A comparison of item-fit statistics for the three-parameter logistic model

Applied Psychological Measurement

Volumn 27, Issue 2, 2003, Pages 87-106

  Glas, Cees A W ^a   Falcón, Juan Carlos Suárez ^b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b UNIVERSIDAD NACIONAL DE EDUCACIÓN A DISTANCIA   (Spain)

Author keywords

Chi square distribution; Efficient score test; Goodness of fit; Item fit; Item response theory (item fit); Lagrange multiplier test; Modification indices; Power studies; Three parameter logistic model; Type I error

Indexed keywords

EID: 0037238031     PISSN: 01466216     EISSN: None     Source Type: Journal    
DOI: 10.1177/0146621602250530     Document Type: Article

References (26)

1. Aitchison, J., & Silvey, S. D. (1958). Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, 813-828.
2. Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975). Discrete multivariate analysis: Theory and practice, Cambridge, MA: MIT Press.
3. Bock, R. D., & Mislevy, R. J. (1982). Adaptive EAP estimation of ability in a microcomputer environment. Applied Psychological Measurement, 6, 431-444.
4. Cressie, N., & Holland, P. W. (1983). Characterizing the manifest probabilities of latent trait models. Psychometrika, 48, 129-141.
5. Efron, B. (1977). Discussion on maximum likelihood from incomplete data via the EM algorithm (by A. Dempster, N. Liard, and D. Rubin). Journal of the Royal Statistical Society, Series B, 39, 1-38.
6. Glas, C. A. W. (1988). The derivation of some tests for the Rasch model from the multinomial distribution. Psychometrika, 53, 525-546.
7. Glas, C. A. W. (1998) Detection of differential item functioning using Lagrange multiplier tests. Statistica Sinica, 8(1), 647-667.
8. Glas, C. A. W. (1999). Modification indices for the 2-pl and the nominal response model. Psychometrika, 64, 273-294.
9. Glas, C. A. W. (2001). Differential item functioning depending on general covariates. In A. Boomsma, M. A. J. van Duijn, & T. A. B. Snijders (Eds.), Essays on item response theory (pp.131-148). New York: Springer.
10. Glas, C. A. W., & Verhelst, N. D. (1989). Extensions of the partial credit model. Psychometrika, 54, 635-659.
11. Glas, C. A. W., & Verhelst, N. D. (1995). Testing the Rasch model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments and applications (pp. 69-96). New York: Springer.
12. Jannarone, R. J. (1986). Conjunctive item response theory kernels. Psychometrika, 51, 357-373.
13. Jansen, M. G. H., & Glas, C. A. W. (2001). Statistical tests for differential test functioning in Rasch's model for speed tests. In A. Boomsma, M. A. J. van Duijn, & T. A. B. Snijders (Eds.), Essays on item response theory (pp. 149-162). New York: Springer.
14. Kelderman, H. (1984). Loglinear Rasch model tests, Psychometrika, 49, 223-245.
15. Lord, F. M., & Wingersky, M. S. (1984). Comparison of IRT true-score and equipercentile observed-score "equatings." Applied Psychological Measurement, 8, 453-461.
16. Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226-233.
17. McKinley, R., & Mills, C. (1985). A comparison of several goodness-of-fit statistics. Applied Psychological Measurement, 9, 49-57.
18. Mislevy, R. J. (1986). Bayes modal estimation in item response models. Psychometrika, 51, 177-195.
19. Mislevy, R. J., & Bock, R. D. (1990). PC-BILOG. Item analysis and test scoring with binary logistic models. Mooresville, IN: Scientific Software.
20. Orlando, M., & Thissen, D. (2000). Likelihood-based item-fit indices for dichotomous item response theory models. Applied Psychological Measurement, 24, 50-64.
21. Rao, C. R. (1947). Large sample tests of statistical hypothesis concerning several parameters with applications to problems of estimation. Proceedings of the Cambridge Philosophical Society, 44, 50-57.
22. van den Wollenberg, A. L. (1982). Two new tests for the Rasch model. Psychometrika, 47, 123-140.
23. Yen, W. M. (1981). Using simultaneous results to choose a latent trait model. Applied Psychological Measurement, 5, 245-262.
24. Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8, 125-145.
25. Yen, W. M. (1993). Scaling performance assessments: Strategies for managing local item dependence. Journal of Educational Measurement, 30, 187-213.
26. Zimowski, M. F., Muraki, E., Mislevy, R. J., & Bock, R. D. ( 1996). Bilog MG: Multiple-group IRT analysis and test maintenance for binary items. Chicago: Scientific Software International.