Some remarks on Scheiblechner's treatment of ISOP models

Psychometrika

Volumn 63, Issue 1, 1998, Pages 73-85

  Junker, Brian W ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Comonotonicity; Covariances given a sum; Isotonic ordinal probabilistic models; Item response theory foundations; Manifest monotonicity; Stochastic ordering; Strict unidimensionality

Indexed keywords

EID: 0032351484     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02295438     Document Type: Article

References (35)

1. Andrich, D. (1995). Distinctive and incompatible properties of two common classes of IRT models for graded responses. Applied Psychological Measurement, 19, 101-119.
2. Bartholomew, D. J. (1987). Latent variable models and factor analysis. New York: Oxford University Press.
3. Clarke, B. S., & Ghosh, J. K. (1991). Posterior convergence given the mean (Tech. Rep. No. 91-51). West Lafayette, IN: Purdue University, Department of Statistics.
4. Clarke, B. S., & Ghosh, J. K. (1995). Posterior convergence given the mean. Annals of Statistics, 23, 2116-2144.
5. Ellis, J. L., & Junker, B. W. (in press). Tail-measurability in monotone latent variable models. Psychometrika.
6. Ellis, J. L., & van den Wollenberg, A. L. (1993). Local homogeneity in latent trait models. A characterization of the homogeneous monotone IRT model. Psychometrika, 58, 417-429.
7. Fischer, G. H. (1995). Derivations of the Rasch model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 15-38). New York: Springer-Verlag.
8. Grayson, D. A. (1988). Two-group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika, 53, 383-392.
9. Hemker, B. T., Sijtsma K., Molenaar, I. W., & Junker, B. W. (1996). Polytomous IRT models and monotone likelihood ratio of the total score. Psychometrika, 61, 679-693.
10. Hemker, B. T., Sijtsma, K., Molenaar, I. W., & Junker, B. W. (1997). Stochastic ordering using the latent trait and the sum score in polytomous IRT models. Psychometrika, 62, 331-347.
11. Holland, P. W. (1990). On the sampling theory foundations of item response theory models. Psychometrika, 55, 577-601.
12. Holland, P. W., & Rosenbaum, P. R. (1986). Conditional association and unidimensionality in monotone latent trait models. Annals of Statistics, 14, 1523-1543.
13. Huynh, H. (1994). A new proof for monotone likelihood ratio for the sum of independent bernoulli random variables. Psychometrika, 59, 77-79.
14. Jansen, P. G., & Roskam, E. E. (1986). Latent trait models and dichotomization of graded responses. Psychometrika, 51, 69-91.
15. Junker, B. W. (1990). Progress in characterizing strictly unidimensional IRT representations (Office of Naval Research Tech. Rep., Contract No. N00014-90-J-1984, and CMU Statistics Department Tech. Rep. No. 498). Washington, DC: Office of Naval Research.
16. Junker, B. W. (1991). Essential independence and likelihood-based ability estimation for polytomous items. Psychometrika, 56, 255-278.
17. Junker, B. W. (1993). Conditional association, essential independence and monotone unidimensional item response models. The Annals of Statistics, 21, 1359-1378.
18. Junker, B. W. (1994, November). A view of nonparametric item response theory. Invited presentation to the 10th Annual Workshop on Item Response Theory. Enschede, The Netherlands: University of Twente.
19. Junker, B. W., & Ellis, J. L. (1997). A characterization of monotone unidimensional latent variable models. Annals of Statistics, 25, 1327-1343.
20. Junker, B. W., & Sijtsma, K. (1997). Latent and manifest monotonicity in item response models. Submitted for publication.
21. Messick, S. (1989). Validity. In R. L. Linn (Ed.), Educational Measurement (3rd ed., pp. 13-103). New York: American Council on Education and Macmillan Publishing Company.
22. Mokken, R. J. (1971). A theory and procedure of scale analysis. The Hague: Mouton.
23. Mokken, R. J., & Lewis, C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6, 417-430.
24. Molenaar, I. W. (1991). A weighted Loevinger H-coefficient extending Mokken scaling to multicategory items. Kwantitatieve Methoden, 37, 97-117.
25. Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests (Expanded edition). Chicago, IL: University of Chicago Press.
26. Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611-630.
27. Rosenbaum, P. R. (1987a). Probability inequalities for latent scales. British Journal of Mathematical and Statistical Psychology, 40, 157-168.
28. Rosenbaum, P. R. (1987b). Comparing item characteristic curves. Psychometrika, 52, 217-233.
29. Samejima, F. (1969). Estimation of latent trait ability using a pattern of graded scores. Psychometrika, Monograph Supplement No. 17, 34 (4, Pt. 2).
30. Samejima, F. (1972). A general model for free-response data. Psychometrika, Monograph Supplement No. 18, 37 (1, Pt. 2).
31. Scheiblechner, H. (1995). Isotonic ordinal probabilistic models (ISOP). Psychometrika, 60, 281-304.
32. Sijtsma, K. (1988). Contributions to Mokken's nonparametric item response theory. Amsterdam: Free University Press.
33. Sijtsma, K., & Hemker, B. T. (in press). Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models. Psychometrika.
34. Sijtsma, K., & Junker, B. W. (1996). A survey of theory and methods of invariant item ordering. British Journal of Mathematical and Statistical Psychology, 49, 79-105.
35. Stout, W. F. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 55, 293-325.