Abstract
It is shown that the presently available statistical tests for the Rasch model are insensitive to violation of the unidimensionality axiom. Two new test statistics are presented. The first one,Q 1, is sensitive to the same effects as the presently available statistics, but has some desirable properties of a nonstatistical nature. The second statistic,Q 2, is sensitive to violation of local stochastic independence and unidimensionality and thus fills an existing gap.
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Martin Löf, P.Statistika Modeller, Anteckningar från seminarier Lasåret 1969–1970 utarbetade av Rolf Sunberg obetydligt ändrat nytryk, oktober 1973. Institutet för Försäkringsmatematik och Matematisk Statistik vid Stockholms Universitet, 1973.
Allerup, P. & Sorber, G.The Rasch model for questionnaires. With a computer program (2nd ed.). Copenhagen: The Danish Institute for Educational Research, 1977.
Gustafsson, J. E. & Lindblad, T.The Rasch model for dichotomous items: A solution of the conditional estimation problem for long tests and some thoughts about item screening procedures. Paper presented at the European Conference on Psychometrics and Mathematical Psychology, Uppsala, June 15–17, 1978.
Wollenberg, van den, A. L. On the Wright-Panchapakesan goodness of fit test for the Rasch model. Intern Rapport 80-MA-02, K.U. Nijmegen, 1980.
Molenaar, I. W. Some improved diagnostics for failure of the Rasch model.Heymans Bulletin 80-482-EX, 1980.
References
Andersen, E. B. A goodness of fit test for the Rasch model.Psychometrika, 1973,38, 123–140.
Fischer, G. H.Einführung in die Theorie psychologischer Tests. Bern: Huber, 1974.
Fischer, G. H. & Scheiblechner, H. H. Algorithmen und Programmen für das probabilistische Testmodel von Rasch.Psychologische Beiträge, 1970,12, 23–51.
Gustafsson, J. E. Testing and obtaining fit of data to the Rasch model.British Jorunal of Mathematical and Statistical Psychology, 1980,32, 205–233.
Rasch, G.Probabilistic models for some intelligence and attainment tests. Kopenhagen: Nielsen & Lydiche, 1960.
Rasch, G. An informal report on a theory of objectivity in comparisons. In: L. T. J. van der Kamp & C. A. J. Vlek (Eds.),Psychological measurement theory, proceedings of the NUFFIC international summer session in science at “Het Oude Hof” The Hague, July 14–28, 1966. (a).
Rasch, G. An individual-centered approach to item analysis with two categories of answers. In: L. J. T. van der Kamp & C. A. J. Vlek (Eds.),Psychological measurement theory, proceedings of the NUFFIC international session of science at “Het Oude Hof” The Hague, July 14–28, 1966. (b).
Rasch, G. An individualistic approach to item analysis. In: P. F. Lazarsfeld & N. W. Henry (Eds.),Readings in mathematical social science. Chicago: M.I.T. Press, 1966. (c).
Rasch, G. An item analysis that takes individual differences into account.British Journal of Mathematical and Statistical Psychology, 1966,19, 49–57. (d).
Stelzl, I. Ist der Modelltest des Rasch-Modells geeignet, Homogenitäts Hypothesen zu prüfen? Ein Bericht über Simulation Studien mit inhomogene Daten.Zeitschrift für experimentelle und angewandte Psychologie, 1979, XXVI, 652–672.
Wollenberg, A. L. van den.The Rasch model and time limit tests. (Dissertation). Nijmegen: Studentenpers, 1979.
Wright, B. D. & Panchapakesan, N. A procedure for sample-free item analysis.Educational and Psychological Measurement, 1969,29, 23–57.
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van den Wollenberg, A.L. Two new test statistics for the rasch model. Psychometrika 47, 123–140 (1982). https://doi.org/10.1007/BF02296270
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DOI: https://doi.org/10.1007/BF02296270