Browsing by Author "McDonald, Roderick P."

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    Latent trait item analysis and facet theory--a useful combination.
    (1985) Balla, John R.; McDonald, Roderick P.
    Computer programs for fitting latent trait models to data provide indices of item misfit. An analysis of the consistency of item misfit determination is presented. Two content-equivalent forms of 71 items representing the behavioral domain of arithmetic skills were generated. Each item was defined in terms of its combination of facet elements, and the ith item on each form represented the same selection of facets. The dichotomously scored responses to the two forms were analyzed using the computer programs NOHARM and BICAL. Misfitting items were identified by use of the residual covariances in the case of NOHARM and Total-t and Between-t in the case of BICAL. The consistency of misfit was measured by the extent of agreement in selection of misfitting items across the parallel forms. It was found that the analysis of residual covariances provided a more consistent means of determining item misfit. It was concluded that the use of the Between-t and Total-t indices as a basis for editing items should be viewed cautiously. In addition, misfitting items were grouped according to common facet elements and reasons for misfit were postulated. Thus, the analysis of residual covariances of items defined in terms of their combination of facet elements seems to provide a very satisfactory method of item analysis.
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    Linear versus nonlinear models in item response theory
    (1982) McDonald, Roderick P.
    A broad framework for examining the class of unidimensional and multidimensional models for item responses is provided by nonlinear factor analysis, with a classification of models as strictly linear, linear in their coefficients, or strictly nonlinear. These groups of models are compared and contrasted with respect to the associated problems of estimation, testing fit, and scoring an examinee. The invariance of item parameters is related to the congruence of common factors in linear theory.