Conditional Covariance-Based Representation of Multidimensional Test Structure

Abstract

A new nonparametric method for constructing a spatial representation of multidimensional test structure is presented. CCSCAL (for Conditional Covariance-based SCALing) constructs an item vector representation of test structure using conditional covariance-based scaling. A conditional covariance-based dissimilarity measure between items, and a form of multidimensional scaling in which dissimilarities are represented by angles between vectors, are used. This method can be used to investigate a broad range of multidimensional test structures. An index is described to measure the accuracy of the representation. Several simulated and real-data analyses show that the method provides a suitable approximation to multidimensional test structures.