Functionally unidimensional item response models for multivariate binary data

Edward Ip, Geert Molenberghs, Shyh-Huei Chen, Yuri Goegebeur, Paul De Boeck

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The problem of fitting unidimensional item response models to potentially multidimensional data has been extensively studied. The focus of this article is on response data that have a strong dimension but also contain minor nuisance dimensions. Fitting a unidimensional model to such multidimensional data is believed to result in ability estimates that represent a combination of the major and minor dimensions. We conjecture that the underlying dimension for the fitted unidimensional model, which we call the functional dimension, represents a nonlinear projection. In this article we investigate 2 issues: (a) can a proposed nonlinear projection track the functional dimension well, and (b) what are the biases in the ability estimate and the associated standard error when estimating the functional dimension? To investigate the second issue, the nonlinear projection is used as an evaluative tool. An example regarding a construct of desire for physical competency is used to illustrate the functional unidimensional approach.
Original languageEnglish
JournalMultivariate Behavioral Research
Volume48
Pages (from-to)534-562
ISSN0027-3171
DOIs
Publication statusPublished - 2013

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Binary Data
Multivariate Data
Multidimensional Data
Projection
Minor
Model
Standard error
Estimate

Cite this

Ip, Edward ; Molenberghs, Geert ; Chen, Shyh-Huei ; Goegebeur, Yuri ; De Boeck, Paul. / Functionally unidimensional item response models for multivariate binary data. In: Multivariate Behavioral Research. 2013 ; Vol. 48. pp. 534-562.
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Functionally unidimensional item response models for multivariate binary data. / Ip, Edward; Molenberghs, Geert ; Chen, Shyh-Huei; Goegebeur, Yuri; De Boeck, Paul.

In: Multivariate Behavioral Research, Vol. 48, 2013, p. 534-562.

Research output: Contribution to journalJournal articleResearchpeer-review

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