A basis for multidimensional item response theory

Independent clusters, as treated in classical linear factor analysis, provide a desirable basis for multidimensional item response models, yielding interpretable and useful results. The independent-clusters basis serves to determine dimensionality, while establishing a pattern for the item parameter matrix that provides identifiability conditions and facilitates interpretation of the traits. It also provides a natural extension of known results on convergent/discriminant "construct" validity to binary items, allowing the quantification of the validity of test and subtest scores. The independent-clusters basis simplifies item/test response and information hypersurfaces, which cannot otherwise be easily studied except in the trivial case of two dimensions, and provides estimates of latent traits with uncorrelated measurement errors. In addition, the affine transformation needed for the informative analysis of the causes of differential item functioning is simplified using the independent-clusters basis. These classically based procedures are already well-established in the context of the linear common-factor model and, accordingly, they set a standard against which more recently developed procedures for the same purposes need to be judged. Index terms: construct validity, differential item functioning, dimensionality, identifiability, independent clusters basis, multidimensional item response theory, measurement error.