Assessing the Correspondence of One or More Vectors to a Symmetric Matrix Using Ordinal Regression

A statistical model for interpreting psychological scaling research, based on the heuristic work of Reynolds (1983), is developed. This new approach has certain advantages over the standard property fitting approach (Chang and Carroll, 1969) currently used to interpret multidimensional scaling spaces (Shepard, 1962; Torgerson, 1965). These advantages are (a) the ability to directly assess the correspondence of a descriptor vector(s) to a symmetric matrix, and (b) to provide a method in which only ordinal properties of such descriptors are required: thus standard rating, ranking, or sorting data collection methods can be used as the basis to interpret the multidimensional space resulting from the distance data.