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A Procedure for Dimensionality Analyses of Response Data from Various Test Designs

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  • Jinming Zhang

Abstract

In some popular test designs (including computerized adaptive testing and multistage testing), many item pairs are not administered to any test takers, which may result in some complications during dimensionality analyses. In this paper, a modified DETECT index is proposed in order to perform dimensionality analyses for response data from such designs. It is proven in this paper that under certain conditions, the modified DETECT can successfully find the dimensionality-based partition of items. Furthermore, the modified DETECT index is decomposed into two parts, which can serve as indices of the reliability of results from the DETECT procedure when response data are judged to be multidimensional. A simulation study shows that the modified DETECT can successfully recover the dimensional structure of response data under reasonable specifications. Finally, the modified DETECT procedure is applied to real response data from two-stage tests to demonstrate how to utilize these indices and interpret their values in dimensionality analyses. Copyright The Psychometric Society 2013

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  • Jinming Zhang, 2013. "A Procedure for Dimensionality Analyses of Response Data from Various Test Designs," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 37-58, January.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:1:p:37-58
    DOI: 10.1007/s11336-012-9287-z
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    References listed on IDEAS

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    1. William Stout, 1987. "A nonparametric approach for assessing latent trait unidimensionality," Psychometrika, Springer;The Psychometric Society, vol. 52(4), pages 589-617, December.
    2. Frederic Lord, 1971. "A theoretical study of two-stage testing," Psychometrika, Springer;The Psychometric Society, vol. 36(3), pages 227-242, September.
    3. Jinming Zhang & William Stout, 1999. "The theoretical detect index of dimensionality and its application to approximate simple structure," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 213-249, June.
    4. Jinming Zhang, 2007. "Conditional Covariance Theory and Detect for Polytomous Items," Psychometrika, Springer;The Psychometric Society, vol. 72(1), pages 69-91, March.
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    Cited by:

    1. Xiao Li & Hanchen Xu & Jinming Zhang & Hua-hua Chang, 2023. "Deep Reinforcement Learning for Adaptive Learning Systems," Journal of Educational and Behavioral Statistics, , vol. 48(2), pages 220-243, April.
    2. Hermosa del Vasto Paola & del Campo Cristina & Urquía-Grande Elena & Jorge Susana, 2019. "Designing an Accountability Index: A Case Study of South America Central Governments," Central European Journal of Public Policy, Sciendo, vol. 13(2), pages 1-14, December.

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