A maximin model for test design with practical constraints

Willem J. van der Linden, Ellen Boekkooi-Timminga

Research output: Book/ReportReportOther research output

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Abstract

A "maximin" model for item response theory based test design is proposed. In this 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 there may be several demands with respect to the properties of the test. The way in which these can be formulated as linear constraints in the model is demonstrated. The constraints discussed include: (1) test composition; (2) administration time; (3) selection of item features; (4) group-dependent item parameters; (5) inclusion or exclusion of individual items; and (6) inter-item dependencies. An example of a test construction problem with practical constraints is presented. Using the three-parameter logistic model, an item bank of 1,000 items was drawn for the application of the test construction model, which was solved using the computer program LINPROG. Some alternative models of test construction are discussed. Three tables provide information about four solutions and list alternative objective functions in test construction.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Publication statusPublished - Dec 1987

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.87-10

Keywords

  • Latent Trait Theory
  • Testing Problems
  • Test Construction
  • Test Items
  • IR-103748
  • Mathematical Models
  • Algorithms
  • Foreign Countries
  • Linear Programming
  • Item Banks

Cite this

van der Linden, W. J., & Boekkooi-Timminga, E. (1987). A maximin model for test design with practical constraints. (OMD research report; No. 87-10). Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology.
van der Linden, Willem J. ; Boekkooi-Timminga, Ellen. / A maximin model for test design with practical constraints. Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1987. (OMD research report; 87-10).
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series = "OMD research report",
publisher = "University of Twente, Faculty Educational Science and Technology",
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van der Linden, WJ & Boekkooi-Timminga, E 1987, A maximin model for test design with practical constraints. OMD research report, no. 87-10, University of Twente, Faculty Educational Science and Technology, Enschede, the Netherlands.

A maximin model for test design with practical constraints. / van der Linden, Willem J.; Boekkooi-Timminga, Ellen.

Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1987. (OMD research report; No. 87-10).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - A maximin model for test design with practical constraints

AU - van der Linden, Willem J.

AU - Boekkooi-Timminga, Ellen

N1 - Project Psychometric Aspects of Item Banking No. 25

PY - 1987/12

Y1 - 1987/12

N2 - A "maximin" model for item response theory based test design is proposed. In this 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 there may be several demands with respect to the properties of the test. The way in which these can be formulated as linear constraints in the model is demonstrated. The constraints discussed include: (1) test composition; (2) administration time; (3) selection of item features; (4) group-dependent item parameters; (5) inclusion or exclusion of individual items; and (6) inter-item dependencies. An example of a test construction problem with practical constraints is presented. Using the three-parameter logistic model, an item bank of 1,000 items was drawn for the application of the test construction model, which was solved using the computer program LINPROG. Some alternative models of test construction are discussed. Three tables provide information about four solutions and list alternative objective functions in test construction.

AB - A "maximin" model for item response theory based test design is proposed. In this 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 there may be several demands with respect to the properties of the test. The way in which these can be formulated as linear constraints in the model is demonstrated. The constraints discussed include: (1) test composition; (2) administration time; (3) selection of item features; (4) group-dependent item parameters; (5) inclusion or exclusion of individual items; and (6) inter-item dependencies. An example of a test construction problem with practical constraints is presented. Using the three-parameter logistic model, an item bank of 1,000 items was drawn for the application of the test construction model, which was solved using the computer program LINPROG. Some alternative models of test construction are discussed. Three tables provide information about four solutions and list alternative objective functions in test construction.

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KW - IR-103748

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KW - Algorithms

KW - Foreign Countries

KW - Linear Programming

KW - Item Banks

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van der Linden WJ, Boekkooi-Timminga E. A maximin model for test design with practical constraints. Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology, 1987. (OMD research report; 87-10).