Abstract
The partial credit model (PCM) by Masters (1982, this volume) is a unidimensional item response model for analyzing responses scored in two or more ordered categories. The model has some very desirable properties: it is an exponential family, so minimal sufficient statistics for both the item and person parameters exist, and it allows conditional-maximum likelihood (CML) estimation. However, it will be shown that the relation between the response categories and the item parameters is rather complicated. As a consequence, the PCM may not always be the most appropriate model for analyzing data.
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References
Abramowitz, M. and Stegun, I.A. (1974). Handbook of Mathematical Functions. New York: Dover Publications.
Aitchison, J. and Silvey, S.D. (1958). Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics 29, 813–828.
Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F.M. Lord and M.R. Novick, Statistical Theories of Mental Test Scores. Reading, MA: Addison-Wesley.
Bock, R.D. and Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of an EM-algorithm. Psychometrika 46, 443–459.
Cressie, N. and Holland, P.W. (1983). Characterizing the manifest probabilities of latent trait models. Psychometrika 48, 129–141.
De Leeuw, J. and Verhelst, N.D. (1986). Maximum likelihood estimation in generalized Rasch models. Journal of Educational Statistics 11, 183–196.
De Vries, H.H. (1988). Het Partial Credit Model en het Sequentiële Rasch Model met Stochastisch Design [The partial credit model and the sequential Rasch model with stochastic design]. Amsterdam, the Netherlands: Universiteit van Amsterdam
Fischer, G.H. (1974). Einfiihrung in die Theorie psychologischer Tests [Introduction to the Theory of Psychological Tests]. Bern: Huber.
Fischer, G.H. (1981). On the existence and uniqueness of maximum likelihood estimates in the Rasch model. Psychometrika 46, 59–77.
Follmann, D. (1988). Consistent estimation in the Rasch model based on nonparametric margins. Psychometrika 53, 553–562.
Glas, C.A.W. (1988). The Rasch model and multi-stage testing. Journal of Educational Statistics 13, 45–52.
Glas, C.A.W. (1989). Contributions to Estimating and Testing Rasch Models. Doctoral dissertation, University of Twente, Enschede, The Netherlands.
Glas, C.A.W. and Verhelst, N.D. (1989). Extensions of the partial credit model. Psychometrika 54, 635–659.
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika 47, 149–174.
Mislevy, R.J. (1984). Estimating latent distributions. Psychometrika 49, 359–381.
Molenaar, I.W. (1983). Item Steps (Heymans Bulletins HB-83–630-EX). Groningen, The Netherlands: Psychologisch Instituut RU Groningen.
Rao, C.R. (1948). Large sample tests of statistical hypothesis concerning several parameters with applications to problems of estimation. Proceedings of the Cambridge Philosophical Society 44, 50–57.
Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attain- ment Tests. Copenhagen: Danish Institute for Educational Research.
Verhelst, N.D. and Eggen, T.J.H.M. (1989). Psychometrische en Statistische Aspecten yen Peilingsonderzoek [Psychometric and Statistical Aspects of Assessment Research] (PPON-Rapport, 4 ). Arnhem: Cito.
Verhelst, N.D. and Glas, C.A.W. (1993). A dynamic generalization of the Rasch model. Psychometrika 58, 395–415.
Verhelst, N.D., Glas, C.A.W., and Verstralen, H.H.F.M. (1995). OPLM: One Parameter Logistic Model: Computer Program and Manual. Arnhem: Cito.
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Verhelst, N.D., Glas, C.A.W., de Vries, H.H. (1997). A Steps Model to Analyze Partial Credit. In: van der Linden, W.J., Hambleton, R.K. (eds) Handbook of Modern Item Response Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2691-6_7
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DOI: https://doi.org/10.1007/978-1-4757-2691-6_7
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