Nonparametric Models for Dichotomous Responses

  • Robert J. Mokken
Chapter

Abstract

The development of nonparametric approaches to psychometric and sociometric measurement dates back to the days before the establishment of regular item response theory (IRT). It has its roots in the early manifestations of scalogram analysis (Guttman, 1950), latent structure analysis (Lazarsfeld, 1950), and latent trait theory (Lord, 1953).

Keywords

Item Response Theory Nonparametric Model Dichotomous Item Dichotomous Response Polytomous Item 
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References

  1. 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 (pp. 397–479 ). Reading, MA: Addison-Wesley.Google Scholar
  2. Debets, P., Sijtsma, K., Brouwer, E., and Molenaar, I.W. (1989). MSP: A computer program for item analysis according to a nonparametric IRT approach. Psychometrika 54, 534–536.Google Scholar
  3. Giampaglia, G. (1990). Lo Scaling Unidimensionale Nella Ricerca Sociale. Napoli: Liguori Editore.Google Scholar
  4. Gillespie, M., TenVergert, E.M., and Kingma, J. (1988). Secular trends in abortion attitudes: 1975–1980–1985. Journal of Psychology 122, 232–341.CrossRefGoogle Scholar
  5. Grayson, D.A. (1988). Two-group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika 53, 383–392.MathSciNetMATHCrossRefGoogle Scholar
  6. Guttman, L. (1950). The basis for scalogram analysis. In S.A. Stouffer et al. (Eds.), Measurement and Prediction (pp. 60–90 ). Princeton, NJ: Princeton University Press.Google Scholar
  7. Heinz, W. (1981). Klassifikation und Latente Struktur. Unpublished doctoral dissertation. Rheinischen Friedrich-Wilhelms-Universität, Bonn, Germany.Google Scholar
  8. Henning, H.J. (1976). Die Technik der Mokken-Skalenanalyse. Psychologische Beiträge 18, 410–430.Google Scholar
  9. Henning, H.J. and Six, B. (1977). Konstruktion einer MachiavellismusSkala. Zeitschrift für Sozial Psychologie 8, 185–198.Google Scholar
  10. Holland, P.W. and Rosenbaum, P.R. (1986). Conditional association and unidimensionality in monotone latent variable models. Annals of Statistics 14, 1523–1543.MathSciNetMATHCrossRefGoogle Scholar
  11. Karlin, S. (1968). Total Positivity I. Stanford, CA: Stanford University Press.MATHGoogle Scholar
  12. Lazarsfeld, P.F. (1950). The logical and mathematical foundation of latent structure analysis. In S.A. Stouffer et al. (Eds), Measurement and Prediction (pp. 362–412 ). Princeton, NJ: Princeton University Press.Google Scholar
  13. Lewis, C. (1983). Bayesian inference for latent abilities. In S.B. Anderson and J.S. Helmick (Eds.), On Educational Testing (pp. 224–251 ). San Francisco: Jossey-Bass.Google Scholar
  14. Lippert, E., Schneider, P., and Wakenhut, R. (1978). Die Verwendung der Skalierungsverfahren von Mokken und Rasch zur Überprüfung und Revision von Einstellungsskalen. Diagnostica 24, 252–274.Google Scholar
  15. Loevinger, J. (1947). A systematic approach to the construction and evaluation of tests of ability. Psychological Monographs 61, No. 4.Google Scholar
  16. Loevinger, J. (1948). The technic of homogeneous tests compared with some aspects of “scale analysis” and factor analysis. Psychological Bulletin 45, 507–530.CrossRefGoogle Scholar
  17. Lord, F.M. (1953). An application of confidence intervals and of maximum likelihood to the estimation of an examinee’s ability. Psychometrika 18, 57–77.MATHCrossRefGoogle Scholar
  18. Lord, F.M. and Novick, M.R. (1968). Statistical Theories of Mental Test Scores. Reading, MA: Addison-Wesley.MATHGoogle Scholar
  19. Meijer, R.R. and Sijtsma, K. (1993). Reliability of item scores and its use in person fit research. In R. Steyer, K.F. Wender, and K.F. Widaman (Eds.), Psychometric Methodology: Proceedings of the 7th European Meeting of the Psychometric Society (pp. 326–332 ). Stuttgart, Germany: Gustav Fischer Verlag.Google Scholar
  20. Meijer, R.R., Sijtsma, K., and Smid, N.G. (1990). Theoretical and empirical comparison of the Mokken and the Rasch approach to IRT. Applied Psychological Measurement 11, 283–298.CrossRefGoogle Scholar
  21. Mokken, R.J. (1971). A Theory and Procedure of Scale Analysis with Applications in Political Research. New York, Berlin: Walter de Gruyter, Mouton.CrossRefGoogle Scholar
  22. Mokken, R.J. and Lewis, C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement 6, 417–430.CrossRefGoogle Scholar
  23. Molenaar, I.W., Debets, P., Sijtsma, K., and Hemker, B.T. (1994). MSP, A Program for Mokken Scale Analysis for Polytomous Items, Version 3.0, (User’s Manual). Groningen, The Netherlands: iec ProGAMMA.Google Scholar
  24. Niemöller, B. and van Schuur, W.H. (1980). Stochastic Cumulative Scaling. STAP User’s Manual, Vol. 4. Amsterdam, The Netherlands: Technisch Centrum FSW, University of Amsterdam.Google Scholar
  25. Niemöller, B. and van Schuur, W.H. (1983). Stochastic models for unidimensional scaling: Mokken and Rasch. In D. McKay, N. Schofield, and P. Whiteley (Eds.), Data Analysis and the Social Sciences (pp. 120–170 ). London: Francis Pinter.Google Scholar
  26. Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen: Nielsen and Lydiche.Google Scholar
  27. Rosenbaum, P.R. (1984). Testing the conditional independence and mono-tonicity assumptions of item response theory. Psychometrika 49, 425–435.MathSciNetMATHCrossRefGoogle Scholar
  28. Rosenbaum, P.R. (1987a). Probability inequalities for latent scales. British Journal of Mathematical and Statistical Psychology 40, 157–168.MathSciNetMATHCrossRefGoogle Scholar
  29. Rosenbaum, P.R. (1987b). Comparing item characteristic curves. Psychometrika 52, 217–233.MathSciNetMATHCrossRefGoogle Scholar
  30. Schriever, B.F. (1985). Order Dependence. Unpublished doctoral dissertation, Free University. Amsterdam, The Netherlands.Google Scholar
  31. Sijtsma, K. (1988). Contributions to Mokken’s Nonparametric Item Response Theory. Unpublished doctoral dissertation, Free University, Amsterdam, The Netherlands.Google Scholar
  32. Sijtsma, K. and Molenaar, I.W. (1987). Reliability of test scores in non-parametric item response theory. Psychometrika 52, 79–97.MathSciNetMATHCrossRefGoogle Scholar
  33. Sijtsma, K. and Meijer, R.R. (1992). A method for investigating the intersection of item response functions in Mokken’s nonparametric IRT model. Applied Psychological Measurement 16, 149–157.CrossRefGoogle Scholar
  34. Stouffer, S.A., Guttman, L., Suchman, E.A., Lazarsfeld, P.F., Star, S.A., and Clausen, J.A. (1950). Measurement and Prediction. Studies in Social Psychology in World War II, vol. IV. Princeton, NJ: Princeton University Press.Google Scholar

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© Springer Science+Business Media New York 1997

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  • Robert J. Mokken

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