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It is not unusual for several tests measuring different abilities to be given in one test administration. A common practice is to estimate these abilities independently of each other, but this paper proposes a more efficient method of estimating these abilities that takes into account the correlational structure of the abilities. The method uses a hierarchical Bayesian approach to simultaneous estimation of abilities based on a simple structure multidimensional item response model. Whether the simultaneous estimation of abilities from different dimensions yields more accurate estimates was studied, as well as how the number of dimensions, the number of items in each dimension, and the degree of correlation between abilities affect the accuracy of these estimates. For each combination of number of abilities and number of items, item parameters were randomly drawn from a pool of 550 items from nationally standardized mathematics tests, with 1,000 examinees simulated for each experimental condition. Results show that the proposed multidimensional approach gives more general outcomes, yielding results similar to those of the unidimensional method when abilities are uncorrelated. When abilities are correlated, taking the correlation into account can result in noticeable improvements in ability estimates. (Contains 24 tables and 15 references.) (SLD) Reproductions supplied by EDRS are the best that can be made from the original document