title: Functionally Unidimensional Item Response Models for Multivariate Binary Data.
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.
authors.affiliation: a Department of Biostatistical Sciences, Department of Social Sciences & Health Policy , Wake Forest School of Medicine.
authors.forename: Edward H
authors.initials: EH
authors.lastname: Ip
authors.affiliation: b Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Universiteit Hasselt and K.U. Leuven.
authors.forename: Geert
authors.initials: G
authors.lastname: Molenberghs
authors.affiliation: c Department of Biostatistical Sciences , Wake Forest School of Medicine.
authors.forename: Shyh-Huei
authors.initials: SH
authors.lastname: Chen
authors.affiliation: d Department of Mathematics and Computer Science , University of Southern Denmark.
authors.forename: Yuri
authors.initials: Y
authors.lastname: Goegebeur
authors.affiliation: e Department of Psychology , K.U. Leuven and University of Amsterdam.
authors.forename: Paul
authors.initials: P
authors.lastname: De Boeck