Multidimensional Scaling Versus Components Analysis of Test Intercorrelations

The relation between coordinate estimates in components analysis and multidimensional scaling (MDS) is considered. Algebraic relations between metric MDS and components analysis are reviewed. Three small Monte Carlo studies suggest that the same relations usually, although not universally, characterize components and nonmetric MDS analyses of correlation matrices. Although the relation between components and scaling solutions is generally complex, in one special case the K-dimensional scaling solution forms a subspace of the (K + 1)-factor components solution. In a second special case, the solutions are essentially equivalent. Two examples-one based on human abilities tests and one on vocational interest data-conform to the first special case. The merits of the MDS and factor approaches are compared. Results are related to other methodological issues surrounding research on the general ability factor, response tendencies in self-ratings, and halo in employee evaluations.