Abstract
A generalized partial credit model (GPCM) was formulated by Muraki (1992) based on Masters’ (1982, this volume) partial credit model (PCM) by relaxing the assumption of uniform discriminating power of test items. However, the difference between these models is not only the parameterization of item characteristics but also the basic assumption about the latent variable. An item response model is viewed here as a member of a family of latent variable models which also includes the linear or nonlinear factor analysis model, the latent class model, and the latent profile model (Bartholomew, 1987).
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References
Andersen, E.B. (1973). Conditional inference for multiple-choice questionnaires. British Journal of Mathematical and Statistical Psychology 26, 31–44.
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika 43, 561–573.
Bartholomew, D.J. (1987). Latent Variable Models and Factor Analysis. London: Charles Griffin and Company.
Beaton, A.E. and Zwick, R. (1992). Overview of the national assessment of educational progress. Journal of Educational Statistics 17, 95–109.
Bock, R.D. and Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika 41, 443–459.
Bock, R.D. and Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika 35, 179–197.
Bock, R.D. and Mislevy, R.J. (1982). Adaptive EAP estimation of ability in a microcomputer environment. Applied Psychological Measurement 6, 431–444.
Chang, H. and Mazzeo, J. (1944). The unique correspondence of item response function and item category response functions in polytomously scored item response models. Psychometrika 59, 391–404.
Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B 39, 1-38.
Fisher, G.H. and Parzer, P. (1991). An extension of the rating scale model with an application to the measurement of change. Psychometrika 56, 637–651.
Grima, A.M. and Johnson, E.G. (1992). Data analysis for the writing assessment. In E.G. Johnson and N.L. Allen (Eds.), The NAEP 1990 Technical Report. Princeton, NJ: Educational Testing Service.
Kendall, M.G. and Stuart, A. (1973). The Advanced Theory of Statistics, vol. 2. New York, NY: Hafner Publishing Company.
Lord, F.M. (1980). Application of Item Response Theory to Practical Testing Problems. Hillsdale, NJ: Erlbaum.
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika 47, 149–174.
Mislevy, R.J. and Bock, R.D. (1990). BILOG 3: Item Analysis and Test Scoring with Binary Logistic Models [Computer program]. Chicago, IL: Scientific Software, Inc.
Muraki, E. (1990). Fitting a polytomous item response model to Likerttype data. Applied Psychological Measurement 14, 59–71.
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement 16, 159–176.
Muraki, E. (1993). Information functions of the generalized partial credit model. Applied Psychological Measurement 17, 351–363.
Muraki, E. and Bock, R.D. (1991). PARSCALE: Parameter Scaling of Rat- ing Data [Computer program]. Chicago, IL: Scientific Software, Inc.
Muraki, E. and Wang, M. (1992). Issues Relating to the marginal maximum likelihood estimation of the partial credit model. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA.
Neyman, J. and Scott, E.L. (1948). Consistent estimates based on partially consistent observations. Econometrika 16, 1 -32.
Samejima, F. (1969). Estimating of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, No. 17.
Stroud, A.H. and Secrest, D. (1966). Gaussian Quadrature Formulas. Englewood Cliffs, NJ: Prentice Hall.
Wright, B.D. and Masters, G. (1982). Rating Scale Analysis. Chicago, IL: MESA Press.
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Muraki, E. (1997). A Generalized 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_9
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DOI: https://doi.org/10.1007/978-1-4757-2691-6_9
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