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Optimal Bayesian Adaptive Design for Test-Item Calibration

Published online by Cambridge University Press:  01 January 2025

Wim J. van der Linden  and
Hao Ren
Wim J. van der Linden*
Affiliation:
CTB/McGraw-Hill
Hao Ren
Affiliation:
CTB/McGraw-Hill
*
Requests for reprints should be sent to Wim J. van der Linden, CTB/McGraw-Hill, 20 Ryan Ranch Road, Monterey, CA 93940, USA. E-mail: wim_vanderlinden@ctb.com
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Abstract

An optimal adaptive design for test-item calibration based on Bayesian optimality criteria is presented. The design adapts the choice of field-test items to the examinees taking an operational adaptive test using both the information in the posterior distributions of their ability parameters and the current posterior distributions of the field-test parameters. Different criteria of optimality based on the two types of posterior distributions are possible. The design can be implemented using an MCMC scheme with alternating stages of sampling from the posterior distributions of the test takers’ ability parameters and the parameters of the field-test items while reusing samples from earlier posterior distributions of the other parameters. Results from a simulation study demonstrated the feasibility of the proposed MCMC implementation for operational item calibration. A comparison of performances for different optimality criteria showed faster calibration of substantial numbers of items for the criterion of D-optimality relative to A-optimality, a special case of c-optimality, and random assignment of items to the test takers.

Keywords

adaptive testingBayesian optimalityitem calibrationitem response modelsoptimal design
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 2 , June 2015 , pp. 263 - 288
Copyright
Copyright © 2013 The Psychometric Society

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