Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-07T18:30:57.117Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimum Examinee Samples for Item Parameter Estimation in Item Response Theory: A Multi-Objective Programming Approach

Published online by Cambridge University Press:  01 January 2025

Ellen Timminga
Ellen Timminga*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Ellen Timminga, University of Groningen, Grote Rozenstraat 15, 9712 TG Groningen, THE NETHERLANDS. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a multi-objective programming method for determining samples of examinees needed for estimating the parameters of a group of items. In the numerical experiments, optimum samples are compared to uniformly and normally distributed samples. The results show that the samples usually recommended in the literature are well suited for estimating the difficulty parameters. Furthermore, they are also adequate for estimating the discrimination parameters in the three-parameter model, but not for the guessing parameters.

Keywords

item response theoryIRT item parametersIRT estimationoptimum examineesinformation functionslinear programmingmulti-objective programming
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 1 , March 1995 , pp. 137 - 154
Copyright
Copyright © 1995 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

The author would like to thank Wire J. van der Linden and the anonymous reviewers for their comments and suggestions. Terry Ackerman, University of Illinois, and Judith Messick, North Western University, are acknowledged for editing the English. Of course, responsibility for errors rests solely with the author.

References

PcProg (1986). Amsterdam: Quantitative Management Software.Google Scholar
Rao, S. S. (1985). Optimization: Theory and applications 2nd ed.,, New Delhi: Wiley Eastern.Google Scholar
Ree, M. J. (1979). Estimating item characteristic curves. Applied Psychological Measurement, 3, 371–385.CrossRefGoogle Scholar
Stocking, M. L. (1990). Specifying optimum examinees for item parameter estimation in item response theory. Psychometrika, 55, 461–475.CrossRefGoogle Scholar
Swaminathan, H., Gifford, J. (1983). Estimation of parameters in the three-parameter latent trait model. In Weiss, D. J. (Eds.), New horizons in testing: Latent trait theory and computerized adaptive testing (pp. 13–30). New York: Academic Press.Google Scholar
Thissen, D., Wainer, H. (1982). Some standard errors in item response theory. Psychometrika, 47, 397–412.CrossRefGoogle Scholar
van der Linden, W. J. (1988). Optimizing incomplete sample designs for item response model parameters, Enschede: University of Twente.Google Scholar
van der Linden, W. J., Boekkooi-Timminga, E. (1989). A maximin model for test design with practical constraints. Psychometrika, 54, 237–247.CrossRefGoogle Scholar
Wagner, H. M. (1972). Principles of operations research: With applications to managerial decisions, London: Prentice Hall.Google Scholar
Williams, H. P. (1978). Model building in mathematical programming, New York: John Wiley & Sons.Google Scholar
Wingersky, M. S., Lord, F. M. (1984). An investigation of methods for reducing sampling error in certain IRT procedures. Applied Psychological Measurement, 8, 347–364.CrossRefGoogle Scholar