Abstract
In the polytomous Rasch model (PRM) rating scale parameterization—one set of thresholds is estimated for all items. In the PRM partial credit parameterisation—a different set of thresholds are estimated for each of the items. A category coefficient\( \kappa_{k} \) is the negative sum of the exceeded thresholds for response category k. The slope of the expected value curve is the rate of change of the expected value at the location value of the item—it is a function of the distance between the thresholds. Latent threshold curvescan be inferred for each polytomousitem. Disorderedthresholds show that an item’s response categories are not functioning in the intended order.
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References
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika,43, 357–374.
Andrich, D. (2010a). Educational measurement: Rasch models. In P. Peterson, E. L. Baker, & B. McGaw (Eds.), International encyclopedia of education (3rd ed., Vol. 4, pp. 111–122). Elsevier.
Andrich, D. (2010b). Understanding the response structure and process in the polytomous Rasch model. In M. Nering & R. Ostini (Eds.), Handbook of polytomous item response theory models: Developments and applications (pp. 123–152). Mahwah, NJ: Lawrence Erlbaum Associates Inc.
Andrich, D. (2011). Rating scales and Rasch measurement. Expert Review of Pharmacoeconomics & Outcomes Research,11(5), 571–585.
Dawes, R. M. (1972). Fundamentals of attitude measurement. New York: Wiley.
Masters, G. N. (2016). Partial credit model. In W. J. van der Linden (Ed.), Handbook of item response theory: Models (Vol. 1, Chap. 7, pp. 109–126). Boca Raton, Florida: Taylor and Francis.
Rasch, G. (1966). An individualistic approach to item analysis. In P. F. Lazarsfeld & N. W. Henry (Eds.), Readings in mathematical social science (pp. 89–108). Chicago: Science Research Associates.
van Wyke, J. F. (2003). Constructing and interpreting achievement scales using polytomously scored items: A comparison between the Rasch and Thurstone models. Professional Doctorate thesis, Murdoch University, Western Australia.
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Exercises
Exercises
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Exercise 2: Basic analysis of dichotomous andpolytomousresponses in Appendix C.
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Exercise 4: Advanced analysis ofpolytomousresponses in Appendix C.
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Andrich, D., Marais, I. (2019). The Polytomous Rasch Model II. In: A Course in Rasch Measurement Theory. Springer Texts in Education. Springer, Singapore. https://doi.org/10.1007/978-981-13-7496-8_21
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DOI: https://doi.org/10.1007/978-981-13-7496-8_21
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