoogle Scholar
Wright, B. D. & Stone, M. H. Best test design, Rasch measurement, MESA PRESS, 5835 Kimbark Ave. Chicago (Ill), 1979.Google Scholar