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A Bayesian Random Effects Model for Testlets

Published online by Cambridge University Press:  01 January 2025

Eric T. Bradlow ,
Howard Wainer  and
Xiaohui Wang
Eric T. Bradlow*
Affiliation:
Marketing and Statistics, The Wharton School, The University of Pennsylvania
Howard Wainer
Affiliation:
Educational Testing Service
Xiaohui Wang
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Eric T. Bradlow, Marketing Department, The Wharton School, University of Pennsylvania, 1400 Steinberg Hall-Dietrich Hall, Philadelphia PA 19104-6371.
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Abstract

Standard item response theory (IRT) models fit to dichotomous examination responses ignore the fact that sets of items (testlets) often come from a single common stimuli (e.g. a reading comprehension passage). In this setting, all items given to an examinee are unlikely to be conditionally independent (given examinee proficiency). Models that assume conditional independence will overestimate the precision with which examinee proficiency is measured. Overstatement of precision may lead to inaccurate inferences such as prematurely ending an examination in which the stopping rule is based on the estimated standard error of examinee proficiency (e.g., an adaptive test). To model examinations that may be a mixture of independent items and testlets, we modified one standard IRT model to include an additional random effect for items nested within the same testlet. We use a Bayesian framework to facilitate posterior inference via a Data Augmented Gibbs Sampler (DAGS; Tanner & Wong, 1987). The modified and standard IRT models are both applied to a data set from a disclosed form of the SAT. We also provide simulation results that indicates that the degree of precision bias is a function of the variability of the testlet effects, as well as the testlet design.

Keywords

Gibbs samplerData augmentationTestlets
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 2 , June 1999 , pp. 153 - 168
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

The authors wish to thank Robert Mislevy, Andrew Gelman and Donald B. Rubin for their helpful suggestions and comments, Ida Lawrence and Miriam Feigenbaum for providing us with the SAT data analyzed in section 5, and to the two anonymous referees for their careful reading and thoughtful suggestions on an earlier draft. We are also grateful to the Educational Testing service for providing the resources to do this research.

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