Abstract
Item sampling procedures employed in many assessment studies are designed so that each respondent answers a small number of items in each of a large number of skill areas. If the item population contains several items designed to measure an underlying variable such as computation skill, it may be desirable to fit an item response model to the data. In studies that employ multiple matrix sampling there are not enough answers from each individual to employ such a model. To circumvent this problem, a model is formulated on the assumption that individual level variability appears as independent error within the cells of the cross classification of manifest demographic variables such as sex and race. This model is successfully fit to a scale of items, involving addition of fractions, from the National Assessment Study.
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