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Ip EH, Molenberghs G, Chen SH, et al. Functionally Unidimensional Item Response Models for Multivariate Binary Data. Multivariate Behav Res. 2013;48(4):534-62doi: 10.1080/00273171.2013.796281.
Ip, E. H., Molenberghs, G., Chen, S. H., Goegebeur, Y., & De Boeck, P. (2013). Functionally Unidimensional Item Response Models for Multivariate Binary Data. Multivariate behavioral research, 48(4), 534-62. https://doi.org/10.1080/00273171.2013.796281
Ip, Edward H, et al. "Functionally Unidimensional Item Response Models for Multivariate Binary Data." Multivariate behavioral research vol. 48,4 (2013): 534-62. doi: https://doi.org/10.1080/00273171.2013.796281
Ip EH, Molenberghs G, Chen SH, Goegebeur Y, De Boeck P. Functionally Unidimensional Item Response Models for Multivariate Binary Data. Multivariate Behav Res. 2013 Jul;48(4):534-62. doi: 10.1080/00273171.2013.796281. PMID: 26742004.
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Multivariate Behav Res. 2013 Jul;48(4):534-62. doi: 10.1080/00273171.2013.796281.

Functionally Unidimensional Item Response Models for Multivariate Binary Data.

Multivariate behavioral research

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

Affiliations

  1. a Department of Biostatistical Sciences, Department of Social Sciences & Health Policy , Wake Forest School of Medicine.
  2. b Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Universiteit Hasselt and K.U. Leuven.
  3. c Department of Biostatistical Sciences , Wake Forest School of Medicine.
  4. d Department of Mathematics and Computer Science , University of Southern Denmark.
  5. e Department of Psychology , K.U. Leuven and University of Amsterdam.

PMID: 26742004 DOI: 10.1080/00273171.2013.796281

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.

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