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Several methods for estimating item response theory scores for multiple subtests were compared. These methods included two multidimensional item response theory models: a bifactor model where each subtest was a composite score based on the primary trait measured by the set of tests and a secondary trait measured by the individual subtest, and a model where the traits measured by the subtests were separate but correlated. Composite scores based on unidimensional item response theory, with each subtest borrowing information from the other subtest, as well as independent unidimensional scores for each subtest were also considered. Correlations among scores from all methods were high, though somewhat lower for the independent unidimensional scores. Correlations between course grades and test scores, a measure of validity, were similar for all methods, though again slightly lower for the unidimensional scores. To assess bias and RMSE, data were simulated using the parameters estimated for the correlated factors model. The independent unidimensional scores showed the greatest bias and RMSE; the relative performance of the other three methods varied with the subscale.
DeMars, C. E. (2005, August). Scoring subscales using multidimensional item response theory models. Poster presented at the annual meeting of the American Psychological Association, Washington, DC.