Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T09:54:03.414Z Has data issue: false hasContentIssue false
  • English
  • Français

On Separable Tests, Correlated Priors, and Paradoxical Results in Multidimensional Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Giles Hooker
Giles Hooker*
Affiliation:
Cornell University
*
Requests for reprints should be sent to Giles Hooker, Cornell University, Ithaca, NY, USA. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a study of the impact of prior structure on paradoxical results in multidimensional item response theory. Paradoxical results refer to the possibility that an incorrect response could be beneficial to an examinee. We demonstrate that when three or more ability dimensions are being used, paradoxical results can be induced by using priors in which all abilities are positively correlated where they would not occur if the abilities were modeled as being independent. In the case of separable tests, we demonstrate the mathematical causes of paradoxical results, develop a computationally feasible means to check whether they can occur in any given test, and demonstrate a class of prior covariance matrices that can be guaranteed to avoid them.

Keywords

item response theorymultidimensionalposteriorparadoxical resultMAPEAP
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 4 , December 2010 , pp. 694 - 707
Copyright
Copyright © 2010 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Finkelman, M., Hooker, G., & Wang, Z. (2010, in press). Prevalence and severity of paradoxical results in multidimensional item response theory. Journal of Educational and Behavioural Statistics. doi: 10.3102/1076998610381402.CrossRefGoogle Scholar
Hooker, G., Finkelman, M. (2010). Paradoxical results and item bundles. Psychometrika, 75, 249–271.CrossRefGoogle Scholar
Hooker, G., Finkelman, M., Schwartzman, A. (2009). Paradoxical results in multidimensional item response theory. Psychometrika, 74(3), 419–442.CrossRefGoogle Scholar
Mardia, K.V., Kent, J.T., Bibby, J.M. (1979). Multivariate analysis, London: Academic Press.Google Scholar
R Development Core Team (2008). R: a language and environment for statistical computing, Vienna: R Foundation for Statistical Computing. http://www.R-project.orgGoogle Scholar
Segall, D.O. (2000). Principles of multidimensional adaptive testing. In van der Linden, W.J., Glas, C.A.W. (Eds.), Computerized adaptive testing: theory and practice (pp. 53–73). Boston: Kluwer Academic.CrossRefGoogle Scholar
Wainer, H., Vevea, J., Camacho, F., Reeve, B., Rosa, K., Nelson, L., Swygert, K., Thissen, D. (2001). Augmented scores—“borrowing strength” to compute scores based on small numbers of items. In Thissen, D., Wainer, H. (Eds.), Test scoring (pp. 343–387). Mahwah: Erlbaum.Google Scholar