The estimation of the IRT reliability coefficient and its lower and upper bounds, with comparisons to CTT reliability statistics

Asia Pacific Education Review

Volumn 11, Issue 2, 2010, Pages 179-188

  Kim, Seonghoon ^a   Feldt, Leonard S ^b  

^a Keimyung University   (South Korea)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Item response theory (IRT); Lower and upper bounds of reliability coefficient; Test reliability; Test score metric versus ability score metric

Indexed keywords

EID: 77952875413     PISSN: 15981037     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12564-009-9062-8     Document Type: Article

References (29)

1. 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.
2. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
3. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334.
4. Dimitrov, D. M. (2003). Marginal true-score measures and reliability for binary items as a function of their IRT parameters. Applied Psychological Measurement, 27, 440-458.
5. Feldt, L. S. (2002). Estimating the internal consistency reliability of tests composed of testlets varying in length. Applied Measurement in Education, 15, 33-48.
6. Feldt, L. S., & Brennan, R. L. (1989). Reliability. In R. L. Linn (Ed.), Educational measurement (3rd ed., pp. 105-146). New York: Macmillan.
7. Gilmer, J. S., & Feldt, L. S. (1983). Reliability estimation for a test with parts of unknown lengths. Psychometrika, 48, 99-111.
8. Gulliksen, H. (1950). Theory of mental tests. New York: Wiley.
9. Haertel, E. H. (2006). Reliability. In R. L. Brennan (Ed.), Educational measurement (4th ed., pp. 65-110). Westport, CT: American Council on Education and Praeger.
10. Harwell, M. R., & Baker, F. B. (1991). The use of prior distributions in marginalized Bayesian item parameter estimation: A didactic. Applied Psychological Measurement, 15, 375-389.
11. Harwell, M. R., Baker, F. B., & Zwarts, M. (1988). Item parameter estimation via marginal maximum likelihood and an EM algorithm: A didactic. Journal of Educational Statistics, 13, 243-271.
12. Holland, P. W., & Hoskens, M. (2003). Classical test theory as a first-order item response theory: Application to true-score prediction from a possibly nonparallel test. Psychometrika, 68, 123-149.
13. Kolen, M. J., & Brennan, R. L. (2004). Test equating, scaling, and linking: Methods and practices (2nd ed.). New York: Springer.
14. Kolen, M. J., Zeng, L., & Hanson, B. A. (1996). Conditional standard errors of measurement for scale scores using IRT. Journal of Educational Measurement, 33, 129-140.
15. Lord, F. M. (1980). Applications of item response theory to practical testing applications. Hillsdale, NJ: Lawrence Erlbaum.
16. May, K., & Nicewander, W. A. (1994). Reliability and information functions for percentile ranks. Journal of Educational Measurement, 31, 313-325.
17. Meredith, W. (1965). Some results based on a general stochastic model for mental tests. Psychometrika, 30, 419-440.
18. Mislevy, R. J. (1984). Estimating latent distributions. Psychometrika, 49, 359-381.
19. Mislevy, R. J. (1986). Bayes modal estimation in item response models. Psychometrika, 51, 177-195.
20. Mislevy, R. J., & Bock, R. D. (1990). BILOG 3: Item analysis and test scoring with binary logistic models (2nd ed.). Mooresville, IN: Scientific Software International.
21. Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159-176.
22. Muraki, E., & Bock, R. D. (2003). PARSCALE 4: IRT item analysis and test scoring for rating-scale data. Lincolnwood, IL: Scientific Software International.
23. Novick, M. R., & Lewis, C. (1967). Coefficient alpha and the reliability of composite measurements. Psychometrika, 32, 1-13.
24. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical recipes in C: The art of scientific computing (2nd ed.). New York, NY: Cambridge University Press.
25. Shojima, K., & Toyoda, H. (2002). Estimation of Cronbach's alpha coefficient in the context of item response theory. The Japanese Journal of Psychology, 73, 227-233. (In Japanese).
26. Thissen, D. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175-186.
27. Thissen, D., Pommerich, M., Billeaud, K., & Williams, V. S. L. (1995). Item response theory for scores on tests including polytomous items with ordered responses. Applied Psychological Measurement, 19, 39-49.
28. Tsutakawa, R. K., & Lin, H. Y. (1986). Bayesian estimation of item response curves. Psychometrika, 51, 251-267.
29. Woodruff, D. J., & Hanson, B. A. (1996). Estimation of item response models using the EM algorithm for finite mixtures. Iowa City, IA: ACT, Inc. (ACT Research Report 96-6).