Nonparametric item response function estimates with the EM algorithm

Journal of Educational and Behavioral Statistics

Volumn 27, Issue 3, 2002, Pages 291-317

  Rossi, Natasha ^a   Wang, Xiaohui ^b   Ramsay, James O ^a  

^a MCGILL UNIVERSITY   (Canada)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

Differential geometry; Functional data analysis; Item response theory; Manifold; Nonparametric; Penalized likelihood

Indexed keywords

EID: 0036763603     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/10769986027003291     Document Type: Article

References (21)

1. Abrahamowicz, M., & Ramsay, J.O. (1992). Multicategorical spline model for item response theory. Psychometrika, 57, 5-28.
2. Bock, R.D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
3. 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.
4. Green, P.J., & Silverman, B.W. (1994). Nonparametric regression and generalized linear models. London: Chapman & Hall.
5. Hastie, T. & Tibshirani, R. (1990). Generalized additive models. New York: Chapman and Hall.
6. Heckman, N., & Ramsay, J.O. (2000). Penalized regression with model-based penalties. Canadian Journal of Statistics, 28, 241-258.
7. Ramsay, J.O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611-630.
8. Ramsay, J.O. (1995). A similarity-based smoothing approach to nondimensional item analysis. Psychometrika, 60, 323-339.
9. Ramsay, J.O. (1996). A geometrical approach to item response theory. Behaviormetrika, 23, 3-17.
10. Ramsay, J.O. (1998). Estimating smooth monotone functions. Journal of the Royal Statistical Society, Series B, 60, 365-375.
11. Ramsay, J.O. (2000). TESTGRAF Manual, McGill University: Unpublished manuscript.
12. Ramsay, J.O., & Abrahamowicz, M. (1989). Binonomial regression with monotone splines: A psychometric application. Journal of the American Statistical Association, 84, 906-915.
13. Ramsay, J.O., & Silverman, B.W. (1997). Functional data analysis. New York: Springer.
14. Ramsay, J.O., & Winsberg, S. (1991). Maximum marginal likelihood estimation in semi-parametric data analysis. Psychometrika, 56, 365-380.
15. Rossi, N.T. (2001). Nonparametric estimation of item response functions using the EM algorithm. Unpublished masters thesis, McGill University, Montreal Quebec, Canada.
16. Samejima, F. (1998). Efficient nonparametric approaches for estimating the operating characteristics of discrete item responses. Psychometrika, 63, 111-130.
17. Simonoff, J.S. (1996). Smoothing methods in statistics. New York: Springer.
18. Stoer, J., & Bulirsch, R. (1980). Introduction to numerical analysis. New York: Springer.
19. Thurstone, L.L. (1927). A law of Comparative judgement. Psychological Review, 34, 273-286.
20. Wang, X. (1993). Combining the generalized linear model and spline smoothing to analyze examination data. McGill University, Unpublished master's thesis, Montreal Quebec, Canada.
21. Wingersky, M.S., Patrick, R., & Lord, F.M. (1988). LOGIST Users guide [computer program]. Princeton, NJ: Educational Testing Service.