Stochastic order in dichotomous item response models for fixed, adaptive, and multidimensional tests

Psychometrika

Volumn 63, Issue 3, 1998, Pages 211-226

  Van Der Linden, Wim J ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Classical test theory; Computerize adaptive testing (CAT)multidimensional tests; Item response theory (IRT); Stochastic order

Indexed keywords

EID: 0032336770     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02294852     Document Type: Article

References (42)

1. Ahmed, A. N., León, R., & Proschan, F. (1981). Generalized association, with applications in multivariate statistics. Annals of Statistics, 9, 168-176.
2. Apostol, T. M. (1967). One-variable calculus, with an introduction to linear algebra (Vol. 1). New York, NY: Wiley.
3. Casella, G., & Berger, R. L. (1990). Statistical inference. Pacific Grove, CA: Wadsworth & Brooks/Cole.
4. Chuan, D. T., Chen, J. J., & Novick, M. R. (1981). Theory and practice for the use of cut-scores for personnel decisions. Journal of Educational Statistics, 6, 129-152.
5. Ellis, J. L. (1993). Subpopulation invariance of patterns in covariance matrices. British Journal of Mathematical and Statistical Psychology, 46, 231-254.
6. Ellis, J. L., & van den Wollenberg, A. L. (1993). Local homogeneity in latent trait models: A characterization of the homogenous monotone IRT model. Psychometrika, 58, 417-429.
7. Esary, J. D., Proschan, F., & Walkup, D. W. (1967). Association of random variables, with applications. Annals of Mathematical Statistics, 38, 1466-1474.
8. Fischer, G. H. & Molenaar, I. W. (Eds.) (1995). Rasch models: Foundations, recent developments, and applications. New York City, NY: Springer-Verlag.
9. Glas, C. A. W. (1992). A Rasch model with a multivariate distribution of ability. In M. Wilson (Ed.), Objective measurement: Theory into practice (Vol. 1). Norwood, NJ: Ablex.
10. Grayson, D. A. (1988). Two-group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika, 53, 283-292.
11. Hambleton, R. K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston, MA: Kluwer-Nijhoff Publishing.
12. 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.
13. 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.
14. Holland, P. W. (1981). When are item response models consistent with observed data? Psychometrika, 46, 79-92.
15. Holland, P. W. (1990). On the sampling theory foundations of item response theory models. Psychometrika, 55, 577-601.
16. Holland, P. W., & Rosenbaum, P. R. (1986). Conditional association and unidimensionality in monotone latent variable models. Annals of Statistics, 14, 1523-1543.
17. Huynh, H. (1994). A new proof for monotone likelihood ratio for the sum of independent Bernoulli random variables. Psychometrika, 59, 77-79.
18. Junker, B. W. (1991). Essential independence and likelihood-based ability estimations for polytomous items. Psychometrika, 56, 255-278.
19. Junker, B. W. (1993). Conditional association, essential independence, and monotone unidimensional item response models. Annals of Statistics, 21, 1359-1378.
20. Kelley, T. L. (1939). The selection of upper and lower groups for the validation of test items. Journal of Educational Psychology, 30, 17-24.
21. Lehmann, E. L. (1986). Testing statistical hypotheses (2nd ed.). New York, NY: Wiley.
22. Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
23. Mislevy, R. J., & Wu, P.-K. (1988). Inferring examinee ability when some item responses are missing (Research Report 88-8). Princeton, NJ: Educational Testing Service.
24. Mokken, R. J. (1971). A theory and procedure of scale analysis. Den Haag, The Netherlands: Mouton.
25. Mokken, R. J. (1997). Nonparametric models for dichotomous responses. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 351-368). New York, NY: Springer-Verlag.
26. Mokken, R. J., & Lewis, C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6, 417-430.
27. Molenaar, W. (1997). Nonparametric models for polytomous responses. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 369-380). New York, NY: Springer-Verlag.
28. Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611-630.
29. Ramsay, J. O. (1997). A functional approach to modeling test data. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 381-394). New York, NY: Springer-Verlag.
30. Reckase, M. D. (1997). A linear logistic multidimensional model for dichotomous item response data. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 271-286). New York, NY: Springer-Verlag.
31. Rosenbaum, P. R. (1984). Testing the conditional independence and monotonicity assumptions of item response theory. Psychometrika, 49, 425-435.
32. Rosenbaum, P. R. (1985). Comparing distributions of item responses for two groups. British Journal of Mathematical and Statistical Psychology, 38, 206-215.
33. Stout, W. F. (1987). A nonparametric approach for assessing latent trait unidimensionality. Psychometrika, 52, 589-617.
34. Stout, W. F. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 55, 293-325.
35. Sijtsma, K. (1988). Contributions to Mokken's nonparametric item response theory. Unpublished doctoral dissertation, University of Groningen, The Netherlands.
36. Sijtsma, K., & Junker, B. W. (1994). A survey of theory and methods of invariant item ordering (Methods Series MS-94-4). Utrecht, The Netherlands: Department of Methodology and Statistics, Faculty of Social Sciences, Utrecht University.
37. Sijtsma, K., & Meijer, R. R. (1992). A method for investigating the intersection of item response functions in Mokken's nonparametric IRT model. Applied Psychological Measurement, 16, 149-158.
38. Stout, W. F. (1987). A nonparametric approach for assessing latent trait unidimensionality. Psychometrika, 52, 589-617.
39. Stout, W. F. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 55, 293-325.
40. Tsutakawa, R. K., & Johnson, J. C. (1990). The effect of uncertainty of item parameter estimation on ability estimates. Psychometrika, 55, 371-390.
41. van der Linden, W. J. (1998). A decision theory model for course placement. Journal of Educational and Behavioral Statistics, 23, 18-34.
42. van der Linden, W. J., & Vos, H. J. (1996). A compensatory approach to optimal selection with mastery scores. Psychometrika, 61, 155-172.