The use of the two-parameter logistic, three-parameter logistic, and generalized partial credit item response models implies that the scales are unidimensional. In other words, the items within a scale all measure the same construct. When the items within a scale measure different constructs, the scale is described as a multi-dimensional scale and more complex item scaling models may be required to fit the data.
The scales in NAEP are determined a priori by grouping items into content areas for which overall performance is deemed to be of interest, as defined by the NAEP frameworks. Each score scale is defined a priori by the collection of items representing that scale. What is important, therefore, is that the models capture salient information in the response data to effectively summarize the overall performance on the content area of the populations and subpopulations being assessed in the content areas. Nonetheless, a limited number of dimensionality studies have been conducted with NAEP data.