Adaptive Item Selection Under Matroid Constraints
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Adaptive Item Selection Under Matroid Constraints. / Bengs, Daniel; Brefeld, Ulf; Kröhne, Ulf.
In: Journal of Computerized Adaptive Testing, Vol. 6, No. 2, 07.08.2018, p. 15-36.Research output: Journal contributions › Journal articles › Research › peer-review
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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 -