Efficient nonparametric approaches for estimating the operating characteristics of discrete item responses

Psychometrika

Volumn 63, Issue 2, 1998, Pages 111-130

  Samejima, Fumiko ^a  

^a UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Ability estimation; Asymptotic normality; Bias; Constant information model; Information functions; Latent trait models; Maximum likelihood estimation; Tests

Indexed keywords

EID: 0032383264     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02294770     Document Type: Article

References (37)

1. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord and M. R. Novick, Statistical theories of mental test scores (chap. 17-20). Reading, MA: Addison Wesley.
2. Elderton, W. P., & Johnson, N. L. (1969). Systems of frequency curves. New York, NY: Cambridge University Press.
3. Hirschman, I. I., & Widder, D. V. (1955). The convolution transform. Princeton, NJ: Princeton University Press.
4. Levine, M. V. (1984). An introduction to multilinear formula score theory (Office of Naval Research Report 84-4, N00014-83-K-0397). Champaign, IL: Model-Based Measurement Laboratory, Educational Building, University of Illinois.
5. Levine, M., & Williams, B. (1991). Nonparametric item response function estimation strategies. Paper presented at the ONR Conference on Model-Based Measurement, Princeton, New Jersey.
6. Lord, F. M. (1952). A theory of test scores. Psychometric Monograph, No. 7.
7. Lord, F. M. (1970). Item characteristic curves estimated without knowledge of their mathematical form: A confrontation of Birnbaum's logistical model. Psychometrika, 35, 43-50.
8. Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison Wesley.
9. Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic estimation. Psychometrika, 56, 611-630.
10. Samejima, F. (1969). Estimation of ability using a response pattern of graded scores. Psychometrika Monograph, No. 17.
11. Samejima, F. (1972). A general model for free-response data. Psychometrika Monograph, No. 18.
12. Samejima, F. (1973). A comment on Birnbaum's three-parameter logistic model in the latent trait theory, Psychometrika, 38, 221-233.
13. Samejima, F. (1977a). Effects of individual optimization in setting the boundaries of dichotomous items on the accuracy of estimation. Applied Psychological Measurement, 1, 77-94.
14. Samejima, F. (1977b). A method of estimating item characteristic functions using the maximum likelihood estimate of ability. Psychometrika, 42, 163-191.
15. Samejima, F. (1977c). Estimation of the operating characteristics of item response categories I: Introduction to the Two-Parameter Beta Method (Office of Naval Research Report 77-1, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
16. Samejima, F. (1978a). Estimation of the operating characteristics of item response categories II: Further development of the Two-Parameter Beta Method (Office of Naval Research Report 78-1, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
17. Samejima, F. (1978b). Estimation of the operating characteristics of item response categories III: The Normal Approach Method and the Pearson System Method (Office of Naval Research Report 78-2, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
18. Samejima, F. (1978c). Estimation of the operating characteristics of item response categories IV: Comparison of the different methods (Office of Naval Research Report 78-3, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
19. Samejima, F. (1978d). Estimation of the operating characteristics of item response categories V: Weighted Sum Procedure in the Conditional P.D.F. Approach (Office of Naval Research Report 78-4, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
20. Samejima, F. (1978e). Estimation of the operating characteristics of item response categories VI: Proportioned Sum Procedure in the Conditional P.D.F. Approach (Office of Naval Research Report 78-5, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
21. Samejima, F. (1978f). Estimation of the operating characteristics of item response categories VII: Bivariate P.D.F. Approach with Normal Approach Method (Office of Naval Research Report 78-6, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
22. Samejima, F. (1980a). Estimation of the operating characteristics when the test information of the Old Test is not constant I: Rationale (Office of Naval Research Report 80-2, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
23. Samejima, F. (1980b). Estimation of the operating characteristics when the test information of the Old Test is not constant II: Simple Sum Procedure of the Conditional P.D.F. Approach/Normal Approach Method using three subsets of the Old Test (Office of Naval Research Report 80-4, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
24. Samejima, F. (1981a). Estimation of the operating characteristics when the test information of the Old Test is not constant II: Simple Sum Procedure of the Conditional P.D.F. Approach/Normal Approach Method using three subsets of the Old Test, No. 2 (Office of Naval Research Report 81-2, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
25. Samejima, F. (1981b). Final Report: Efficient methods of estimating the operating characteristics of item response categories and challenge to a new model for the multiple-choice item (Office of Naval Research Final Research Report of N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
26. Samejima, F. (1984). Plausibility functions of Iowa Vocabulary test items estimated by the Simple Sum Procedure of the Conditional P.D.F. Approach (Office of Naval Research Report 84-1, N00014-81-C-0569). Knoxville, TN: Department of Psychology, University of Tennessee.
27. Samejima, F. (1988). Final Report: Advancement of latent trait theory (Office of Naval Research Final Research Report of N00014-81-C-0569). Knoxville, TN: Department of Psychology, University of Tennessee.
28. Samejima, F. (1990a). Modifications of the test information function (Office of Naval Research Report 90-1, N00014-87-K-0320). Knoxville, TN: Department of Psychology, University of Tennessee.
29. Samejima, F. (1990b). Differential Weight Procedure of the Conditional P.D.F. Approach for estimating the operating characteristics of discrete item responses (Office of Naval Research Report 90-4, N00014-87-K-0320). Knoxville, TN: Department of Psychology, University of Tennessee.
30. Samejima, F. (1990c). Final Report: Validity study in multidimensional latent space and efficient computerized adaptive testing (Office of Naval Research Final Research Report of N00014-87-K-0320). Knoxville, TN: Department of Psychology, University of Tennessee.
31. Samejima, F. (1993a). An approximation for the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete. Psychometrika, 58, 119-138.
32. Samejima, F. (1993b). The bias function of the maximum likelihood estimate of ability for the dichotomous response level. Psychometrika, 58, 195-209.
33. Samejima, F. (1993c). Human psychological behavior: approached by latent trait models. Proceedings of the IEEE International Workshop on Neuro-Fuzzy Control (26-33). Muroran, Japan.
34. Samejima, F. (1994). Nonparametric estimation of the plausibility functions of the distractors of vocabulary test items. Applied Psychological Measurement, 18, 35-51.
35. Samejima, F. (1995). A cognitive diagnosis method using latent trait models: competency space approach and its relationship with DiBello and Stout's unified cognitive/psychometric diagnosis model. In P. D. Nichols, S. E. Chipman & R. L. Brennan (Eds.), Cognitively diagnostic assessment. Hillsdale, NJ: Lawrence Erlbaum.
36. Samejima, F., & Livingston, P. S. (1979). Methods of moments as the least squares solution for fitting a plynomial (Office of Naval Research Report 79-2, N00014-77-C-0360). Knoxville, TN: Department of Psychology, University of Tennessee.
37. Trumpler, R. J., & Weaver, H. F. (1953). Statistical astronomy. Berkeley, CA: University of California Press.