, Volume 58, Issue 1, pp 87–99 | Cite as

The partial credit model and null categories

  • Mark Wilson
  • Geofferey N. Masters


A category where the frequency of responses is zero, either for sampling or structural reasons, will be called anull category. One approach for ordered polytomous item response models is to downcode the categories (i.e., reduce the score of each category above the null category by one), thus altering the relationship between the substantive framework and the scoring scheme for items with null categories. It is discussed why this is often not a good idea, and a method for avoiding the problem is described for the partial credit model while maintaining the integrity of the original response framework. This solution is based on a simple reexpression of the basic parameters of the model.

Key words

sampling zero structural zero partial credit model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams, R. A., & Khoo, S. T. (1992).Quest [computer program]. Hawthorn, Australia: Australian Council for Educational Research.Google Scholar
  2. Andersen, E. B. (1972). The numerical solution of a set of conditional estimation equations.Journal of the Royal Statistical Society, Series B, 34, 42–50.Google Scholar
  3. Andersen, E. B. (1973). Conditional inference for multiple choice questionnaires.British Journal of Mathematical and Statistical Psychology, 26, 31–44.Google Scholar
  4. Andersen, E. B. (1977). Sufficient statistics and latent trait models.Psychometrika, 42, 69–81.Google Scholar
  5. Andersen, E. B. (1983). A general latent structure model for contingency table data. In, H. Wainer & S. Messick (Eds.),Principals of modern psychological measurement (pp. 117–138). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  6. Biggs, J. B., & Collis, K. F. (1982).Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.Google Scholar
  7. Fienberg, S. (1977).The analysis of cross-classified categorical data. Cambridge, MA: MIT Press.Google Scholar
  8. Fischer, G. H. (1974).Einführing in die theorie psychologischer tests [Introduction to the theory of psychological tests]. Berne: Huber Verlag.Google Scholar
  9. Fischer, G., & Parzer, P. (1991). An extension of the rating scale model with an application to the measurement of change.Psychometrika, 56, 637–652.Google Scholar
  10. Glas, C. A. W. (1989).Contributions to estimating and testing Rasch models. Unpublished doctoral dissertation, Twente University, Twente, The Netherlands.Google Scholar
  11. Glas, C. A. W. (1991, April).Testing Rasch models for polytomous items with an example concerning detection of item bias. Paper presented at the annual meeting of the American Educational Association, Chicago.Google Scholar
  12. Gustafsson, J. E. (1980). Testing and obtaining fit of data to the Rasch model.British Journal of Mathematical and Statistical Psychology, 33, 205–233.Google Scholar
  13. Jansen, P. G. W., & Roskam, E. E. (1986). Latent trait models and dichotomization of graded responses.Psychometrika, 51, 69–91.Google Scholar
  14. Masters, G. N. (1982). A Rasch model for partial credit scoring.Psychometrika, 47, 149–174.Google Scholar
  15. Masters, G. N., & Wright, B. D. (1984). The essential process in a family of measurement models.Psychometrika, 49, 529–544.Google Scholar
  16. Rasch, G. (1960).Probabilistic models for some intelligence and attainment tests. Copenhagen: Denmark's Paedagogistic Institut.Google Scholar
  17. Romberg, T. A., Collis, K. F., Donovan, B. F., Buchanan, A. E., & Romberg, M. N. (1982).The development of mathematical problem solving superitems (Report of NIE/EC Item Development Project). Madison, WI: Wisconsin Center for Education Research.Google Scholar
  18. Romberg, T. A., Jurdak, M. E., Collis, K. F., & Buchanan, A. E. (1982).Construct validity of a set of mathematical superitems (Report on NIE/ECS Item Development Project). Madison, WI: Wisconsin Center for Education Research.Google Scholar
  19. Webb, N. L., Day, R., & Romberg, T. A. (1988).Evaluation of the use of “Exploring Data” and “Exploring Probability”. Madison, WI: Wisconsin Center for Education Research.Google Scholar
  20. Wilson, M., & Adams, R. A. (in press). Marginal maximum likelihood estimation for the ordered partition model.Journal of Educational Statistics.Google Scholar
  21. Wright, B., Congdon, R., & Schultz, M. (1988).MSTEPS [computer program]. Chicago: University of Chicago, MESA Psychometrics Laboratory.Google Scholar
  22. Wright, B., & Masters, G. N. (1982).Rating scale analysis. Chicago: MESA Press.Google Scholar
  23. Wright, B., Masters, G. N., & Ludlow, L. H. (1982).CREDIT [computer program]. Chicago: MESA Press.Google Scholar

Copyright information

© The Psychometric Society 1993

Authors and Affiliations

  • Mark Wilson
    • 1
  • Geofferey N. Masters
    • 2
  1. 1.Graduate School of EducationUniversity of CaliforniaBerkeley
  2. 2.Australian Council for Educational ResearchAustralia

Personalised recommendations