Multiple person dimensions and latent item predictors

  • Frank Rijmen
  • Derek Briggs
Part of the Statistics for Social Science and Public Policy book series (SSBS)


In this chapter, we discuss two extensions to the item response models presented in the first two parts of this book: more than one random effect for persons (multidimensionality) and latent item predictors. We only consider models with random person weights (following a normal distribution), and with no inclusion of person predictors (except for the constant). The extensions can be applied in much the same way to the other models that were discussed in the first two parts of this book.


Item Response Theory Item Parameter Random Weight Discrimination Parameter Item Response Model 
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  1. Ackerman, T. (1992). A didactic explanation of item bias, item impact, and item validity from a multidimensional perspective. Journal of Educational Measurement, 29, 67–91.CrossRefGoogle Scholar
  2. Ackerman, T. (1994). Using multidimensional item response theory to understand what items and tests are measuring. Applied Measurement in Education, 7, 255–278.CrossRefGoogle Scholar
  3. Adams, R.J., Wilson, M., & Wang, W.-C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1–23.CrossRefGoogle Scholar
  4. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F.M. Lord & M.R. Novick (Eds). Statistical Theories of Mental Test Scores (pp. 397–479). Reading, MA: Addison-Wesley.Google Scholar
  5. Bock, R.D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of an EM-algorithm. Psychometrika, 46, 443–459.MathSciNetCrossRefGoogle Scholar
  6. Bock, R.D., Gibbons, R., & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12, 261–280.CrossRefGoogle Scholar
  7. Butter, R., De Boeck, P., & Verhelst, N. (1998). An item response model with internal restrictions on item difficulty. Psychometrika, 63, 47–63.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40, 5–22.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Embretson, S.E. (1991). A multidimensional latent trait model for measuring learning and change. Psychometrika, 56, 495–515.zbMATHCrossRefGoogle Scholar
  10. Fischer, G.H. (1973). Linear logistic test model as an instrument in educational research. Acta Psychologica, 37, 359–374.CrossRefGoogle Scholar
  11. Folk, V.G., & Green, B.F. (1989). Adaptive estimation when the unidimen-sionality assumption of IRT is violated. Applied Psychological Measurement, 13, 373–389.CrossRefGoogle Scholar
  12. Fraser, C., & McDonald, R. (1986). NOHARM II: A FORTRAN program for fitting unidimensional and multidimensional normal ogive models of latent trait theory. Armidale, NSW, Australia: University of New England.Google Scholar
  13. Kelderman, H. (1997). Loglinear multidimensional item response models for polytomously scored items. In W. van der Linden & R. Hambleton (Eds), Handbook of Modern Item Response Theory (pp. 287–304). New York: Springer.CrossRefGoogle Scholar
  14. Kelderman, H., & Rijkes, C.P.M. (1994). Loglinear multidimensional IRT models for polytomously scored items. Psychometrika, 59, 149–176.zbMATHCrossRefGoogle Scholar
  15. Knol, D. & Berger, M. (1991). Empirical comparison between factor analysis and multidimensional item response models. Multivariate Behavioral Research, 26, 457–477.CrossRefGoogle Scholar
  16. Kupermintz, H., Ennis, M.M., Hamilton, L.S., Talbert, J.E., & Snow, R.E. (1995). Enhancing the validity and usefulness of large-scale educational assessments.1. Nels-88 Mathematics Achievement. American Educational Research Journal, 32, 525–554.Google Scholar
  17. Luecht, R.M., & Miller, R. (1992). Unidimensional calibrations and interpretations of composite traits for multidimensional tests. Applied Psychological Measurement, 16, 279–293.CrossRefGoogle Scholar
  18. McDonald, R.R (1967). Nonlinear factor analysis. Psychometric Monographs, No. 15.Google Scholar
  19. McDonald, R.P. (1997). Normal-ogive multidimensional model. In W.J. van der Linden & R.K. Hambleton (Eds). Handbook of Modern Rem Response Theory (pp.257–269). New York: Springer.CrossRefGoogle Scholar
  20. McKinley, R.L. (1989). Confirmatory analysis of test structure using multidimensional item response theory. Research Report No. RR-89–31, Princeton, NJ: ETS.Google Scholar
  21. McKinley, R.L., & Reckase, M.D. (1983). MAXLOG: A computer program for the estimation of the parameters of a multidimensional logistic model. Behavior Research Methods and Instrumentation, 15, 389–390.CrossRefGoogle Scholar
  22. Muraki, E. & Carlson, J.E. (1995). Full-information factor analysis for polytomous item responses. Applied Psychological Measurement, 19, 73–90.CrossRefGoogle Scholar
  23. Muthén, B.O. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551–560.MathSciNetzbMATHCrossRefGoogle Scholar
  24. Reckase, M.D. (1997). A linear logistic multidimensional model for dichotomous item response data. In W. van der Linden & R. Hambleton (Eds), Handbook of Modern Rem Response Theory (pp. 271–286). New York: Springer.CrossRefGoogle Scholar
  25. Rijmen, F., & De Boeck, P. (2002). The random weights linear logistic test model. Applied Psychological Measurement, 26, 269–283.CrossRefGoogle Scholar
  26. Verbeke, G., & Molenberghs, G. (1997). Linear Mixed Models in Practice: A SAS-Oriented Approach. New York: Springer.zbMATHCrossRefGoogle Scholar
  27. Walker, C.M., & Beretvas, S.N. (2000). Using multidimensional versus unidimensional ability estimates to determine student proficiency in mathematics. Paper presented at the 2000 Annual Meeting of the American Educational Research Association, New Orleans, LA.Google Scholar
  28. Wang, W.-C., Wilson, M., & Adams, R.J. (1997). Rasch models for multidi-mensionality between items and within items. In M. Wilson, K. Draney, & G. Eglehard (Eds), Objective Measurement (Vol. 4,). Norwood, NY: Ablex.Google Scholar
  29. Wilson, D., Wood, R. & Gibbons, R. (1984). TESTFACT. Test Scoring, Item Statistics and Item Factor Analysis [Computer software and manual]. Mooreville, IN: Scientific Software.Google Scholar

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© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Frank Rijmen
  • Derek Briggs

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