Skip to main content
SpringerLink
Log in

Optimum Design in Item Response Theory: Test Assembly and Item Calibration

  • Chapter
Book cover Contributions to Mathematical Psychology, Psychometrics, and Methodology

Part of the book series: Recent Research in Psychology ((PSYCHOLOGY))

Abstract

The idea of optimizing experimental design to give estimators maximal efficiency has been around in the statistical literature for several decades, but its applicability to sampling problems in item response theory (IRT) has not been widely noticed. It is the purpose of this paper to show how optimum design principles can be used to improve item and examinee sampling in IRT-based test assembly and item calibration. For both applications a result based on the maximin principle is given. The maxim in principle fits these applications naturally, because IRT models are nonlinear and involve criteria of optimality that are dependent on the unknown parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Adema, J.J. (1988). A note on solving large-scale zero-one programming problems (Research Report 88–4 ). Enschede, The Netherlands: Department of Education, University of Twente.

    Google Scholar 

  • Adema, J.J. (1990a). The construction of customized two-stage tests. Journal of Educational Measurement, 27, 241–253.

    Article  Google Scholar 

  • Adema, J.J. (1990b). Models and algorithms for the construction of achievement tests. Doctoral thesis. Enschede, The Netherlands: University of Twente.

    Google Scholar 

  • Adema, J.J., Boekkooi-Timminga, E., & van der Linden, W.J. (1992). Achievement test construction using 0–1 linear programming. European Journal of Operational Research, 55, 103–111.

    Article  Google Scholar 

  • Adema, J.J., & van der Linden, W.J. (1989). Algorithms for computerized test construction using classical item parameters. Journal of Educational Statistics, 14, 279–290.

    Article  Google Scholar 

  • Amstrong, R.D., Jones, D.H., & Wu, I.-L. (1992). An automated test development of parallel tests from a seed test. Psychometrika, 51, 271–288.

    Article  Google Scholar 

  • Atkinson, A.C. (1982). Developments in the design of experiments. International Statistical Review, 50, 161–177.

    Article  Google Scholar 

  • Berger, M.P.F. (1992). Sequential sampling designs for the two-parameter item response theory model. Psychometrika, 51, 521–538.

    Article  Google Scholar 

  • Berger, M.P.F., & van der Linden, W.J. (1992). Optimality of sampling designs in item response theory models. In M. Wilson (Ed.), Objective measurement: Theory into practice (Vol. 1 ). Norwood, N.J.: Ablex.

    Google Scholar 

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

    Google Scholar 

  • Boekkooi-Timminga, E. (1989). Models for computerized test construction. Doctoral thesis, University of Twente. De Lier, The Netherlands: Academisch Boeken Centrum.

    Google Scholar 

  • Boekkooi-Timminga, E. (1990a). The construction of parallel tests from IRT-based item banks. Journal of Educational Statistics, 15, 129–145.

    Article  Google Scholar 

  • Boekkooi-Timminga, E. (1990b). A cluster-based method for test construction. Applied Psychological Measurement, 14, 341–354.

    Article  Google Scholar 

  • Davey, T.C. ( 1992, April). Optimal common-item anchors for ability metric linking. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, California.

    Google Scholar 

  • Fedorov, V.V. (1972). Theory of optimal experiments. New York: Academic Press.

    Google Scholar 

  • Fischer, G.H. (1981). On the existence and uniqueness of maximum likelihood estimates in the Rasch model. Psychometrika, 46, 59–77.

    Article  Google Scholar 

  • Hambleton, R.K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston: Kluwer-Nijhoff.

    Google Scholar 

  • Kalton, G. (1983). Introduction to survey sampling (Quantitative Applications in the Social Sciences, Series Nr. 35 ). Newbury Park, CA: Sage.

    Google Scholar 

  • Kiefer, J., & Wolfowitz, J. (1960). The equivalence of two extremum problems. Canadian Journal of Mathematics, 12, 363–366.

    Article  Google Scholar 

  • Nemhauser, G.L., & Wolsey, L.A. (1988). Integer and combinatorial optimization. New York: Wiley.

    Google Scholar 

  • Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Paedogogiske Institut.

    Google Scholar 

  • Sanders, P.F., Theunissen, T.J.J.M., & Baas, S.M. (1989). Minimizing the number of observations: A generalization of the Spearman-Brown formula. Psychometrika, 54, 587–598.

    Article  Google Scholar 

  • Sanders, P.F., Theunissen, T.J.J.M., & Baas, S.M. (1991). Maximizing the coefficient of generalizability under the constraint of limited resources. Psychometrika, 56, 87–96.

    Article  Google Scholar 

  • Särndal, C.-E., Swensson, B., & Wretman, J. (1992). Model-assisted survey sampling. New York: Springer-Verlag.

    Book  Google Scholar 

  • Silvey, S.D. (1980). Optimal design. London: Chapman and Hall.

    Google Scholar 

  • Steinburg, D.M., & Hunter, W.G. (1984). Experimental design: Review and comment. Technometrics, 26, 71–130.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Timminga, E. (1985). Geautomatiseerd toetsontwerp: Itemselectie met behulp van binair programmeren [Automated test design: Item selection using binary programming]. Master’s thesis. Enschede, The Netherlands: University of Twente.

    Google Scholar 

  • Vale, CD. (1986). Linking item parameters onto a common scale. Applied Psychological Measurement, 10, 333–344.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • van der Linden, W.J., & Boekkooi-Timminga, E. (1989). A maximin model for test design with practical constraints. Psychometrika, 53, 237–247.

    Article  Google Scholar 

  • van der Linden, W.J., & Eggen, T.J.J.M. (1986). An empirical Bayes approach to item banking. Applied Psychological Measurement, 10, 345–354.

    Article  Google Scholar 

  • Verschoor, A. (1991). Optimal test design (computer program). Arnhem, The Netherlands: Cito.

    Google Scholar 

  • Wingersky, M.S., & Lord, F.M. (1984). An investigation of methods for reducing sampling error in some IRT procedures. Applied Psychological Measurement, 8, 347–364.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Twente, Enschede, The Netherlands

    W. J. van der Linden

Authors
  1. W. J. van der Linden
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Psychology, University of Vienna, Liebiggasse 5, A-1010, Vienna, Austria

    Gerhard H. Fischer Ph.D.

  2. Department of Experimental Psychology, Cambridge University, Cambridge, England, CB2 3EB

    Donald Laming Ph.D.

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

van der Linden, W.J. (1994). Optimum Design in Item Response Theory: Test Assembly and Item Calibration. In: Fischer, G.H., Laming, D. (eds) Contributions to Mathematical Psychology, Psychometrics, and Methodology. Recent Research in Psychology. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4308-3_22

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4308-3_22

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94169-1

  • Online ISBN: 978-1-4612-4308-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation