USE OF GENERALIZED RESIDUALS TO EXAMINE GOODNESS OF FIT OF ITEM RESPONSE MODELS

ETS Research Report Series

Volumn 2009, Issue 1, 2009, Pages i-17

  Haberman, Shelby J ^a  

^a EDUCATIONAL TESTING SERVICE   (United States)

Author keywords

conditional estimation; contingency tables; marginal distributions; marginal estimation; normal approximations; rasch model; two parameter logistic model

Indexed keywords

EID: 85150977009     PISSN: None     EISSN: 23308516     Source Type: Journal    
DOI: 10.1002/j.2333-8504.2009.tb02172.x     Document Type: Article

References (19)

1. Andersen, E. B. (1970). Asymptotic properties of conditional maximum-likelihood estimators. Journal of the Royal Statistical Society, Series B, 32, 283–301.
2. Andersen, E. B. (1972). The numerical solution of a set of conditional estimation equations. Journal of the Royal Statistical Society, Series B, 34, 42–54.
3. Armitage, P. (1955). Tests for linear trends in proportions and frequencies. Biometrics, 11, 375–386.
4. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an em algorithm. Psychometrika, 46, 443–459.
5. 2 tests. Biometrics, 10, 417–451.
6. Cochran, W. G. (1955). A test of a linear function of the deviations between observed and expected numbers. Journal of the American Statistical Association, 50, 377–397.
7. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1–38.
8. Glas, C. A. W., & Verhelst, N. D. (1989). Extensions of the partial credit model. Psychometrika, 54, 635–659.
9. 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. 69–95). New York: Springer.
10. Haberman, S. J. (1976). Generalized residuals for log-linear models. In Proceedings of the ninth International Biometrics Conference (Vol. 1, pp. 104–172). Raleigh, NC: Biometrics Society.
11. Haberman, S. J. (1978). Analysis of qualitative data: Vol. 1. Introductory topics. New York: Academic Press.
12. Haberman, S. J. (1979). Analysis of qualitative data: Vol. 2. New developments. New York: Academic Press.
13. Haberman, S. J. (2004). Maximum likelihood for the Rasch model for binary responses (ETS Research Rep. No. RR-04-20). Princeton, NJ: ETS.
14. Haberman, S. J. (2005). Latent-class item response models (ETS Research Rep. No. RR-05-28). Princeton, NJ: ETS.
15. Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park, CA: Sage.
16. Mantel, N., & Haenszel, W. (1959). Statistical aspects of the analysis of data from retrospective studies. Journal of the National Cancer Institute, 22, 719–748.
17. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.
18. Tjur, T. (1982). A connection between Rasch's item analysis model and a multiplicative Poisson model. Scandinavian Journal of Statistics, 9, 23–30.
19. Yates, F. (1948). The analysis of contingency tables with groupings based on quantitative characters. Biometrika, 35, 176–181.