The Bayesian Covariance Structure Model for Testlets

Jean Paul Fox*, Jeremias Wenzel, Konrad Klotzke

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    1 Citation (Scopus)
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    Standard item response theory (IRT) models have been extended with testlet effects to account for the nesting of items; these are well known as (Bayesian) testlet models or random effect models for testlets. The testlet modeling framework has several disadvantages. A sufficient number of testlet items are needed to estimate testlet effects, and a sufficient number of individuals are needed to estimate testlet variance. The prior for the testlet variance parameter can only represent a positive association among testlet items. The inclusion of testlet parameters significantly increases the number of model parameters, which can lead to computational problems. To avoid these problems, a Bayesian covariance structure model (BCSM) for testlets is proposed, where standard IRT models are extended with a covariance structure model to account for dependences among testlet items. In the BCSM, the dependence among testlet items is modeled without using testlet effects. This approach does not imply any sample size restrictions and is very efficient in terms of the number of parameters needed to describe testlet dependences. The BCSM is compared to the well-known Bayesian random effects model for testlets using a simulation study. Specifically for testlets with a few items, a small number of test takers, or weak associations among testlet items, the BCSM shows more accurate estimation results than the random effects model.

    Original languageEnglish
    Pages (from-to)219-243
    Number of pages25
    JournalJournal of educational and behavioral statistics
    Issue number2
    Early online date23 Jul 2020
    Publication statusPublished - 1 Apr 2021


    • UT-Hybrid-D
    • hierarchical linear modeling
    • item response theory
    • testlet response theory
    • Bayesian covariance structure model


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