Unidimensional calibrations and interpretations of composite traits for multidimensional tests

Abstract

A two-stage process that considers the multidimensionality of tests under the framework of unidimensional item response theory (IRT) is described and evaluated. In the first stage, items are clustered in a multidimensional latent space with respect to their direction of maximum discrimination. The separate item clusters are subsequently calibrated using a unidimensional IRT model to provide item parameter and trait estimates for composite traits in the context of the multidimensional trait space. This application is proposed as a workable compromise to some of the estimation, indeterminacy, and interpretation problems that affect the direct use of multidimensional IRT procedures for item calibration and trait estimation. The findings of a study based on simulated multidimensional data indicate that there are identifiable gains in estimation robustness and score interpretation with almost no sacrifice in goodness-of-fit using this two-stage approach to modeling composite latent traits. Index terms: item response theory, model fit, multidimensionality, parameter estimation; model fit; multidimensionality in IRT; parameter estimation; person fit; reference composites; trait estimation.