Applications of robust optimization to automated test assembly

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Abstract

Executive Summary In automated test assembly (ATA), 0-1 linear programming (0-1 LP) methods are applied to select questions (items) from an item bank to assemble an optimal test. The objective in this 0-1 LP optimization problem is to assemble a test that measures, in as precise a way as possible, the ability of candidates. Item response theory (IRT) is commonly applied to model the relationship between the responses of candidates and their ability level. Parameters that describe the characteristics of each item, such as difficulty level and the extent to which an item differentiates between more and less able test takers (discrimination) are estimated in the application of the IRT model. Unfortunately, since all parameters in IRT models have to be estimated, they do have a level of uncertainty to them. Some of the other parameters in the test assembly model, such as average response times, have been estimated with uncertainty as well. General 0-1 LP methods do not take this uncertainty into account, and overestimate the predicted level of measurement precision. In this paper, alternative robust optimization methods are applied. It is demonstrated how the Bertsimas and Sim method can be applied to take this uncertainty into account in ATA. The impact of applying this method is illustrated in two numerical examples. Implications are discussed, and some directions for future research are presented.
Original languageEnglish
Place of PublicationNewtown
PublisherLSAC
Publication statusPublished - 2012

Publication series

NameLSAC Research Report Series
PublisherLSAC
No.12-02
Volume12-02

Fingerprint

linear programing
test
method
parameter

Keywords

  • METIS-291706
  • IR-83911

Cite this

Veldkamp, B. P. (2012). Applications of robust optimization to automated test assembly. (LSAC Research Report Series; Vol. 12-02, No. 12-02). Newtown: LSAC.
Veldkamp, Bernard P. / Applications of robust optimization to automated test assembly. Newtown : LSAC, 2012. (LSAC Research Report Series; 12-02).
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Veldkamp, BP 2012, Applications of robust optimization to automated test assembly. LSAC Research Report Series, no. 12-02, vol. 12-02, LSAC, Newtown.

Applications of robust optimization to automated test assembly. / Veldkamp, Bernard P.

Newtown : LSAC, 2012. (LSAC Research Report Series; Vol. 12-02, No. 12-02).

Research output: Book/ReportReportProfessional

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N2 - Executive Summary In automated test assembly (ATA), 0-1 linear programming (0-1 LP) methods are applied to select questions (items) from an item bank to assemble an optimal test. The objective in this 0-1 LP optimization problem is to assemble a test that measures, in as precise a way as possible, the ability of candidates. Item response theory (IRT) is commonly applied to model the relationship between the responses of candidates and their ability level. Parameters that describe the characteristics of each item, such as difficulty level and the extent to which an item differentiates between more and less able test takers (discrimination) are estimated in the application of the IRT model. Unfortunately, since all parameters in IRT models have to be estimated, they do have a level of uncertainty to them. Some of the other parameters in the test assembly model, such as average response times, have been estimated with uncertainty as well. General 0-1 LP methods do not take this uncertainty into account, and overestimate the predicted level of measurement precision. In this paper, alternative robust optimization methods are applied. It is demonstrated how the Bertsimas and Sim method can be applied to take this uncertainty into account in ATA. The impact of applying this method is illustrated in two numerical examples. Implications are discussed, and some directions for future research are presented.

AB - Executive Summary In automated test assembly (ATA), 0-1 linear programming (0-1 LP) methods are applied to select questions (items) from an item bank to assemble an optimal test. The objective in this 0-1 LP optimization problem is to assemble a test that measures, in as precise a way as possible, the ability of candidates. Item response theory (IRT) is commonly applied to model the relationship between the responses of candidates and their ability level. Parameters that describe the characteristics of each item, such as difficulty level and the extent to which an item differentiates between more and less able test takers (discrimination) are estimated in the application of the IRT model. Unfortunately, since all parameters in IRT models have to be estimated, they do have a level of uncertainty to them. Some of the other parameters in the test assembly model, such as average response times, have been estimated with uncertainty as well. General 0-1 LP methods do not take this uncertainty into account, and overestimate the predicted level of measurement precision. In this paper, alternative robust optimization methods are applied. It is demonstrated how the Bertsimas and Sim method can be applied to take this uncertainty into account in ATA. The impact of applying this method is illustrated in two numerical examples. Implications are discussed, and some directions for future research are presented.

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Veldkamp BP. Applications of robust optimization to automated test assembly. Newtown: LSAC, 2012. (LSAC Research Report Series; 12-02).