Basic structure content scaling

Abstract

A basic structure approach is proposed for obtaining multidimensional scale values for attitude, achievement, or personality items from response data. Based on conventional components analysis, and described in terms of singular value or Eckart-Young decomposition of a data matrix, basic structure scaling yields projections of items upon axes in the person space, equivalent to obtaining component scores for items, with component loadings associated with individuals. Unlike multidimensional scaling methods, the scaling of large sets of stimuli is practical and judgments of items are obviated. In attitude and personality item scaling, the technique permits the unconfounding of scale values due to response bias and to content. It also permits the partitioning of item indices of popularity or difficulty among a number of relevant dimensions, a property of possible relevance to tailored or adaptive testing.