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Adaptive Item Selection Under Matroid Constraints

Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet

Standard

Adaptive Item Selection Under Matroid Constraints. / Bengs, Daniel; Brefeld, Ulf; Kröhne, Ulf.
in: Journal of Computerized Adaptive Testing, Jahrgang 6, Nr. 2, 07.08.2018, S. 15-36.

Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet

Harvard

Bengs, D, Brefeld, U & Kröhne, U 2018, 'Adaptive Item Selection Under Matroid Constraints', Journal of Computerized Adaptive Testing, Jg. 6, Nr. 2, S. 15-36. https://doi.org/10.7333/1808-0602015

APA

Bengs, D., Brefeld, U., & Kröhne, U. (2018). Adaptive Item Selection Under Matroid Constraints. Journal of Computerized Adaptive Testing, 6(2), 15-36. https://doi.org/10.7333/1808-0602015

Vancouver

Bengs D, Brefeld U, Kröhne U. Adaptive Item Selection Under Matroid Constraints. Journal of Computerized Adaptive Testing. 2018 Aug 7;6(2):15-36. doi: 10.7333/1808-0602015

Bibtex

@article{769099fc630a4720bfd7b350760021ae,
title = "Adaptive Item Selection Under Matroid Constraints",
abstract = "The shadow testing approach (STA; van der Linden & Reese, 1998) is considered the state of the art in constrained item selection for computerized adaptive tests. The present paper shows that certain types of constraints (e.g., bounds on categorical item attributes) induce a matroid on the item bank. This observation is used to devise item selection algorithms that are based on matroid optimization and lead to optimal tests, as the STA does. In particular, a single matroid constraint can be treated optimally by an efficient greedy algorithm that selects the most informative item preserving the integrity of the constraints. A simulation study shows that for applicable constraints, the optimal algorithms realize a decrease in standard error (SE) corresponding to a reduction in test length of up to 10% compared to the maximum priority index (Cheng & Chang, 2009) and up to 30% compared to Kingsbury and Zara's (1991) constrained computerized adaptive testing.",
keywords = "Business informatics",
author = "Daniel Bengs and Ulf Brefeld and Ulf Kr{\"o}hne",
year = "2018",
month = aug,
day = "7",
doi = "10.7333/1808-0602015",
language = "English",
volume = "6",
pages = "15--36",
journal = "Journal of Computerized Adaptive Testing",
issn = "2165-6592",
publisher = "University of Minnesota Press",
number = "2",

}

RIS

TY - JOUR

T1 - Adaptive Item Selection Under Matroid Constraints

AU - Bengs, Daniel

AU - Brefeld, Ulf

AU - Kröhne, Ulf

PY - 2018/8/7

Y1 - 2018/8/7

N2 - The shadow testing approach (STA; van der Linden & Reese, 1998) is considered the state of the art in constrained item selection for computerized adaptive tests. The present paper shows that certain types of constraints (e.g., bounds on categorical item attributes) induce a matroid on the item bank. This observation is used to devise item selection algorithms that are based on matroid optimization and lead to optimal tests, as the STA does. In particular, a single matroid constraint can be treated optimally by an efficient greedy algorithm that selects the most informative item preserving the integrity of the constraints. A simulation study shows that for applicable constraints, the optimal algorithms realize a decrease in standard error (SE) corresponding to a reduction in test length of up to 10% compared to the maximum priority index (Cheng & Chang, 2009) and up to 30% compared to Kingsbury and Zara's (1991) constrained computerized adaptive testing.

AB - The shadow testing approach (STA; van der Linden & Reese, 1998) is considered the state of the art in constrained item selection for computerized adaptive tests. The present paper shows that certain types of constraints (e.g., bounds on categorical item attributes) induce a matroid on the item bank. This observation is used to devise item selection algorithms that are based on matroid optimization and lead to optimal tests, as the STA does. In particular, a single matroid constraint can be treated optimally by an efficient greedy algorithm that selects the most informative item preserving the integrity of the constraints. A simulation study shows that for applicable constraints, the optimal algorithms realize a decrease in standard error (SE) corresponding to a reduction in test length of up to 10% compared to the maximum priority index (Cheng & Chang, 2009) and up to 30% compared to Kingsbury and Zara's (1991) constrained computerized adaptive testing.

KW - Business informatics

UR - https://www.mendeley.com/catalogue/111d4283-c401-332d-a124-608203b006a4/

U2 - 10.7333/1808-0602015

DO - 10.7333/1808-0602015

M3 - Journal articles

VL - 6

SP - 15

EP - 36

JO - Journal of Computerized Adaptive Testing

JF - Journal of Computerized Adaptive Testing

SN - 2165-6592

IS - 2

ER -

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