Psychometric Methods for Diagnostic Assessment and Dimensionality Representation
A second part of the thesis investigates a new methodology for the representation of multidimensional test structure based on item-pair conditional covariances. The multidimensional ability composite best measured (in terms of information) for an item is sometimes regarded as the measurement direction of the item. We demonstrate how a directional representation of an item can be reconstructed on the basis of the item's pattern of conditional covariances with all of the other items on the test. A proximity measure for item pairs is derived, and circular and spherical scaling techniques are shown to provide a method by which the unique measurement directions of items might be recovered and represented. Several real and simulated data analyses suggest that the approach may be a useful tool for investigating and describing the dimensional structure of tests.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign