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Minimax D-Optimal Designs for Item Response Theory Models

Published online by Cambridge University Press:  01 January 2025

Martijn P. F. Berger ,
C. Y. Joy King  and
Weng Kee Wong
Martijn P. F. Berger*
Affiliation:
Department of Methodology and Statistics, University of Maastricht
C. Y. Joy King
Affiliation:
Department of Biostatistics, UCLA
Weng Kee Wong
Affiliation:
Department of Biostatistics, UCLA
*
Requests for reprints should be sent to Martijn R F. Berger, Department of Methodology and Statistics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands. E-mail: [email protected]
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Abstract

Various different item response theory (IRT) models can be used in educational and psychological measurement to analyze test data. One of the major drawbacks of these models is that efficient parameter estimation can only be achieved with very large data sets. Therefore, it is often worthwhile to search for designs of the test data that in some way will optimize the parameter estimates. The results from the statistical theory on optimal design can be applied for efficient estimation of the parameters.

A major problem in finding an optimal design for IRT models is that the designs are only optimal for a given set of parameters, that is, they are locally optimal. Locally optimal designs can be constructed with a sequential design procedure. In this paper minimax designs are proposed for IRT models to overcome the problem of local optimality. Minimax designs are compared to sequentially constructed designs for the two parameter logistic model and the results show that minimax design can be nearly as efficient as sequentially constructed designs.

Keywords

optimal designIRT modelsminimaxsequential designs
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 3 , September 2000 , pp. 377 - 390
Copyright
Copyright © 2000 The Psychometric Society

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