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A maximin model for IRT-based test design with practical constraints

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Abstract

A maximin model for IRT-based test design is proposed. In the model only the relative shape of the target test information function is specified. It serves as a constraint subject to which a linear programming algorithm maximizes the information in the test. In the practice of test construction, several demands as linear constraints in the model. A worked example of a text construction problem with practical constraints is presented. The paper concludes with a discussion of some alternative models of test construction.

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References

  • Anthonisse, J. M. (1984).Linprog. Amsterdam: Centre for Mathematics and Computer Science CWI.

    Google Scholar 

  • Birnbaum, A. (1968) Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick, Statistical theories of mental test scores (pp. 379–397). Reading, MA: Addison-Wesley.

    Google Scholar 

  • Boekkooi-Timminga, E. (1987) Simultaneous test construction by zero-one programming.Mehtodika, 1, 101–112.

    Google Scholar 

  • Boekkooi-Timminga, E., & van der Linden, W. J. (1987). Algroithms for automated test construction. In F. J. Maarse, L. J. M. Mulder, W. P. B. Sjouw, & A. E. AkkerComputers in psychology: Methods, instrumentation and psychodiagnostics (pp. 165–170). Lisses: Swets & Zeitlinger.

    Google Scholar 

  • Dantzig, G. (1957). Discrete-variable extremum problems.Operations Research, 5, 266–277.

    Google Scholar 

  • Kelderman, H. (1987)Some procedures to assess target information functions. In W. J. van der Linden (Ed.), IRT-based test construction (Research Report 87-2, chap. 4). Enschede: University of Twente, Department of Education.

    Google Scholar 

  • Lord, F. M. (1980) Applications of item response theroy to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Pandey, T. N. (1986). State of the art of large-scale assessment in the United States. In W. J. van der Linden & J. M. Wijnstra (Eds.), Ontwikkelingen in de methodologie van het onderzoek [Developments in the methodology of educational research] (pp. 5–25). Lisse: Swets &Zeitlinger.

    Google Scholar 

  • Rao, S. S. (1985).Optimization: Theory and applications (2nd Ed.). New Delhi: Wiley Eastern.

    Google Scholar 

  • Rasch, G. (1960).Probabilistic models for soem intelligence and attainment tests. Copenhagen: Denmark Paedagogiske Institut.

    Google Scholar 

  • Theunissen, G. J. J. M. (1985). Binary programming and test design.Psychometrika, 50, 411–420.

    Google Scholar 

  • Theunissen, T. J. J. M. (1986). Optimization algorithms in test design.Applied Psychological Measuremetn, 10, 381–389.

    Google Scholar 

  • Theunissen, T. J. J. M., & Verstralen, H. H. F. M. (1986). Algoritmen voor het samenstellen van toetsen [Algorithms for constructin tests]. In W. J. van der Linden (Ed.),Moderne methoden voor toetsconstructie en -gebruik [Modern methods for test construction and use] (pp. 32–39). Lisse: Swets & Zeitlinger.

    Google Scholar 

  • Timminga, E. (1985).Geautomatiseered toetsontwerp: Itemselectie m.b.v. binair programmeren [Automated test design: Item selection usin binary programming]. Unpublished masters thesis, Uniersity of Twente, Enschede, The Netherlands.

    Google Scholar 

  • van der Linden, W. J. (1987). Automated test construction using minimax programming. In W. J. van der Linden (Ed.),IRT-based test construction (Research Report 87-2, chap. 3). Enschede: University of Twente, Department of Education.

    Google Scholar 

  • van der Linden, W. J., & Boekkooi-Timminga, E. (1988). A zero-one programming approach to Gulliksen's matched random subtests method.Applied Psychological Measurement, 12, 201–209.

    Google Scholar 

  • Wagner, H. M. (1975.Principles of operations reserarch. London: Prentice-Hall.

    Google Scholar 

  • Yen, W. M. (1983). use of the three-parmeter model in the development of a standardized achievement test. In R. K. Hambleton (Ed.),Applications of item response theory (pp. 123–141). Vancouver: Educational Research Institute of British Columbia.

    Google Scholar 

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Authors and Affiliations

  1. Department of Education, University of Twente, PO Box, 7500 AE, Enschede, The Netherlands

    Wim J. van ver Linden & Ellen Boekkooi-Timminga

Authors
  1. Wim J. van ver Linden
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  2. Ellen Boekkooi-Timminga
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Additional information

The authors are indebted to Jos J. Adea for suggesting Equation 17 as a Simplification of an earlier version of this constraint. This research was suuorted in part by a grant from the Dutch Organization for Research (NWO) through the Foundation for Psychological and Psychonomic Research in the Netherlands (Psychon).

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van ver Linden, W.J., Boekkooi-Timminga, E. A maximin model for IRT-based test design with practical constraints. Psychometrika 54, 237–247 (1989). https://doi.org/10.1007/BF02294518

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  • DOI: https://doi.org/10.1007/BF02294518

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