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

Published online by Cambridge University Press:  01 January 2025

Jinming Zhang
Jinming Zhang*
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Jinming Zhang, Department of Educational Psychology, University of Illinois at Urbana-Champaign, 1310 South Sixth Street, 236A Education Building, Champaign, IL 61820, USA. E-mail: jmzhang@illinois.edu
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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.

Keywords

item response theory (IRT)dimensionalitymultidimensionalDETECTmultistage testingtwo-stage testing

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 1 , January 2013, pp. 37 - 58
Copyright
Copyright © The Psychometric Society

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