A general Bayesian model for testlets: Theory and applications

Applied Psychological Measurement

Volumn 26, Issue 1, 2002, Pages 109-128

  Wang, Xiaohui ^a,d   Bradlow, Eric T ^b,d   Wainer, Howard ^c  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c NATIONAL BOARD OF MEDICAL EXAMINERS   (United States)

^d c/o Howard Wainer ^*  (United States)

Author keywords

Bayesian hierarchical model; Item response theory; Polytomously scored items

Indexed keywords

EID: 0036100904     PISSN: 01466216     EISSN: None     Source Type: Journal    
DOI: 10.1177/0146621602026001007     Document Type: Article

References (29)

1. Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669-679.
2. Baker, F. B. (1992). Item response theory. New York: Marcel-Dekker.
3. 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 (Chaps. 17-20). Reading, MA: Addison-Wesley.
4. Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more latent categories. Psychometrika, 37, 29-51.
5. Bradlow, E. T., Wainer, H., & Wang, X. (1999). A Bayesian random effects model for testlets. Psychometrika, 64, 153-168.
6. Bradlow, E. T., & Zaslavsky, A. M. (1999). A hierarchical latent variable model for ordinal data from a customer satisfaction survey with "no answer" responses. Journal of the American Statistical Association, 94(445), 43-52.
7. Braun, H., & Wainer, H. (1989). Making essay test scores fairer with statistics. In J. Tanur, F. Mosteller, W. H. Kruskal, E. L. Lehmann, R. F. Link, R. S. Peters, G. R. Rising (Eds.), Statistics: A guide to the unknown (3rd ed., pp. 178-187). San Francisco: Holden Day.
8. Drasgow, F., Levine, M. A., & Williams, E. A. (1985). Appropriateness measurement with polychotomous item response models and standardized indices. The British Journal of Mathematical Psychology, 38, 67-86.
9. Educational Testing Service. (1995). ITSE score user's manual. Princeton, NJ: Author.
10. Gelfand, A. E., & Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409.
11. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian data analysis. London: Chapman & Hall.
12. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 54, 93-108.
13. Levine, M. V., & Drasgow, F. (1988). Optimal appropriateness measurement. Psychometrika, 53, 161-176.
14. Lord, F. M. (1952). A theory of test scores. Psychometric Monographs, Whole No. 7.
15. Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
16. Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests. (Original work published 1960)
17. Roberts, G. O., & Smith, A.F.M. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B, 55, 3-23.
18. Rosa, K., Swygert, K., Nelson, L., & Thissen, D. (2000). Item response theory applied to combinations of multiple-choice and constructed response items - Scale scores for patterns of summed scores. In D. Thissen & H. Wainer (Eds.), Test scoring (Chap. 7). Hillsdale, NJ: Lawrence Erlbaum.
19. Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monographs, Whole No. 17.
20. Stout, W. F. (1987). A nonparametric approach for assessing latent trait dimensionality. Psychometrika, 52, 589-617.
21. Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 528-540.
22. Thissen, D. (1991). MULTILOG user's guide (Version 6). Mooresville, IN: Scientific Software.
23. Thissen, D., Steinberg, L., & Mooney, J. A. (1989). Trace lines for testlets: A use of multiple-categorical-response models. Journal of Educational Measurement, 26, 247-260.
24. Thissen, D., & Wainer, H. (2001). Test scoring. Hillsdale, NJ: Lawrence Erlbaum.
25. Wainer, H. (1995). Precision & differential item functioning on a testlet-based test: The 1991 Law School Admissions Test as an example. Applied Measurement in Education, 8(2), 157-187.
26. Wainer, H., Bradlow, E. T., & Du, Z. (2000). Testlet response theory. An analog for the 3-PL useful in testlet-based adaptive testing. In W. J. van der Linden & C.A.W. Glas (Eds.), Computerized adaptive testing: Theory and practice (pp. 245-270). Boston, MA: Kluwer-Nijhoff.
27. Wainer, H., Dorans, N., Eignor, D., Flaugher, R., Green, B., Mislevy, R., et al. (2000). Computerized adaptive testing: A primer (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.
28. Wainer, H., & Kiely, G. (1987). Item clusters and computerized adaptive testing: A case for testlets. Journal of Educational Measurement, 24, 185-202.
29. Zhang, J., & Stout, W. F. (1999). The theoretical DETECT index of dimensionality and its application to approximate simple structure. Psychometrika, 64, 213-249.