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Abstract

The Partial Credit Model (PCM) is a unidimensional model for the analysis of responses recorded in two or more ordered categories. In this sense, the model is designed for the same purpose as several other models in this book, including Samejima’s graded response model (Samejima, 1969). The PCM differs from the graded response model, however, in that it belongs to the Rasch family of models and so shares the distinguishing characteristics of that family: separable person and item parameters, sufficient statistics, and, hence, conjoint additivity. These features enable “specifically objective” comparisons of persons and items (Rasch, 1977) and allow each set of model parameters to be conditioned out of the estimation procedure for the other.

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References

  • Adams, R.J. (1988). Applying the PCM to educational diagnosis. Applied Measurement in Education 4, 347–362.

    Article  Google Scholar 

  • Adams, R.J., Doig, B.A., and Rosier, M.R. (1991). Science Learning in Victorian Schools: 1990 (Monograph 41 ). Melbourne, Victoria: Australian Council for Educational Research.

    Google Scholar 

  • Adams, R.J., Griffin, P.E., and Martin, L. (1987). A latent trait method for measuring a dimension in second language proficiency. Language Testing 4, 9–27.

    Article  Google Scholar 

  • Adams, R.J. and Khoo, S.T. (1992). QUEST: The Interactive Test Analysis System. Melbourne, Victoria: Australian Council for Educational Research.

    Google Scholar 

  • Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika 43, 561-–573.

    Google Scholar 

  • Bock, R.D. and Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika 46, 443–459.

    Article  MathSciNet  Google Scholar 

  • Doig, B.A., Mellor, S., Piper, K., and Masters, G.N. (1994). Conceptual Understanding in Social Education. Melbourne, Victoria: Australian Council for Educational Research.

    Google Scholar 

  • Edwards, A.L. and Thurstone, L.L. (1952). An internal consistency check for scale values determined by the method of successive intervals. Psychometrika 17, 169-–180.

    Google Scholar 

  • Glas, C.A.W. (1988). The derivation of some tests for the Rasch model

    Google Scholar 

  • from the multinomial distribution. Psychometrika 53 525–546.

    Google Scholar 

  • Glas, C.A.W. and Verhelst, N.D. (1989). Extensions of the PCM. Psychometrika 53, 525–-546.

    Google Scholar 

  • Guthke, J., Wolschke, P., Willmes, K., and Huber, W. (1992). Leipziger Lerntest - Diagnostisches Programm zum begriffsanalogen Klassifizieren (DP-BAK). Aufbau und Konstruktionseigenschaften. Heilpaedagogische Forschung 18, 153–161.

    Google Scholar 

  • Harris, J. Laan, S., and Mossenson, L.T. (1988). Applying partial credit analysis to the construction of narrative writing tests. Applied Measurement in Education 4, 335–346.

    Google Scholar 

  • Julian, E.R. and Wright, B.D. (1988). Using computerized patient simulations to measure the clinical competence of physicians. Applied Measurement in Education 4, 299–318.

    Article  Google Scholar 

  • Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika 49, 223–245.

    Article  MATH  Google Scholar 

  • Koch, W.R. and Dodd, B.G. (1989). An investigation of procedures for computerized adaptive testing using partial credit scoring. Applied Measurement in Education 2, 335-–357.

    Google Scholar 

  • Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika 47, 149–174.

    Article  MATH  Google Scholar 

  • Masters, G.N. (1984). Constructing an item bank using partial credit scoring. Journal of Educational Measurement 21, 19–32.

    Article  Google Scholar 

  • Masters, G.N. (1985). A comparison of latent trait and latent class analyses of Likert-type data. Psychometrika 50, 69–82.

    Article  Google Scholar 

  • Masters, G.N. (1987). Measurement models for ordered response categories. In R. Langeheine and J. Rost (Eds.). Latent Trait and Latent Class Models (pp. 11–29 ). New York: Plenum Publishing Corporation.

    Google Scholar 

  • Masters, G.N. (1988a), Partial credit models. In J.P. Keeves (Ed.). Educational Research Methodology, Measurement and Evaluation (pp. 292296 ). Oxford: Pergamon Press.

    Google Scholar 

  • Masters, G.N. (1988b). The analysis of partial credit scoring. Applied Measurement in Education 1, 279–298.

    Article  Google Scholar 

  • Masters, G.N. and Evans, J. (1986). Banking non-dichotomously scored items. Applied Psychological Measurement 10, 355–367.

    Article  Google Scholar 

  • Masters, G.N. and Mislevy, R. (1993). New views of student learning: Implications for educational measurement. In N. Frederiksen, R.J. Mislevy, and I.I. Begar (Eds.). Test Theory for a New Generation of Tests (pp. 219–242 ). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Masters, G.N. and Wright, B.D. (1982). Defining a fear-of-crime variable: A comparison of two Rasch models. Education Research and Perspectives 9, 18–32.

    Google Scholar 

  • Masters, G.N. and Wright, B.D. (1984). The essential process in a family of measurement models. Psychometrika 49, 529–544.

    Article  Google Scholar 

  • Molenaar, I W (1983). Some improved diagnostics for failure of the Rasch model. Psychometrika 48, 49–73.

    Article  Google Scholar 

  • Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement 16, 159–176.

    Article  Google Scholar 

  • Pennings, A. (1987). The Diagnostic Embedded Figures Test. Paper presented at the Second Conference on Learning and Instruction of the European Association of Learning and Instruction, University of Tübingen.

    Google Scholar 

  • Pollitt, A. and Hutchinson, C. (1987). Calibrating graded assessments: Rasch partial credit analysis of performance in writing. Language Testing 4, 72–92.

    Article  Google Scholar 

  • Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen: Denmarks Paedagogiske Institut.

    Google Scholar 

  • Rasch, G. (1977). On specific objectivity: An attempt at formalizing the request for generality and validity of scientific statements. Danish Yearbook of Philosophy 14, 58–94.

    Google Scholar 

  • Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika, Monograph Supplement No. 17.

    Google Scholar 

  • Thurstone, L.L. (1931). Measurement of social attitudes. Journal of Abnormal and Social Psychology 26, 249–-269.

    Google Scholar 

  • Titmanis, P., Murphy, F., Cook, J., Brady, K., and Brown, M. (1993). Profiles of Student Achievement: English and Mathematics in Western Australian Government Schools, 1992. Perth: Ministry of Education.

    Google Scholar 

  • Van den Wollenberg, A.L. (1982). Two new test statistics for the Rasch model. Psychometrika 47, 123–140.

    Article  MATH  Google Scholar 

  • Willmes, K. (1992). Psychometric evaluation of neuropsychological test performances. In N. von Steinbuechel, D.Y. von Cramon, and E. Poeppel (Eds.) Neuropsychological Rehabilitation (pp. 103–113 ). Heidelberg: Springer-Verlag.

    Chapter  Google Scholar 

  • Wilson, M.R. (1992). The ordered partition model: An extension of the PCM. Applied Psychological Measurement 16, 309–325.

    Article  Google Scholar 

  • Wilson, M.R. and Adams, R.J. (1993). Marginal maximum likelihood estimation for the partial order model. Journal of Educational Statistics 18, 69–90.

    Article  Google Scholar 

  • Wilson, M. and Iventosch, L. (1988). Using the PCM to investigate responses to structured subtests. Applied Measurement in Education 1, 319–334.

    Article  Google Scholar 

  • Wilson, M. and Masters, G.N. (1993). The PCM and null categories. Psychometrika 58, 87–99.

    Article  Google Scholar 

  • Wright, B.D. and Linacre, J.M. (1992). BIGSTEPS Rasch Analysis Computer Program. Chicago: MESA Press.

    Google Scholar 

  • Wright, B.D. and Masters, G.N. (1982). Rating Scale Analysis. Chicago: MESA Press.

    Google Scholar 

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© 1997 Springer Science+Business Media New York

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Masters, G.N., Wright, B.D. (1997). The Partial Credit Model. 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_6

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  • DOI: https://doi.org/10.1007/978-1-4757-2691-6_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2849-8

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