Nonmetric Interactive Multidimensional Scaling with Multiple Subjects

Abstract

A method for nonmetric interactive multidimensional scaling (MDS) of similarity judgments is described which is also capable of using responses from previous judges to supplement the judgments of a current subject. The method combines recent advances in interactive MDS with recent advances in numerical methods in MDS to produce a program capable (1) of performing nonmetric interactive MDS and (2) of fitting a wide variety of models, such as the individual differences model. The empirical investigation compared three versions of the system: (1) a metric simple Euclidean modelfitting version (similar to previous interactive scaling programs); (2) a metric individual differences version; and (3) a nonmetric individual differences version. There were no statistically significant differences among the three versions. This paper describes a method for nonmetric interactive multidimensional scaling (MDS) of judgments capable of using responses from previous judges to supplement the judgments of a current subject. The computer algorithm uses two mathematical models: (1) the interactive scaling model (Young & Cliff, 1972), which derives an r-dimensional space containing the stimuli in which r +1 of the points lie on the axes of the space and (2) a Euclidean distance model used to represent the subject's judgments about successive subsets of the stimuli.