Hostname: page-component-5f745c7db-96s6r Total loading time: 0 Render date: 2025-01-06T07:42:11.608Z Has data issue: true hasContentIssue false
  • English
  • Français

Efficient Nonparametric Approaches for Estimating the Operating Characteristics of Discrete Item Responses

Published online by Cambridge University Press:  01 January 2025

Fumiko Samejima
Fumiko Samejima*
Affiliation:
University of Tennessee
*
Requests for reprints should be sent to Fumiko Samejima, 405 Austin Peay Bldg., University of Tennessee, Knoxville, Tennessee 37996-0900.
Get access Rights & Permissions [Opens in a new window]

Abstract

Rationale and the actual procedures of two nonparametric approaches, called Bivariate P.D.F. Approach and Conditional P.D.F. Approach, for estimating the operating characteristic of a discrete item response, or the conditional probability, given latent trait, that the examinee's response be that specific response, are introduced and discussed. These methods are featured by the facts that: (a) estimation is made without assuming any mathematical forms, and (b) it is based upon a relatively small sample of several hundred to a few thousand examinees.

Some examples of the results obtained by the Simple Sum Procedure and the Differential Weight Procedure of the Conditional P.D.F. Approach are given, using simulated data. The usefulness of these nonparametric methods is also discussed.

Keywords

latent trait modelsconstant information modelinformation functionsability estimationasymptotic normalitytestbiasmaximum likelihood estimation
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 2 , June 1998 , pp. 111 - 130
Copyright
Copyright © 1998 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was mostly supported by the Office of Naval Research (N00014-77-C-0360, N00014-81-C-0569, N00014-87-K-0320, N00014-90-J-1456).

References

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., & Novick, M. R. (Eds.), Statistical theories of mental test scores (chap. 17–20), Reading, MA: Addison Wesley.Google Scholar
Elderton, W. P., & Johnson, N. L. (1969). Systems of frequency curves, New York, NY: Cambridge University Press.CrossRefGoogle Scholar
Hirschman, I. I., & Widder, D. V. (1955). The convolution transform, Princeton, NJ: Princeton University Press.Google Scholar
Levine, M. V. (1984). An introduction to multilinear formula score theory, Champaign, IL: Model-Based Measurement Laboratory, Educational Building, University of Illinois.Google Scholar
Levine, M., & Williams, B. (1991). Nonparametric item response function estimation strategies. Paper presented at the ONR Conference on Model-Based Measurement, Princeton, New Jersey.Google Scholar
Lord, F. M. (1952). A theory of test scores. Psychometric Monograph, No. 7.Google Scholar
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.CrossRefGoogle Scholar
Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores, Reading, MA: Addison Wesley.Google Scholar
Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic estimation. Psychometrika, 56, 611–630.CrossRefGoogle Scholar
Samejima, F. (1969). Estimation of ability using a response pattern of graded scores. Psychometrika Monograph, No. 17.Google Scholar
Samejima, F. (1972). A general model for free-response data. Psychometrika Monograph, No. 18.Google Scholar
Samejima, F. (1973). A comment on Birnbaum's three-parameter logistic model in the latent trait theory. Psychometrika, 38, 221–233.CrossRefGoogle Scholar
Samejima, F. (1977). Effects of individual optimization in setting the boundaries of dichotomous items on the accuracy of estimation. Applied Psychological Measurement, 1, 77–94.CrossRefGoogle Scholar
Samejima, F. (1977). A method of estimating item characteristic functions using the maximum likelihood estimate of ability. Psychometrika, 42, 163–191.CrossRefGoogle Scholar
Samejima, F. (1977). Estimation of the operating characteristics of item response categories I: Introduction to the Two-Parameter Beta Method, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1978). Estimation of the operating characteristics of item response categories II: Further development of the Two-Parameter Beta Method, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1978). Estimation of the operating characteristics of item response categories III: The Normal Approach Method and the Pearson System Method, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1978). Estimation of the operating characteristics of item response categories IV: Comparison of the different methods, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1978). Estimation of the operating characteristics of item response categories V: Weighted Sum Procedure in the Conditional P.D.F. Approach, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1978). Estimation of the operating characteristics of item response categories VI: Proportioned Sum Procedure in the Conditional P.D.F. Approach, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1978). Estimation of the operating characteristics of item response categories VII: Bivariate P.D.F. Approach with Normal Approach Method, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1980). Estimation of the operating characteristics when the test information of the Old Test is not constant I: Rationale, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1980). 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, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1981). 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, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1981). Final Report: Efficient methods of estimating the operating characteristics of item response categories and challenge to a new model for the multiple-choice item, Knoxville, TN: Department of Psychology, University of Tennessee.CrossRefGoogle Scholar
Samejima, F. (1984). Plausibility functions of Iowa Vocabulary test items estimated by the Simple Sum Procedure of the Conditional P.D.F. Approach, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1988). Final Report: Advancement of latent trait theory, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1990). Modifications of the test information function, Knoxville, TN: Department of Psychology, University of Tennessee.CrossRefGoogle Scholar
Samejima, F. (1990). Differential Weight Procedure of the Conditional P.D.F. Approach for estimating the operating characteristics of discrete item responses, Knoxville, TN: Department of Psychology, University of Tennessee.CrossRefGoogle Scholar
Samejima, F. (1990). Final Report: Validity study in multidimensional latent space and efficient computerized adaptive testing, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Samejima, F. (1993). 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.CrossRefGoogle Scholar
Samejima, F. (1993). The bias function of the maximum likelihood estimate of ability for the dichotomous response level. Psychometrika, 58, 195–209.CrossRefGoogle Scholar
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.Google Scholar
Samejima, F. (1994). Nonparametric estimation of the plausibility functions of the distractors of vocabulary test items. Applied Psychological Measurement, 18, 35–51.CrossRefGoogle Scholar
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 Nichols, P. D., Chipman, S. E., & Brennan, R. L. (Eds.), Cognitively diagnostic assessment, Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Samejima, F., & Livingston, P. S. (1979). Methods of moments as the least squares solution for fitting a plynomial, Knoxville, TN: Department of Psychology, University of Tennessee.Google Scholar
Trumpler, R. J., & Weaver, H. F. (1953). Statistical astronomy, Berkeley, CA: University of California Press.CrossRefGoogle Scholar