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Binary Programming and Test Design

Published online by Cambridge University Press:  01 January 2025

T. J. J. M. Theunissen
T. J. J. M. Theunissen*
Affiliation:
National Institute for Educational Measurement (CITO), Arnhem, The Netherlands
*
Requests for reprints should be sent to T. J. J. M. Theunissen, Cito, P.O. Box 1034, 6801 MG Arnhem, THE NETHERLANDS.
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Abstract

An algorithmic approach to test design, using information functions, is presented. The approach uses a special branch of linear programming, i.e. binary programming. In addition, results of some benchmark problems are presented. Within the same framework, it is also possible to formulate the problem of individualized testing.

Keywords

linear programmingbinary programminginformation functiontest-designindividualized testingitem bank
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 4 , December 1985 , pp. 411 - 420
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

I would like to thank my colleagues N. Veldhuijzen, H. Verstralen and M. Zwarts for their suggestions and comments. Furthermore, I would like to thank Professor W. van der Linden, Department of Educational Measurement and Data Analysis, Technological University Twente, for offering facilities at his department; Ellen Timminga of the same department and S. Baas, department of Operational Research at the same University for their efforts in linear programming.

References

Birnhaum, A. (1968). Some latent trait models. In Lord, F. M., Novick, M. R. (Eds.), Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Bock, R. D., Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443–459.CrossRefGoogle Scholar
Land, A. H., Doig, A. (1960). An automatic method of solving discrete programming problems. Econometrika, 28, 497–520.CrossRefGoogle Scholar
Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Oosterloo, S. (1984). Confidence intervals for test information and relative efficiency. Statistica Neelandica, 38, 37–54.Google Scholar
Owen, R. J. (1975). A Bayesian sequential procedure for quantal response in the context of adaptive mental testing. Journal of the American Statistical Association, 70, 351–356.CrossRefGoogle Scholar
Papadimitriou, C. H., Steiglitz, K. (1982). Combinatorial optimization: Algorithms and complexity, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Rao, S. S. (1984). Optimization: Theory and applications 2nd ed.,, New Delhi: Wiley Eastern.Google Scholar
Syslo, M. J., Deo, N., Kowalik, J. S. (1983). Discrete optimization algorithms, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Taha, H. A. (1975). Integer programming, New York: Academic Press.Google Scholar
Thissen, D., Steinberg, L. (1984). A response model for multiple choice items. Psychometrika, 49, 501–519.CrossRefGoogle Scholar
Wolfe, J. H. (1981). Optimal item difficulty for the three-parameter normal ogive response model. Psychometrika, 46, 461–464.CrossRefGoogle Scholar